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Spark 把数据和计算拆分到多台机器上并行处理。",[1091,1118,1119],{},"随机模拟是已知公式，让Spark集群算出上亿级别的模拟样本；\n统计推断是已知这上亿个样本，让Spark集群算出背后的公式参数。\n相关的方法主要如下：",[1095,1121,1122,1207,1604,1925,1931,2545,2930],{},[1098,1123,1124,1127,1128,1175,1176,1206],{},[1101,1125,1126],{},"三种随机数生成法",":\n分布函数的逆写得出来 → 逆分布法;\n写不出来但能找到试投密度 ",[1129,1130,1133,1155],"span",{"className":1131},[1132],"katex",[1129,1134,1137],{"className":1135},[1136],"katex-mathml",[1138,1139,1141],"math",{"xmlns":1140},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1142,1143,1144,1151],"semantics",{},[1145,1146,1147],"mrow",{},[1148,1149,1150],"mi",{},"g",[1152,1153,1150],"annotation",{"encoding":1154},"application\u002Fx-tex",[1129,1156,1160],{"className":1157,"ariaHidden":1159},[1158],"katex-html","true",[1129,1161,1164,1169],{"className":1162},[1163],"base",[1129,1165],{"className":1166,"style":1168},[1167],"strut","height:0.625em;vertical-align:-0.1944em;",[1129,1170,1150],{"className":1171,"style":1174},[1172,1173],"mord","mathnormal","margin-right:0.0359em;"," 和常数 ",[1129,1177,1179,1193],{"className":1178},[1132],[1129,1180,1182],{"className":1181},[1136],[1138,1183,1184],{"xmlns":1140},[1142,1185,1186,1191],{},[1145,1187,1188],{},[1148,1189,1190],{},"c",[1152,1192,1190],{"encoding":1154},[1129,1194,1196],{"className":1195,"ariaHidden":1159},[1158],[1129,1197,1199,1203],{"className":1198},[1163],[1129,1200],{"className":1201,"style":1202},[1167],"height:0.4306em;",[1129,1204,1190],{"className":1205},[1172,1173]," → 拒绝接受法(舍选法Ⅱ);\n分布在有限区间且密度有上界 → 舍选法Ⅰ(矩形打点)",[1098,1208,1209,1212,1213,1353,1354,1438,1439,1603],{},[1101,1210,1211],{},"逆分布法公式",":\n",[1129,1214,1216,1260],{"className":1215},[1132],[1129,1217,1219],{"className":1218},[1136],[1138,1220,1221],{"xmlns":1140},[1142,1222,1223,1257],{},[1145,1224,1225,1228,1232,1247,1251,1254],{},[1148,1226,1227],{},"X",[1229,1230,1231],"mo",{},"=",[1233,1234,1235,1238],"msup",{},[1148,1236,1237],{},"F",[1145,1239,1240,1243],{},[1229,1241,1242],{},"−",[1244,1245,1246],"mn",{},"1",[1229,1248,1250],{"stretchy":1249},"false","(",[1148,1252,1253],{},"U",[1229,1255,1256],{"stretchy":1249},")",[1152,1258,1259],{"encoding":1154},"X = F^{-1}(U)",[1129,1261,1263,1286],{"className":1262,"ariaHidden":1159},[1158],[1129,1264,1266,1270,1274,1279,1283],{"className":1265},[1163],[1129,1267],{"className":1268,"style":1269},[1167],"height:0.6833em;",[1129,1271,1227],{"className":1272,"style":1273},[1172,1173],"margin-right:0.0785em;",[1129,1275],{"className":1276,"style":1278},[1277],"mspace","margin-right:0.2778em;",[1129,1280,1231],{"className":1281},[1282],"mrel",[1129,1284],{"className":1285,"style":1278},[1277],[1129,1287,1289,1293,1341,1345,1349],{"className":1288},[1163],[1129,1290],{"className":1291,"style":1292},[1167],"height:1.0641em;vertical-align:-0.25em;",[1129,1294,1296,1300],{"className":1295},[1172],[1129,1297,1237],{"className":1298,"style":1299},[1172,1173],"margin-right:0.1389em;",[1129,1301,1304],{"className":1302},[1303],"msupsub",[1129,1305,1308],{"className":1306},[1307],"vlist-t",[1129,1309,1312],{"className":1310},[1311],"vlist-r",[1129,1313,1317],{"className":1314,"style":1316},[1315],"vlist","height:0.8141em;",[1129,1318,1320,1325],{"style":1319},"top:-3.063em;margin-right:0.05em;",[1129,1321],{"className":1322,"style":1324},[1323],"pstrut","height:2.7em;",[1129,1326,1332],{"className":1327},[1328,1329,1330,1331],"sizing","reset-size6","size3","mtight",[1129,1333,1335,1338],{"className":1334},[1172,1331],[1129,1336,1242],{"className":1337},[1172,1331],[1129,1339,1246],{"className":1340},[1172,1331],[1129,1342,1250],{"className":1343},[1344],"mopen",[1129,1346,1253],{"className":1347,"style":1348},[1172,1173],"margin-right:0.109em;",[1129,1350,1256],{"className":1351},[1352],"mclose",",",[1129,1355,1357,1387],{"className":1356},[1132],[1129,1358,1360],{"className":1359},[1136],[1138,1361,1362],{"xmlns":1140},[1142,1363,1364,1384],{},[1145,1365,1366,1368,1371,1373,1375,1378,1380,1382],{},[1148,1367,1253],{},[1229,1369,1370],{},"∼",[1148,1372,1253],{},[1229,1374,1250],{"stretchy":1249},[1244,1376,1377],{},"0",[1229,1379,1353],{"separator":1159},[1244,1381,1246],{},[1229,1383,1256],{"stretchy":1249},[1152,1385,1386],{"encoding":1154},"U\\sim U(0,1)",[1129,1388,1390,1408],{"className":1389,"ariaHidden":1159},[1158],[1129,1391,1393,1396,1399,1402,1405],{"className":1392},[1163],[1129,1394],{"className":1395,"style":1269},[1167],[1129,1397,1253],{"className":1398,"style":1348},[1172,1173],[1129,1400],{"className":1401,"style":1278},[1277],[1129,1403,1370],{"className":1404},[1282],[1129,1406],{"className":1407,"style":1278},[1277],[1129,1409,1411,1415,1418,1421,1424,1428,1432,1435],{"className":1410},[1163],[1129,1412],{"className":1413,"style":1414},[1167],"height:1em;vertical-align:-0.25em;",[1129,1416,1253],{"className":1417,"style":1348},[1172,1173],[1129,1419,1250],{"className":1420},[1344],[1129,1422,1377],{"className":1423},[1172],[1129,1425,1353],{"className":1426},[1427],"mpunct",[1129,1429],{"className":1430,"style":1431},[1277],"margin-right:0.1667em;",[1129,1433,1246],{"className":1434},[1172],[1129,1436,1256],{"className":1437},[1352],"。指数分布 ",[1129,1440,1442,1479],{"className":1441},[1132],[1129,1443,1445],{"className":1444},[1136],[1138,1446,1447],{"xmlns":1140},[1142,1448,1449,1476],{},[1145,1450,1451,1453,1455,1457,1468,1471,1474],{},[1148,1452,1227],{},[1229,1454,1231],{},[1229,1456,1242],{},[1458,1459,1460],"mstyle",{"scriptlevel":1377,"displaystyle":1249},[1461,1462,1463,1465],"mfrac",{},[1244,1464,1246],{},[1148,1466,1467],{},"λ",[1148,1469,1470],{},"ln",[1229,1472,1473],{},"⁡",[1148,1475,1253],{},[1152,1477,1478],{"encoding":1154},"X=-\\tfrac{1}{\\lambda}\\ln U",[1129,1480,1482,1500],{"className":1481,"ariaHidden":1159},[1158],[1129,1483,1485,1488,1491,1494,1497],{"className":1484},[1163],[1129,1486],{"className":1487,"style":1269},[1167],[1129,1489,1227],{"className":1490,"style":1273},[1172,1173],[1129,1492],{"className":1493,"style":1278},[1277],[1129,1495,1231],{"className":1496},[1282],[1129,1498],{"className":1499,"style":1278},[1277],[1129,1501,1503,1507,1510,1590,1593,1597,1600],{"className":1502},[1163],[1129,1504],{"className":1505,"style":1506},[1167],"height:1.1901em;vertical-align:-0.345em;",[1129,1508,1242],{"className":1509},[1172],[1129,1511,1513,1517,1587],{"className":1512},[1172],[1129,1514],{"className":1515},[1344,1516],"nulldelimiter",[1129,1518,1520],{"className":1519},[1461],[1129,1521,1524,1578],{"className":1522},[1307,1523],"vlist-t2",[1129,1525,1527,1573],{"className":1526},[1311],[1129,1528,1531,1547,1558],{"className":1529,"style":1530},[1315],"height:0.8451em;",[1129,1532,1534,1538],{"style":1533},"top:-2.655em;",[1129,1535],{"className":1536,"style":1537},[1323],"height:3em;",[1129,1539,1541],{"className":1540},[1328,1329,1330,1331],[1129,1542,1544],{"className":1543},[1172,1331],[1129,1545,1467],{"className":1546},[1172,1173,1331],[1129,1548,1550,1553],{"style":1549},"top:-3.23em;",[1129,1551],{"className":1552,"style":1537},[1323],[1129,1554],{"className":1555,"style":1557},[1556],"frac-line","border-bottom-width:0.04em;",[1129,1559,1561,1564],{"style":1560},"top:-3.394em;",[1129,1562],{"className":1563,"style":1537},[1323],[1129,1565,1567],{"className":1566},[1328,1329,1330,1331],[1129,1568,1570],{"className":1569},[1172,1331],[1129,1571,1246],{"className":1572},[1172,1331],[1129,1574,1577],{"className":1575},[1576],"vlist-s","​",[1129,1579,1581],{"className":1580},[1311],[1129,1582,1585],{"className":1583,"style":1584},[1315],"height:0.345em;",[1129,1586],{},[1129,1588],{"className":1589},[1352,1516],[1129,1591],{"className":1592,"style":1431},[1277],[1129,1594,1470],{"className":1595},[1596],"mop",[1129,1598],{"className":1599,"style":1431},[1277],[1129,1601,1253],{"className":1602,"style":1348},[1172,1173],"。",[1098,1605,1606,1609,1610,1783,1784,1353,1896,1924],{},[1101,1607,1608],{},"拒绝接受法",":\n接受条件 ",[1129,1611,1613,1662],{"className":1612},[1132],[1129,1614,1616],{"className":1615},[1136],[1138,1617,1618],{"xmlns":1140},[1142,1619,1620,1659],{},[1145,1621,1622,1624,1627],{},[1148,1623,1253],{},[1229,1625,1626],{},"≤",[1458,1628,1629],{"scriptlevel":1377,"displaystyle":1159},[1461,1630,1631,1643],{},[1145,1632,1633,1636,1638,1641],{},[1148,1634,1635],{},"f",[1229,1637,1250],{"stretchy":1249},[1148,1639,1640],{},"Y",[1229,1642,1256],{"stretchy":1249},[1145,1644,1645,1647,1651,1653,1655,1657],{},[1148,1646,1190],{},[1648,1649,1650],"mtext",{}," ",[1148,1652,1150],{},[1229,1654,1250],{"stretchy":1249},[1148,1656,1640],{},[1229,1658,1256],{"stretchy":1249},[1152,1660,1661],{"encoding":1154},"U \\le \\dfrac{f(Y)}{c\\,g(Y)}",[1129,1663,1665,1684],{"className":1664,"ariaHidden":1159},[1158],[1129,1666,1668,1672,1675,1678,1681],{"className":1667},[1163],[1129,1669],{"className":1670,"style":1671},[1167],"height:0.8193em;vertical-align:-0.136em;",[1129,1673,1253],{"className":1674,"style":1348},[1172,1173],[1129,1676],{"className":1677,"style":1278},[1277],[1129,1679,1626],{"className":1680},[1282],[1129,1682],{"className":1683,"style":1278},[1277],[1129,1685,1687,1691],{"className":1686},[1163],[1129,1688],{"className":1689,"style":1690},[1167],"height:2.363em;vertical-align:-0.936em;",[1129,1692,1694,1697,1780],{"className":1693},[1172],[1129,1695],{"className":1696},[1344,1516],[1129,1698,1700],{"className":1699},[1461],[1129,1701,1703,1771],{"className":1702},[1307,1523],[1129,1704,1706,1768],{"className":1705},[1311],[1129,1707,1710,1738,1746],{"className":1708,"style":1709},[1315],"height:1.427em;",[1129,1711,1713,1716],{"style":1712},"top:-2.314em;",[1129,1714],{"className":1715,"style":1537},[1323],[1129,1717,1719,1722,1725,1728,1731,1735],{"className":1718},[1172],[1129,1720,1190],{"className":1721},[1172,1173],[1129,1723],{"className":1724,"style":1431},[1277],[1129,1726,1150],{"className":1727,"style":1174},[1172,1173],[1129,1729,1250],{"className":1730},[1344],[1129,1732,1640],{"className":1733,"style":1734},[1172,1173],"margin-right:0.2222em;",[1129,1736,1256],{"className":1737},[1352],[1129,1739,1740,1743],{"style":1549},[1129,1741],{"className":1742,"style":1537},[1323],[1129,1744],{"className":1745,"style":1557},[1556],[1129,1747,1749,1752],{"style":1748},"top:-3.677em;",[1129,1750],{"className":1751,"style":1537},[1323],[1129,1753,1755,1759,1762,1765],{"className":1754},[1172],[1129,1756,1635],{"className":1757,"style":1758},[1172,1173],"margin-right:0.1076em;",[1129,1760,1250],{"className":1761},[1344],[1129,1763,1640],{"className":1764,"style":1734},[1172,1173],[1129,1766,1256],{"className":1767},[1352],[1129,1769,1577],{"className":1770},[1576],[1129,1772,1774],{"className":1773},[1311],[1129,1775,1778],{"className":1776,"style":1777},[1315],"height:0.936em;",[1129,1779],{},[1129,1781],{"className":1782},[1352,1516],";接受率 ",[1129,1785,1787,1809],{"className":1786},[1132],[1129,1788,1790],{"className":1789},[1136],[1138,1791,1792],{"xmlns":1140},[1142,1793,1794,1806],{},[1145,1795,1796,1798],{},[1229,1797,1231],{},[1458,1799,1800],{"scriptlevel":1377,"displaystyle":1159},[1461,1801,1802,1804],{},[1244,1803,1246],{},[1148,1805,1190],{},[1152,1807,1808],{"encoding":1154},"=\\dfrac{1}{c}",[1129,1810,1812,1825],{"className":1811,"ariaHidden":1159},[1158],[1129,1813,1815,1819,1822],{"className":1814},[1163],[1129,1816],{"className":1817,"style":1818},[1167],"height:0.3669em;",[1129,1820,1231],{"className":1821},[1282],[1129,1823],{"className":1824,"style":1278},[1277],[1129,1826,1828,1832],{"className":1827},[1163],[1129,1829],{"className":1830,"style":1831},[1167],"height:2.0074em;vertical-align:-0.686em;",[1129,1833,1835,1838,1893],{"className":1834},[1172],[1129,1836],{"className":1837},[1344,1516],[1129,1839,1841],{"className":1840},[1461],[1129,1842,1844,1884],{"className":1843},[1307,1523],[1129,1845,1847,1881],{"className":1846},[1311],[1129,1848,1851,1862,1870],{"className":1849,"style":1850},[1315],"height:1.3214em;",[1129,1852,1853,1856],{"style":1712},[1129,1854],{"className":1855,"style":1537},[1323],[1129,1857,1859],{"className":1858},[1172],[1129,1860,1190],{"className":1861},[1172,1173],[1129,1863,1864,1867],{"style":1549},[1129,1865],{"className":1866,"style":1537},[1323],[1129,1868],{"className":1869,"style":1557},[1556],[1129,1871,1872,1875],{"style":1748},[1129,1873],{"className":1874,"style":1537},[1323],[1129,1876,1878],{"className":1877},[1172],[1129,1879,1246],{"className":1880},[1172],[1129,1882,1577],{"className":1883},[1576],[1129,1885,1887],{"className":1886},[1311],[1129,1888,1891],{"className":1889,"style":1890},[1315],"height:0.686em;",[1129,1892],{},[1129,1894],{"className":1895},[1352,1516],[1129,1897,1899,1912],{"className":1898},[1132],[1129,1900,1902],{"className":1901},[1136],[1138,1903,1904],{"xmlns":1140},[1142,1905,1906,1910],{},[1145,1907,1908],{},[1148,1909,1190],{},[1152,1911,1190],{"encoding":1154},[1129,1913,1915],{"className":1914,"ariaHidden":1159},[1158],[1129,1916,1918,1921],{"className":1917},[1163],[1129,1919],{"className":1920,"style":1202},[1167],[1129,1922,1190],{"className":1923},[1172,1173]," 越小效率越高。",[1098,1926,1927,1930],{},[1101,1928,1929],{},"EM 四步",":\n选初值 → E 步算 Q 函数(隐变量的条件期望)→ M 步极大化 Q 更新参数 → 迭代到收敛。",[1098,1932,1933,1212,1936,1353,2245,2544],{},[1101,1934,1935],{},"遗传模型迭代式",[1129,1937,1939,2010],{"className":1938},[1132],[1129,1940,1942],{"className":1941},[1136],[1138,1943,1944],{"xmlns":1140},[1142,1945,1946,2007],{},[1145,1947,1948,1962,1964,1967,1970],{},[1233,1949,1950,1953],{},[1148,1951,1952],{},"z",[1145,1954,1955,1957,1960],{},[1229,1956,1250],{"stretchy":1249},[1148,1958,1959],{},"i",[1229,1961,1256],{"stretchy":1249},[1229,1963,1231],{},[1244,1965,1966],{},"125",[1229,1968,1969],{},"⋅",[1458,1971,1972],{"scriptlevel":1377,"displaystyle":1159},[1461,1973,1974,1987],{},[1233,1975,1976,1979],{},[1148,1977,1978],{},"θ",[1145,1980,1981,1983,1985],{},[1229,1982,1250],{"stretchy":1249},[1148,1984,1959],{},[1229,1986,1256],{"stretchy":1249},[1145,1988,1989,1992,1995],{},[1244,1990,1991],{},"2",[1229,1993,1994],{},"+",[1233,1996,1997,1999],{},[1148,1998,1978],{},[1145,2000,2001,2003,2005],{},[1229,2002,1250],{"stretchy":1249},[1148,2004,1959],{},[1229,2006,1256],{"stretchy":1249},[1152,2008,2009],{"encoding":1154},"z^{(i)} = 125\\cdot\\dfrac{\\theta^{(i)}}{2+\\theta^{(i)}}",[1129,2011,2013,2068,2088],{"className":2012,"ariaHidden":1159},[1158],[1129,2014,2016,2020,2059,2062,2065],{"className":2015},[1163],[1129,2017],{"className":2018,"style":2019},[1167],"height:0.888em;",[1129,2021,2023,2027],{"className":2022},[1172],[1129,2024,1952],{"className":2025,"style":2026},[1172,1173],"margin-right:0.044em;",[1129,2028,2030],{"className":2029},[1303],[1129,2031,2033],{"className":2032},[1307],[1129,2034,2036],{"className":2035},[1311],[1129,2037,2039],{"className":2038,"style":2019},[1315],[1129,2040,2041,2044],{"style":1319},[1129,2042],{"className":2043,"style":1324},[1323],[1129,2045,2047],{"className":2046},[1328,1329,1330,1331],[1129,2048,2050,2053,2056],{"className":2049},[1172,1331],[1129,2051,1250],{"className":2052},[1344,1331],[1129,2054,1959],{"className":2055},[1172,1173,1331],[1129,2057,1256],{"className":2058},[1352,1331],[1129,2060],{"className":2061,"style":1278},[1277],[1129,2063,1231],{"className":2064},[1282],[1129,2066],{"className":2067,"style":1278},[1277],[1129,2069,2071,2075,2078,2081,2085],{"className":2070},[1163],[1129,2072],{"className":2073,"style":2074},[1167],"height:0.6444em;",[1129,2076,1966],{"className":2077},[1172],[1129,2079],{"className":2080,"style":1734},[1277],[1129,2082,1969],{"className":2083},[2084],"mbin",[1129,2086],{"className":2087,"style":1734},[1277],[1129,2089,2091,2095],{"className":2090},[1163],[1129,2092],{"className":2093,"style":2094},[1167],"height:2.3523em;vertical-align:-0.7873em;",[1129,2096,2098,2101,2242],{"className":2097},[1172],[1129,2099],{"className":2100},[1344,1516],[1129,2102,2104],{"className":2103},[1461],[1129,2105,2107,2233],{"className":2106},[1307,1523],[1129,2108,2110,2230],{"className":2109},[1311],[1129,2111,2114,2176,2184],{"className":2112,"style":2113},[1315],"height:1.565em;",[1129,2115,2117,2120],{"style":2116},"top:-2.296em;",[1129,2118],{"className":2119,"style":1537},[1323],[1129,2121,2123,2126,2129,2132,2135],{"className":2122},[1172],[1129,2124,1991],{"className":2125},[1172],[1129,2127],{"className":2128,"style":1734},[1277],[1129,2130,1994],{"className":2131},[2084],[1129,2133],{"className":2134,"style":1734},[1277],[1129,2136,2138,2142],{"className":2137},[1172],[1129,2139,1978],{"className":2140,"style":2141},[1172,1173],"margin-right:0.0278em;",[1129,2143,2145],{"className":2144},[1303],[1129,2146,2148],{"className":2147},[1307],[1129,2149,2151],{"className":2150},[1311],[1129,2152,2155],{"className":2153,"style":2154},[1315],"height:0.814em;",[1129,2156,2158,2161],{"style":2157},"top:-2.989em;margin-right:0.05em;",[1129,2159],{"className":2160,"style":1324},[1323],[1129,2162,2164],{"className":2163},[1328,1329,1330,1331],[1129,2165,2167,2170,2173],{"className":2166},[1172,1331],[1129,2168,1250],{"className":2169},[1344,1331],[1129,2171,1959],{"className":2172},[1172,1173,1331],[1129,2174,1256],{"className":2175},[1352,1331],[1129,2177,2178,2181],{"style":1549},[1129,2179],{"className":2180,"style":1537},[1323],[1129,2182],{"className":2183,"style":1557},[1556],[1129,2185,2186,2189],{"style":1748},[1129,2187],{"className":2188,"style":1537},[1323],[1129,2190,2192],{"className":2191},[1172],[1129,2193,2195,2198],{"className":2194},[1172],[1129,2196,1978],{"className":2197,"style":2141},[1172,1173],[1129,2199,2201],{"className":2200},[1303],[1129,2202,2204],{"className":2203},[1307],[1129,2205,2207],{"className":2206},[1311],[1129,2208,2210],{"className":2209,"style":2019},[1315],[1129,2211,2212,2215],{"style":1319},[1129,2213],{"className":2214,"style":1324},[1323],[1129,2216,2218],{"className":2217},[1328,1329,1330,1331],[1129,2219,2221,2224,2227],{"className":2220},[1172,1331],[1129,2222,1250],{"className":2223},[1344,1331],[1129,2225,1959],{"className":2226},[1172,1173,1331],[1129,2228,1256],{"className":2229},[1352,1331],[1129,2231,1577],{"className":2232},[1576],[1129,2234,2236],{"className":2235},[1311],[1129,2237,2240],{"className":2238,"style":2239},[1315],"height:0.7873em;",[1129,2241],{},[1129,2243],{"className":2244},[1352,1516],[1129,2246,2248,2320],{"className":2247},[1132],[1129,2249,2251],{"className":2250},[1136],[1138,2252,2253],{"xmlns":1140},[1142,2254,2255,2317],{},[1145,2256,2257,2273,2275],{},[1233,2258,2259,2261],{},[1148,2260,1978],{},[1145,2262,2263,2265,2267,2269,2271],{},[1229,2264,1250],{"stretchy":1249},[1148,2266,1959],{},[1229,2268,1994],{},[1244,2270,1246],{},[1229,2272,1256],{"stretchy":1249},[1229,2274,1231],{},[1458,2276,2277],{"scriptlevel":1377,"displaystyle":1159},[1461,2278,2279,2298],{},[1145,2280,2281,2293,2295],{},[1233,2282,2283,2285],{},[1148,2284,1952],{},[1145,2286,2287,2289,2291],{},[1229,2288,1250],{"stretchy":1249},[1148,2290,1959],{},[1229,2292,1256],{"stretchy":1249},[1229,2294,1994],{},[1244,2296,2297],{},"34",[1145,2299,2300,2312,2314],{},[1233,2301,2302,2304],{},[1148,2303,1952],{},[1145,2305,2306,2308,2310],{},[1229,2307,1250],{"stretchy":1249},[1148,2309,1959],{},[1229,2311,1256],{"stretchy":1249},[1229,2313,1994],{},[1244,2315,2316],{},"72",[1152,2318,2319],{"encoding":1154},"\\theta^{(i+1)} = \\dfrac{z^{(i)}+34}{z^{(i)}+72}",[1129,2321,2323,2382],{"className":2322,"ariaHidden":1159},[1158],[1129,2324,2326,2329,2373,2376,2379],{"className":2325},[1163],[1129,2327],{"className":2328,"style":2019},[1167],[1129,2330,2332,2335],{"className":2331},[1172],[1129,2333,1978],{"className":2334,"style":2141},[1172,1173],[1129,2336,2338],{"className":2337},[1303],[1129,2339,2341],{"className":2340},[1307],[1129,2342,2344],{"className":2343},[1311],[1129,2345,2347],{"className":2346,"style":2019},[1315],[1129,2348,2349,2352],{"style":1319},[1129,2350],{"className":2351,"style":1324},[1323],[1129,2353,2355],{"className":2354},[1328,1329,1330,1331],[1129,2356,2358,2361,2364,2367,2370],{"className":2357},[1172,1331],[1129,2359,1250],{"className":2360},[1344,1331],[1129,2362,1959],{"className":2363},[1172,1173,1331],[1129,2365,1994],{"className":2366},[2084,1331],[1129,2368,1246],{"className":2369},[1172,1331],[1129,2371,1256],{"className":2372},[1352,1331],[1129,2374],{"className":2375,"style":1278},[1277],[1129,2377,1231],{"className":2378},[1282],[1129,2380],{"className":2381,"style":1278},[1277],[1129,2383,2385,2388],{"className":2384},[1163],[1129,2386],{"className":2387,"style":2094},[1167],[1129,2389,2391,2394,2541],{"className":2390},[1172],[1129,2392],{"className":2393},[1344,1516],[1129,2395,2397],{"className":2396},[1461],[1129,2398,2400,2533],{"className":2399},[1307,1523],[1129,2401,2403,2530],{"className":2402},[1311],[1129,2404,2406,2464,2472],{"className":2405,"style":2113},[1315],[1129,2407,2408,2411],{"style":2116},[1129,2409],{"className":2410,"style":1537},[1323],[1129,2412,2414,2452,2455,2458,2461],{"className":2413},[1172],[1129,2415,2417,2420],{"className":2416},[1172],[1129,2418,1952],{"className":2419,"style":2026},[1172,1173],[1129,2421,2423],{"className":2422},[1303],[1129,2424,2426],{"className":2425},[1307],[1129,2427,2429],{"className":2428},[1311],[1129,2430,2432],{"className":2431,"style":2154},[1315],[1129,2433,2434,2437],{"style":2157},[1129,2435],{"className":2436,"style":1324},[1323],[1129,2438,2440],{"className":2439},[1328,1329,1330,1331],[1129,2441,2443,2446,2449],{"className":2442},[1172,1331],[1129,2444,1250],{"className":2445},[1344,1331],[1129,2447,1959],{"className":2448},[1172,1173,1331],[1129,2450,1256],{"className":2451},[1352,1331],[1129,2453],{"className":2454,"style":1734},[1277],[1129,2456,1994],{"className":2457},[2084],[1129,2459],{"className":2460,"style":1734},[1277],[1129,2462,2316],{"className":2463},[1172],[1129,2465,2466,2469],{"style":1549},[1129,2467],{"className":2468,"style":1537},[1323],[1129,2470],{"className":2471,"style":1557},[1556],[1129,2473,2474,2477],{"style":1748},[1129,2475],{"className":2476,"style":1537},[1323],[1129,2478,2480,2518,2521,2524,2527],{"className":2479},[1172],[1129,2481,2483,2486],{"className":2482},[1172],[1129,2484,1952],{"className":2485,"style":2026},[1172,1173],[1129,2487,2489],{"className":2488},[1303],[1129,2490,2492],{"className":2491},[1307],[1129,2493,2495],{"className":2494},[1311],[1129,2496,2498],{"className":2497,"style":2019},[1315],[1129,2499,2500,2503],{"style":1319},[1129,2501],{"className":2502,"style":1324},[1323],[1129,2504,2506],{"className":2505},[1328,1329,1330,1331],[1129,2507,2509,2512,2515],{"className":2508},[1172,1331],[1129,2510,1250],{"className":2511},[1344,1331],[1129,2513,1959],{"className":2514},[1172,1173,1331],[1129,2516,1256],{"className":2517},[1352,1331],[1129,2519],{"className":2520,"style":1734},[1277],[1129,2522,1994],{"className":2523},[2084],[1129,2525],{"className":2526,"style":1734},[1277],[1129,2528,2297],{"className":2529},[1172],[1129,2531,1577],{"className":2532},[1576],[1129,2534,2536],{"className":2535},[1311],[1129,2537,2539],{"className":2538,"style":2239},[1315],[1129,2540],{},[1129,2542],{"className":2543},[1352,1516],"\n四类次数 125\u002F18\u002F20\u002F34、总数 197",[1098,2546,2547,1212,2550,2627,2628,2627,2716,2790,2791,2929],{},[1101,2548,2549],{},"GMM 三个更新式",[1129,2551,2553,2574],{"className":2552},[1132],[1129,2554,2556],{"className":2555},[1136],[1138,2557,2558],{"xmlns":1140},[1142,2559,2560,2571],{},[1145,2561,2562],{},[2563,2564,2565,2568],"msub",{},[1148,2566,2567],{},"μ",[1148,2569,2570],{},"k",[1152,2572,2573],{"encoding":1154},"\\mu_k",[1129,2575,2577],{"className":2576,"ariaHidden":1159},[1158],[1129,2578,2580,2583],{"className":2579},[1163],[1129,2581],{"className":2582,"style":1168},[1167],[1129,2584,2586,2589],{"className":2585},[1172],[1129,2587,2567],{"className":2588},[1172,1173],[1129,2590,2592],{"className":2591},[1303],[1129,2593,2595,2618],{"className":2594},[1307,1523],[1129,2596,2598,2615],{"className":2597},[1311],[1129,2599,2602],{"className":2600,"style":2601},[1315],"height:0.3361em;",[1129,2603,2605,2608],{"style":2604},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1129,2606],{"className":2607,"style":1324},[1323],[1129,2609,2611],{"className":2610},[1328,1329,1330,1331],[1129,2612,2570],{"className":2613,"style":2614},[1172,1173,1331],"margin-right:0.0315em;",[1129,2616,1577],{"className":2617},[1576],[1129,2619,2621],{"className":2620},[1311],[1129,2622,2625],{"className":2623,"style":2624},[1315],"height:0.15em;",[1129,2626],{},"、",[1129,2629,2631,2653],{"className":2630},[1132],[1129,2632,2634],{"className":2633},[1136],[1138,2635,2636],{"xmlns":1140},[1142,2637,2638,2650],{},[1145,2639,2640],{},[2641,2642,2643,2646,2648],"msubsup",{},[1148,2644,2645],{},"σ",[1148,2647,2570],{},[1244,2649,1991],{},[1152,2651,2652],{"encoding":1154},"\\sigma_k^2",[1129,2654,2656],{"className":2655,"ariaHidden":1159},[1158],[1129,2657,2659,2663],{"className":2658},[1163],[1129,2660],{"className":2661,"style":2662},[1167],"height:1.0972em;vertical-align:-0.2831em;",[1129,2664,2666,2669],{"className":2665},[1172],[1129,2667,2645],{"className":2668,"style":1174},[1172,1173],[1129,2670,2672],{"className":2671},[1303],[1129,2673,2675,2707],{"className":2674},[1307,1523],[1129,2676,2678,2704],{"className":2677},[1311],[1129,2679,2681,2693],{"className":2680,"style":1316},[1315],[1129,2682,2684,2687],{"style":2683},"top:-2.4169em;margin-left:-0.0359em;margin-right:0.05em;",[1129,2685],{"className":2686,"style":1324},[1323],[1129,2688,2690],{"className":2689},[1328,1329,1330,1331],[1129,2691,2570],{"className":2692,"style":2614},[1172,1173,1331],[1129,2694,2695,2698],{"style":1319},[1129,2696],{"className":2697,"style":1324},[1323],[1129,2699,2701],{"className":2700},[1328,1329,1330,1331],[1129,2702,1991],{"className":2703},[1172,1331],[1129,2705,1577],{"className":2706},[1576],[1129,2708,2710],{"className":2709},[1311],[1129,2711,2714],{"className":2712,"style":2713},[1315],"height:0.2831em;",[1129,2715],{},[1129,2717,2719,2738],{"className":2718},[1132],[1129,2720,2722],{"className":2721},[1136],[1138,2723,2724],{"xmlns":1140},[1142,2725,2726,2735],{},[1145,2727,2728],{},[2563,2729,2730,2733],{},[1148,2731,2732],{},"α",[1148,2734,2570],{},[1152,2736,2737],{"encoding":1154},"\\alpha_k",[1129,2739,2741],{"className":2740,"ariaHidden":1159},[1158],[1129,2742,2744,2748],{"className":2743},[1163],[1129,2745],{"className":2746,"style":2747},[1167],"height:0.5806em;vertical-align:-0.15em;",[1129,2749,2751,2755],{"className":2750},[1172],[1129,2752,2732],{"className":2753,"style":2754},[1172,1173],"margin-right:0.0037em;",[1129,2756,2758],{"className":2757},[1303],[1129,2759,2761,2782],{"className":2760},[1307,1523],[1129,2762,2764,2779],{"className":2763},[1311],[1129,2765,2767],{"className":2766,"style":2601},[1315],[1129,2768,2770,2773],{"style":2769},"top:-2.55em;margin-left:-0.0037em;margin-right:0.05em;",[1129,2771],{"className":2772,"style":1324},[1323],[1129,2774,2776],{"className":2775},[1328,1329,1330,1331],[1129,2777,2570],{"className":2778,"style":2614},[1172,1173,1331],[1129,2780,1577],{"className":2781},[1576],[1129,2783,2785],{"className":2784},[1311],[1129,2786,2788],{"className":2787,"style":2624},[1315],[1129,2789],{}," 用响应度 ",[1129,2792,2794,2824],{"className":2793},[1132],[1129,2795,2797],{"className":2796},[1136],[1138,2798,2799],{"xmlns":1140},[1142,2800,2801,2821],{},[1145,2802,2803],{},[2563,2804,2805,2814],{},[2806,2807,2808,2811],"mover",{"accent":1159},[1148,2809,2810],{},"γ",[1229,2812,2813],{},"^",[1145,2815,2816,2819],{},[1148,2817,2818],{},"j",[1148,2820,2570],{},[1152,2822,2823],{"encoding":1154},"\\hat\\gamma_{jk}",[1129,2825,2827],{"className":2826,"ariaHidden":1159},[1158],[1129,2828,2830,2834],{"className":2829},[1163],[1129,2831],{"className":2832,"style":2833},[1167],"height:0.9805em;vertical-align:-0.2861em;",[1129,2835,2837,2886],{"className":2836},[1172],[1129,2838,2841],{"className":2839},[1172,2840],"accent",[1129,2842,2844,2877],{"className":2843},[1307,1523],[1129,2845,2847,2874],{"className":2846},[1311],[1129,2848,2851,2861],{"className":2849,"style":2850},[1315],"height:0.6944em;",[1129,2852,2854,2857],{"style":2853},"top:-3em;",[1129,2855],{"className":2856,"style":1537},[1323],[1129,2858,2810],{"className":2859,"style":2860},[1172,1173],"margin-right:0.0556em;",[1129,2862,2863,2866],{"style":2853},[1129,2864],{"className":2865,"style":1537},[1323],[1129,2867,2871],{"className":2868,"style":2870},[2869],"accent-body","left:-0.25em;",[1129,2872,2813],{"className":2873},[1172],[1129,2875,1577],{"className":2876},[1576],[1129,2878,2880],{"className":2879},[1311],[1129,2881,2884],{"className":2882,"style":2883},[1315],"height:0.1944em;",[1129,2885],{},[1129,2887,2889],{"className":2888},[1303],[1129,2890,2892,2920],{"className":2891},[1307,1523],[1129,2893,2895,2917],{"className":2894},[1311],[1129,2896,2898],{"className":2897,"style":2601},[1315],[1129,2899,2901,2904],{"style":2900},"top:-2.55em;margin-left:-0.0556em;margin-right:0.05em;",[1129,2902],{"className":2903,"style":1324},[1323],[1129,2905,2907],{"className":2906},[1328,1329,1330,1331],[1129,2908,2910,2914],{"className":2909},[1172,1331],[1129,2911,2818],{"className":2912,"style":2913},[1172,1173,1331],"margin-right:0.0572em;",[1129,2915,2570],{"className":2916,"style":2614},[1172,1173,1331],[1129,2918,1577],{"className":2919},[1576],[1129,2921,2923],{"className":2922},[1311],[1129,2924,2927],{"className":2925,"style":2926},[1315],"height:0.2861em;",[1129,2928],{}," 加权;响应度是后验概率。",[1098,2931,2932,2935],{},[1101,2933,2934],{},"分布式 EM",":\n充分统计量可加,各节点局部求和、全局汇总更新参数",[2937,2938],"hr",{},[2940,2941,2943],"h2",{"id":2942},"一逆分布法反函数法","一、逆分布法(反函数法)",[1091,2945,2946],{},"计算机只会生成均匀分布的随机数，而我们生成符合对应分布的随机数需要进行一个映射关系的处理，逆分布法是最直接的一种随机数生成方法。",[1091,2948,2949],{},"当随机变量所服从的分布函数已知,并且这个分布函数的逆函数有显式解的时候,就可以直接用它来产生服从该分布的随机数。一旦分布函数的逆写不出来,这个方法就用不了,得改用后面的拒绝接受法。",[1091,2951,2952,2955],{},[1101,2953,2954],{},"原理",":",[1091,2957,2958,2959,2987,2988,3033,3034,3062,3063,3117,3118,3223,3224,3252],{},"设随机变量 ",[1129,2960,2962,2975],{"className":2961},[1132],[1129,2963,2965],{"className":2964},[1136],[1138,2966,2967],{"xmlns":1140},[1142,2968,2969,2973],{},[1145,2970,2971],{},[1148,2972,1227],{},[1152,2974,1227],{"encoding":1154},[1129,2976,2978],{"className":2977,"ariaHidden":1159},[1158],[1129,2979,2981,2984],{"className":2980},[1163],[1129,2982],{"className":2983,"style":1269},[1167],[1129,2985,1227],{"className":2986,"style":1273},[1172,1173]," 的分布函数是 ",[1129,2989,2991,3012],{"className":2990},[1132],[1129,2992,2994],{"className":2993},[1136],[1138,2995,2996],{"xmlns":1140},[1142,2997,2998,3009],{},[1145,2999,3000,3002,3004,3007],{},[1148,3001,1237],{},[1229,3003,1250],{"stretchy":1249},[1148,3005,3006],{},"x",[1229,3008,1256],{"stretchy":1249},[1152,3010,3011],{"encoding":1154},"F(x)",[1129,3013,3015],{"className":3014,"ariaHidden":1159},[1158],[1129,3016,3018,3021,3024,3027,3030],{"className":3017},[1163],[1129,3019],{"className":3020,"style":1414},[1167],[1129,3022,1237],{"className":3023,"style":1299},[1172,1173],[1129,3025,1250],{"className":3026},[1344],[1129,3028,3006],{"className":3029},[1172,1173],[1129,3031,1256],{"className":3032},[1352],",又设 ",[1129,3035,3037,3050],{"className":3036},[1132],[1129,3038,3040],{"className":3039},[1136],[1138,3041,3042],{"xmlns":1140},[1142,3043,3044,3048],{},[1145,3045,3046],{},[1148,3047,1253],{},[1152,3049,1253],{"encoding":1154},[1129,3051,3053],{"className":3052,"ariaHidden":1159},[1158],[1129,3054,3056,3059],{"className":3055},[1163],[1129,3057],{"className":3058,"style":1269},[1167],[1129,3060,1253],{"className":3061,"style":1348},[1172,1173]," 服从 ",[1129,3064,3066,3090],{"className":3065},[1132],[1129,3067,3069],{"className":3068},[1136],[1138,3070,3071],{"xmlns":1140},[1142,3072,3073,3087],{},[1145,3074,3075,3078,3080,3082,3084],{},[1229,3076,3077],{"stretchy":1249},"[",[1244,3079,1377],{},[1229,3081,1353],{"separator":1159},[1244,3083,1246],{},[1229,3085,3086],{"stretchy":1249},"]",[1152,3088,3089],{"encoding":1154},"[0,1]",[1129,3091,3093],{"className":3092,"ariaHidden":1159},[1158],[1129,3094,3096,3099,3102,3105,3108,3111,3114],{"className":3095},[1163],[1129,3097],{"className":3098,"style":1414},[1167],[1129,3100,3077],{"className":3101},[1344],[1129,3103,1377],{"className":3104},[1172],[1129,3106,1353],{"className":3107},[1427],[1129,3109],{"className":3110,"style":1431},[1277],[1129,3112,1246],{"className":3113},[1172],[1129,3115,3086],{"className":3116},[1352]," 上的均匀分布,那么随机变量 ",[1129,3119,3121,3152],{"className":3120},[1132],[1129,3122,3124],{"className":3123},[1136],[1138,3125,3126],{"xmlns":1140},[1142,3127,3128,3150],{},[1145,3129,3130,3132,3134,3144,3146,3148],{},[1148,3131,1227],{},[1229,3133,1231],{},[1233,3135,3136,3138],{},[1148,3137,1237],{},[1145,3139,3140,3142],{},[1229,3141,1242],{},[1244,3143,1246],{},[1229,3145,1250],{"stretchy":1249},[1148,3147,1253],{},[1229,3149,1256],{"stretchy":1249},[1152,3151,1259],{"encoding":1154},[1129,3153,3155,3173],{"className":3154,"ariaHidden":1159},[1158],[1129,3156,3158,3161,3164,3167,3170],{"className":3157},[1163],[1129,3159],{"className":3160,"style":1269},[1167],[1129,3162,1227],{"className":3163,"style":1273},[1172,1173],[1129,3165],{"className":3166,"style":1278},[1277],[1129,3168,1231],{"className":3169},[1282],[1129,3171],{"className":3172,"style":1278},[1277],[1129,3174,3176,3179,3214,3217,3220],{"className":3175},[1163],[1129,3177],{"className":3178,"style":1292},[1167],[1129,3180,3182,3185],{"className":3181},[1172],[1129,3183,1237],{"className":3184,"style":1299},[1172,1173],[1129,3186,3188],{"className":3187},[1303],[1129,3189,3191],{"className":3190},[1307],[1129,3192,3194],{"className":3193},[1311],[1129,3195,3197],{"className":3196,"style":1316},[1315],[1129,3198,3199,3202],{"style":1319},[1129,3200],{"className":3201,"style":1324},[1323],[1129,3203,3205],{"className":3204},[1328,1329,1330,1331],[1129,3206,3208,3211],{"className":3207},[1172,1331],[1129,3209,1242],{"className":3210},[1172,1331],[1129,3212,1246],{"className":3213},[1172,1331],[1129,3215,1250],{"className":3216},[1344],[1129,3218,1253],{"className":3219,"style":1348},[1172,1173],[1129,3221,1256],{"className":3222},[1352]," 就服从以 ",[1129,3225,3227,3240],{"className":3226},[1132],[1129,3228,3230],{"className":3229},[1136],[1138,3231,3232],{"xmlns":1140},[1142,3233,3234,3238],{},[1145,3235,3236],{},[1148,3237,1237],{},[1152,3239,1237],{"encoding":1154},[1129,3241,3243],{"className":3242,"ariaHidden":1159},[1158],[1129,3244,3246,3249],{"className":3245},[1163],[1129,3247],{"className":3248,"style":1269},[1167],[1129,3250,1237],{"className":3251,"style":1299},[1172,1173]," 为分布函数的那个分布。也就是只要能把均匀分布的随机数\"喂\"进逆分布函数,出来的就是目标分布的随机数。",[1091,3254,3255,2955],{},[1101,3256,3257],{},"算法步骤",[3259,3260,3261,3344],"ol",{},[1098,3262,3263,3264,3343],{},"产生一个服从均匀分布 ",[1129,3265,3267,3295],{"className":3266},[1132],[1129,3268,3270],{"className":3269},[1136],[1138,3271,3272],{"xmlns":1140},[1142,3273,3274,3292],{},[1145,3275,3276,3278,3280,3282,3284,3286,3288,3290],{},[1148,3277,1253],{},[1229,3279,1370],{},[1148,3281,1253],{},[1229,3283,1250],{"stretchy":1249},[1244,3285,1377],{},[1229,3287,1353],{"separator":1159},[1244,3289,1246],{},[1229,3291,1256],{"stretchy":1249},[1152,3293,3294],{"encoding":1154},"U \\sim U(0,1)",[1129,3296,3298,3316],{"className":3297,"ariaHidden":1159},[1158],[1129,3299,3301,3304,3307,3310,3313],{"className":3300},[1163],[1129,3302],{"className":3303,"style":1269},[1167],[1129,3305,1253],{"className":3306,"style":1348},[1172,1173],[1129,3308],{"className":3309,"style":1278},[1277],[1129,3311,1370],{"className":3312},[1282],[1129,3314],{"className":3315,"style":1278},[1277],[1129,3317,3319,3322,3325,3328,3331,3334,3337,3340],{"className":3318},[1163],[1129,3320],{"className":3321,"style":1414},[1167],[1129,3323,1253],{"className":3324,"style":1348},[1172,1173],[1129,3326,1250],{"className":3327},[1344],[1129,3329,1377],{"className":3330},[1172],[1129,3332,1353],{"className":3333},[1427],[1129,3335],{"className":3336,"style":1431},[1277],[1129,3338,1246],{"className":3339},[1172],[1129,3341,1256],{"className":3342},[1352]," 的随机数;",[1098,3345,3346,3347,3452,3453,3481,3482,3510],{},"令 ",[1129,3348,3350,3381],{"className":3349},[1132],[1129,3351,3353],{"className":3352},[1136],[1138,3354,3355],{"xmlns":1140},[1142,3356,3357,3379],{},[1145,3358,3359,3361,3363,3373,3375,3377],{},[1148,3360,1227],{},[1229,3362,1231],{},[1233,3364,3365,3367],{},[1148,3366,1237],{},[1145,3368,3369,3371],{},[1229,3370,1242],{},[1244,3372,1246],{},[1229,3374,1250],{"stretchy":1249},[1148,3376,1253],{},[1229,3378,1256],{"stretchy":1249},[1152,3380,1259],{"encoding":1154},[1129,3382,3384,3402],{"className":3383,"ariaHidden":1159},[1158],[1129,3385,3387,3390,3393,3396,3399],{"className":3386},[1163],[1129,3388],{"className":3389,"style":1269},[1167],[1129,3391,1227],{"className":3392,"style":1273},[1172,1173],[1129,3394],{"className":3395,"style":1278},[1277],[1129,3397,1231],{"className":3398},[1282],[1129,3400],{"className":3401,"style":1278},[1277],[1129,3403,3405,3408,3443,3446,3449],{"className":3404},[1163],[1129,3406],{"className":3407,"style":1292},[1167],[1129,3409,3411,3414],{"className":3410},[1172],[1129,3412,1237],{"className":3413,"style":1299},[1172,1173],[1129,3415,3417],{"className":3416},[1303],[1129,3418,3420],{"className":3419},[1307],[1129,3421,3423],{"className":3422},[1311],[1129,3424,3426],{"className":3425,"style":1316},[1315],[1129,3427,3428,3431],{"style":1319},[1129,3429],{"className":3430,"style":1324},[1323],[1129,3432,3434],{"className":3433},[1328,1329,1330,1331],[1129,3435,3437,3440],{"className":3436},[1172,1331],[1129,3438,1242],{"className":3439},[1172,1331],[1129,3441,1246],{"className":3442},[1172,1331],[1129,3444,1250],{"className":3445},[1344],[1129,3447,1253],{"className":3448,"style":1348},[1172,1173],[1129,3450,1256],{"className":3451},[1352],",那么 ",[1129,3454,3456,3469],{"className":3455},[1132],[1129,3457,3459],{"className":3458},[1136],[1138,3460,3461],{"xmlns":1140},[1142,3462,3463,3467],{},[1145,3464,3465],{},[1148,3466,1227],{},[1152,3468,1227],{"encoding":1154},[1129,3470,3472],{"className":3471,"ariaHidden":1159},[1158],[1129,3473,3475,3478],{"className":3474},[1163],[1129,3476],{"className":3477,"style":1269},[1167],[1129,3479,1227],{"className":3480,"style":1273},[1172,1173]," 就是服从目标分布 ",[1129,3483,3485,3498],{"className":3484},[1132],[1129,3486,3488],{"className":3487},[1136],[1138,3489,3490],{"xmlns":1140},[1142,3491,3492,3496],{},[1145,3493,3494],{},[1148,3495,1237],{},[1152,3497,1237],{"encoding":1154},[1129,3499,3501],{"className":3500,"ariaHidden":1159},[1158],[1129,3502,3504,3507],{"className":3503},[1163],[1129,3505],{"className":3506,"style":1269},[1167],[1129,3508,1237],{"className":3509,"style":1299},[1172,1173]," 的随机数。",[3512,3513,3515],"h3",{"id":3514},"例子一指数分布","例子一:指数分布",[1091,3517,3518,3519,3548,3549,3598],{},"要产生 ",[1129,3520,3522,3536],{"className":3521},[1132],[1129,3523,3525],{"className":3524},[1136],[1138,3526,3527],{"xmlns":1140},[1142,3528,3529,3534],{},[1145,3530,3531],{},[1148,3532,3533],{},"n",[1152,3535,3533],{"encoding":1154},[1129,3537,3539],{"className":3538,"ariaHidden":1159},[1158],[1129,3540,3542,3545],{"className":3541},[1163],[1129,3543],{"className":3544,"style":1202},[1167],[1129,3546,3533],{"className":3547},[1172,1173]," 个服从指数分布 ",[1129,3550,3552,3573],{"className":3551},[1132],[1129,3553,3555],{"className":3554},[1136],[1138,3556,3557],{"xmlns":1140},[1142,3558,3559,3570],{},[1145,3560,3561,3564,3566,3568],{},[1648,3562,3563],{},"Exp",[1229,3565,1250],{"stretchy":1249},[1148,3567,1467],{},[1229,3569,1256],{"stretchy":1249},[1152,3571,3572],{"encoding":1154},"\\text{Exp}(\\lambda)",[1129,3574,3576],{"className":3575,"ariaHidden":1159},[1158],[1129,3577,3579,3582,3589,3592,3595],{"className":3578},[1163],[1129,3580],{"className":3581,"style":1414},[1167],[1129,3583,3586],{"className":3584},[1172,3585],"text",[1129,3587,3563],{"className":3588},[1172],[1129,3590,1250],{"className":3591},[1344],[1129,3593,1467],{"className":3594},[1172,1173],[1129,3596,1256],{"className":3597},[1352]," 的随机数。指数分布的概率密度函数与分布函数分别是",[1091,3600,3601],{},[1129,3602,3604,3685],{"className":3603},[1132],[1129,3605,3607],{"className":3606},[1136],[1138,3608,3609],{"xmlns":1140},[1142,3610,3611,3682],{},[1145,3612,3613,3615,3617,3619,3621,3623,3625,3638,3640,3643,3645,3647,3649,3651,3653,3655,3657,3669,3671,3673,3675,3678,3680],{},[1148,3614,1635],{},[1229,3616,1250],{"stretchy":1249},[1148,3618,3006],{},[1229,3620,1256],{"stretchy":1249},[1229,3622,1231],{},[1148,3624,1467],{},[1233,3626,3627,3630],{},[1148,3628,3629],{},"e",[1145,3631,3632,3634,3636],{},[1229,3633,1242],{},[1148,3635,1467],{},[1148,3637,3006],{},[1229,3639,1353],{"separator":1159},[1277,3641],{"width":3642},"1em",[1148,3644,1237],{},[1229,3646,1250],{"stretchy":1249},[1148,3648,3006],{},[1229,3650,1256],{"stretchy":1249},[1229,3652,1231],{},[1244,3654,1246],{},[1229,3656,1242],{},[1233,3658,3659,3661],{},[1148,3660,3629],{},[1145,3662,3663,3665,3667],{},[1229,3664,1242],{},[1148,3666,1467],{},[1148,3668,3006],{},[1277,3670],{"width":3642},[1229,3672,1250],{"stretchy":1249},[1148,3674,3006],{},[1229,3676,3677],{},"≥",[1244,3679,1377],{},[1229,3681,1256],{"stretchy":1249},[1152,3683,3684],{"encoding":1154},"f(x) = \\lambda e^{-\\lambda x}, \\quad F(x) = 1 - e^{-\\lambda x} \\quad (x \\ge 0)",[1129,3686,3688,3715,3795,3814,3876],{"className":3687,"ariaHidden":1159},[1158],[1129,3689,3691,3694,3697,3700,3703,3706,3709,3712],{"className":3690},[1163],[1129,3692],{"className":3693,"style":1414},[1167],[1129,3695,1635],{"className":3696,"style":1758},[1172,1173],[1129,3698,1250],{"className":3699},[1344],[1129,3701,3006],{"className":3702},[1172,1173],[1129,3704,1256],{"className":3705},[1352],[1129,3707],{"className":3708,"style":1278},[1277],[1129,3710,1231],{"className":3711},[1282],[1129,3713],{"className":3714,"style":1278},[1277],[1129,3716,3718,3722,3725,3764,3767,3771,3774,3777,3780,3783,3786,3789,3792],{"className":3717},[1163],[1129,3719],{"className":3720,"style":3721},[1167],"height:1.0991em;vertical-align:-0.25em;",[1129,3723,1467],{"className":3724},[1172,1173],[1129,3726,3728,3731],{"className":3727},[1172],[1129,3729,3629],{"className":3730},[1172,1173],[1129,3732,3734],{"className":3733},[1303],[1129,3735,3737],{"className":3736},[1307],[1129,3738,3740],{"className":3739},[1311],[1129,3741,3744],{"className":3742,"style":3743},[1315],"height:0.8491em;",[1129,3745,3746,3749],{"style":1319},[1129,3747],{"className":3748,"style":1324},[1323],[1129,3750,3752],{"className":3751},[1328,1329,1330,1331],[1129,3753,3755,3758,3761],{"className":3754},[1172,1331],[1129,3756,1242],{"className":3757},[1172,1331],[1129,3759,1467],{"className":3760},[1172,1173,1331],[1129,3762,3006],{"className":3763},[1172,1173,1331],[1129,3765,1353],{"className":3766},[1427],[1129,3768],{"className":3769,"style":3770},[1277],"margin-right:1em;",[1129,3772],{"className":3773,"style":1431},[1277],[1129,3775,1237],{"className":3776,"style":1299},[1172,1173],[1129,3778,1250],{"className":3779},[1344],[1129,3781,3006],{"className":3782},[1172,1173],[1129,3784,1256],{"className":3785},[1352],[1129,3787],{"className":3788,"style":1278},[1277],[1129,3790,1231],{"className":3791},[1282],[1129,3793],{"className":3794,"style":1278},[1277],[1129,3796,3798,3802,3805,3808,3811],{"className":3797},[1163],[1129,3799],{"className":3800,"style":3801},[1167],"height:0.7278em;vertical-align:-0.0833em;",[1129,3803,1246],{"className":3804},[1172],[1129,3806],{"className":3807,"style":1734},[1277],[1129,3809,1242],{"className":3810},[2084],[1129,3812],{"className":3813,"style":1734},[1277],[1129,3815,3817,3820,3858,3861,3864,3867,3870,3873],{"className":3816},[1163],[1129,3818],{"className":3819,"style":3721},[1167],[1129,3821,3823,3826],{"className":3822},[1172],[1129,3824,3629],{"className":3825},[1172,1173],[1129,3827,3829],{"className":3828},[1303],[1129,3830,3832],{"className":3831},[1307],[1129,3833,3835],{"className":3834},[1311],[1129,3836,3838],{"className":3837,"style":3743},[1315],[1129,3839,3840,3843],{"style":1319},[1129,3841],{"className":3842,"style":1324},[1323],[1129,3844,3846],{"className":3845},[1328,1329,1330,1331],[1129,3847,3849,3852,3855],{"className":3848},[1172,1331],[1129,3850,1242],{"className":3851},[1172,1331],[1129,3853,1467],{"className":3854},[1172,1173,1331],[1129,3856,3006],{"className":3857},[1172,1173,1331],[1129,3859],{"className":3860,"style":3770},[1277],[1129,3862,1250],{"className":3863},[1344],[1129,3865,3006],{"className":3866},[1172,1173],[1129,3868],{"className":3869,"style":1278},[1277],[1129,3871,3677],{"className":3872},[1282],[1129,3874],{"className":3875,"style":1278},[1277],[1129,3877,3879,3882,3885],{"className":3878},[1163],[1129,3880],{"className":3881,"style":1414},[1167],[1129,3883,1377],{"className":3884},[1172],[1129,3886,1256],{"className":3887},[1352],[1091,3889,3346,3890,4045],{},[1129,3891,3893,3935],{"className":3892},[1132],[1129,3894,3896],{"className":3895},[1136],[1138,3897,3898],{"xmlns":1140},[1142,3899,3900,3932],{},[1145,3901,3902,3904,3906,3908,3910,3912,3914,3916,3918,3920],{},[1148,3903,1253],{},[1229,3905,1231],{},[1148,3907,1237],{},[1229,3909,1250],{"stretchy":1249},[1148,3911,1227],{},[1229,3913,1256],{"stretchy":1249},[1229,3915,1231],{},[1244,3917,1246],{},[1229,3919,1242],{},[1233,3921,3922,3924],{},[1148,3923,3629],{},[1145,3925,3926,3928,3930],{},[1229,3927,1242],{},[1148,3929,1467],{},[1148,3931,1227],{},[1152,3933,3934],{"encoding":1154},"U = F(X) = 1 - e^{-\\lambda X}",[1129,3936,3938,3956,3983,4001],{"className":3937,"ariaHidden":1159},[1158],[1129,3939,3941,3944,3947,3950,3953],{"className":3940},[1163],[1129,3942],{"className":3943,"style":1269},[1167],[1129,3945,1253],{"className":3946,"style":1348},[1172,1173],[1129,3948],{"className":3949,"style":1278},[1277],[1129,3951,1231],{"className":3952},[1282],[1129,3954],{"className":3955,"style":1278},[1277],[1129,3957,3959,3962,3965,3968,3971,3974,3977,3980],{"className":3958},[1163],[1129,3960],{"className":3961,"style":1414},[1167],[1129,3963,1237],{"className":3964,"style":1299},[1172,1173],[1129,3966,1250],{"className":3967},[1344],[1129,3969,1227],{"className":3970,"style":1273},[1172,1173],[1129,3972,1256],{"className":3973},[1352],[1129,3975],{"className":3976,"style":1278},[1277],[1129,3978,1231],{"className":3979},[1282],[1129,3981],{"className":3982,"style":1278},[1277],[1129,3984,3986,3989,3992,3995,3998],{"className":3985},[1163],[1129,3987],{"className":3988,"style":3801},[1167],[1129,3990,1246],{"className":3991},[1172],[1129,3993],{"className":3994,"style":1734},[1277],[1129,3996,1242],{"className":3997},[2084],[1129,3999],{"className":4000,"style":1734},[1277],[1129,4002,4004,4007],{"className":4003},[1163],[1129,4005],{"className":4006,"style":3743},[1167],[1129,4008,4010,4013],{"className":4009},[1172],[1129,4011,3629],{"className":4012},[1172,1173],[1129,4014,4016],{"className":4015},[1303],[1129,4017,4019],{"className":4018},[1307],[1129,4020,4022],{"className":4021},[1311],[1129,4023,4025],{"className":4024,"style":3743},[1315],[1129,4026,4027,4030],{"style":1319},[1129,4028],{"className":4029,"style":1324},[1323],[1129,4031,4033],{"className":4032},[1328,1329,1330,1331],[1129,4034,4036,4039,4042],{"className":4035},[1172,1331],[1129,4037,1242],{"className":4038},[1172,1331],[1129,4040,1467],{"className":4041},[1172,1173,1331],[1129,4043,1227],{"className":4044,"style":1273},[1172,1173,1331],",反解出",[1091,4047,4048],{},[1129,4049,4051,4089],{"className":4050},[1132],[1129,4052,4054],{"className":4053},[1136],[1138,4055,4056],{"xmlns":1140},[1142,4057,4058,4086],{},[1145,4059,4060,4062,4064,4066,4072,4074,4076,4078,4080,4082,4084],{},[1148,4061,1227],{},[1229,4063,1231],{},[1229,4065,1242],{},[1461,4067,4068,4070],{},[1244,4069,1246],{},[1148,4071,1467],{},[1148,4073,1470],{},[1229,4075,1473],{},[1229,4077,1250],{"stretchy":1249},[1244,4079,1246],{},[1229,4081,1242],{},[1148,4083,1253],{},[1229,4085,1256],{"stretchy":1249},[1152,4087,4088],{"encoding":1154},"X = -\\frac{1}{\\lambda}\\ln(1 - U)",[1129,4090,4092,4110,4208],{"className":4091,"ariaHidden":1159},[1158],[1129,4093,4095,4098,4101,4104,4107],{"className":4094},[1163],[1129,4096],{"className":4097,"style":1269},[1167],[1129,4099,1227],{"className":4100,"style":1273},[1172,1173],[1129,4102],{"className":4103,"style":1278},[1277],[1129,4105,1231],{"className":4106},[1282],[1129,4108],{"className":4109,"style":1278},[1277],[1129,4111,4113,4116,4119,4187,4190,4193,4196,4199,4202,4205],{"className":4112},[1163],[1129,4114],{"className":4115,"style":1506},[1167],[1129,4117,1242],{"className":4118},[1172],[1129,4120,4122,4125,4184],{"className":4121},[1172],[1129,4123],{"className":4124},[1344,1516],[1129,4126,4128],{"className":4127},[1461],[1129,4129,4131,4176],{"className":4130},[1307,1523],[1129,4132,4134,4173],{"className":4133},[1311],[1129,4135,4137,4151,4159],{"className":4136,"style":1530},[1315],[1129,4138,4139,4142],{"style":1533},[1129,4140],{"className":4141,"style":1537},[1323],[1129,4143,4145],{"className":4144},[1328,1329,1330,1331],[1129,4146,4148],{"className":4147},[1172,1331],[1129,4149,1467],{"className":4150},[1172,1173,1331],[1129,4152,4153,4156],{"style":1549},[1129,4154],{"className":4155,"style":1537},[1323],[1129,4157],{"className":4158,"style":1557},[1556],[1129,4160,4161,4164],{"style":1560},[1129,4162],{"className":4163,"style":1537},[1323],[1129,4165,4167],{"className":4166},[1328,1329,1330,1331],[1129,4168,4170],{"className":4169},[1172,1331],[1129,4171,1246],{"className":4172},[1172,1331],[1129,4174,1577],{"className":4175},[1576],[1129,4177,4179],{"className":4178},[1311],[1129,4180,4182],{"className":4181,"style":1584},[1315],[1129,4183],{},[1129,4185],{"className":4186},[1352,1516],[1129,4188],{"className":4189,"style":1431},[1277],[1129,4191,1470],{"className":4192},[1596],[1129,4194,1250],{"className":4195},[1344],[1129,4197,1246],{"className":4198},[1172],[1129,4200],{"className":4201,"style":1734},[1277],[1129,4203,1242],{"className":4204},[2084],[1129,4206],{"className":4207,"style":1734},[1277],[1129,4209,4211,4214,4217],{"className":4210},[1163],[1129,4212],{"className":4213,"style":1414},[1167],[1129,4215,1253],{"className":4216,"style":1348},[1172,1173],[1129,4218,1256],{"className":4219},[1352],[1091,4221,4222,4273,4274,4302,4303,4360,4361],{},[1129,4223,4225,4243],{"className":4224},[1132],[1129,4226,4228],{"className":4227},[1136],[1138,4229,4230],{"xmlns":1140},[1142,4231,4232,4240],{},[1145,4233,4234,4236,4238],{},[1244,4235,1246],{},[1229,4237,1242],{},[1148,4239,1253],{},[1152,4241,4242],{"encoding":1154},"1-U",[1129,4244,4246,4264],{"className":4245,"ariaHidden":1159},[1158],[1129,4247,4249,4252,4255,4258,4261],{"className":4248},[1163],[1129,4250],{"className":4251,"style":3801},[1167],[1129,4253,1246],{"className":4254},[1172],[1129,4256],{"className":4257,"style":1734},[1277],[1129,4259,1242],{"className":4260},[2084],[1129,4262],{"className":4263,"style":1734},[1277],[1129,4265,4267,4270],{"className":4266},[1163],[1129,4268],{"className":4269,"style":1269},[1167],[1129,4271,1253],{"className":4272,"style":1348},[1172,1173]," 与 ",[1129,4275,4277,4290],{"className":4276},[1132],[1129,4278,4280],{"className":4279},[1136],[1138,4281,4282],{"xmlns":1140},[1142,4283,4284,4288],{},[1145,4285,4286],{},[1148,4287,1253],{},[1152,4289,1253],{"encoding":1154},[1129,4291,4293],{"className":4292,"ariaHidden":1159},[1158],[1129,4294,4296,4299],{"className":4295},[1163],[1129,4297],{"className":4298,"style":1269},[1167],[1129,4300,1253],{"className":4301,"style":1348},[1172,1173]," 同分布(都是 ",[1129,4304,4306,4330],{"className":4305},[1132],[1129,4307,4309],{"className":4308},[1136],[1138,4310,4311],{"xmlns":1140},[1142,4312,4313,4327],{},[1145,4314,4315,4317,4319,4321,4323,4325],{},[1148,4316,1253],{},[1229,4318,1250],{"stretchy":1249},[1244,4320,1377],{},[1229,4322,1353],{"separator":1159},[1244,4324,1246],{},[1229,4326,1256],{"stretchy":1249},[1152,4328,4329],{"encoding":1154},"U(0,1)",[1129,4331,4333],{"className":4332,"ariaHidden":1159},[1158],[1129,4334,4336,4339,4342,4345,4348,4351,4354,4357],{"className":4335},[1163],[1129,4337],{"className":4338,"style":1414},[1167],[1129,4340,1253],{"className":4341,"style":1348},[1172,1173],[1129,4343,1250],{"className":4344},[1344],[1129,4346,1377],{"className":4347},[1172],[1129,4349,1353],{"className":4350},[1427],[1129,4352],{"className":4353,"style":1431},[1277],[1129,4355,1246],{"className":4356},[1172],[1129,4358,1256],{"className":4359},[1352],"),结果也可以写成 ",[1129,4362,4364,4396],{"className":4363},[1132],[1129,4365,4367],{"className":4366},[1136],[1138,4368,4369],{"xmlns":1140},[1142,4370,4371,4393],{},[1145,4372,4373,4375,4377,4379,4387,4389,4391],{},[1148,4374,1227],{},[1229,4376,1231],{},[1229,4378,1242],{},[1458,4380,4381],{"scriptlevel":1377,"displaystyle":1159},[1461,4382,4383,4385],{},[1244,4384,1246],{},[1148,4386,1467],{},[1148,4388,1470],{},[1229,4390,1473],{},[1148,4392,1253],{},[1152,4394,4395],{"encoding":1154},"X = -\\dfrac{1}{\\lambda}\\ln U",[1129,4397,4399,4417],{"className":4398,"ariaHidden":1159},[1158],[1129,4400,4402,4405,4408,4411,4414],{"className":4401},[1163],[1129,4403],{"className":4404,"style":1269},[1167],[1129,4406,1227],{"className":4407,"style":1273},[1172,1173],[1129,4409],{"className":4410,"style":1278},[1277],[1129,4412,1231],{"className":4413},[1282],[1129,4415],{"className":4416,"style":1278},[1277],[1129,4418,4420,4423,4426,4488,4491,4494,4497],{"className":4419},[1163],[1129,4421],{"className":4422,"style":1831},[1167],[1129,4424,1242],{"className":4425},[1172],[1129,4427,4429,4432,4485],{"className":4428},[1172],[1129,4430],{"className":4431},[1344,1516],[1129,4433,4435],{"className":4434},[1461],[1129,4436,4438,4477],{"className":4437},[1307,1523],[1129,4439,4441,4474],{"className":4440},[1311],[1129,4442,4444,4455,4463],{"className":4443,"style":1850},[1315],[1129,4445,4446,4449],{"style":1712},[1129,4447],{"className":4448,"style":1537},[1323],[1129,4450,4452],{"className":4451},[1172],[1129,4453,1467],{"className":4454},[1172,1173],[1129,4456,4457,4460],{"style":1549},[1129,4458],{"className":4459,"style":1537},[1323],[1129,4461],{"className":4462,"style":1557},[1556],[1129,4464,4465,4468],{"style":1748},[1129,4466],{"className":4467,"style":1537},[1323],[1129,4469,4471],{"className":4470},[1172],[1129,4472,1246],{"className":4473},[1172],[1129,4475,1577],{"className":4476},[1576],[1129,4478,4480],{"className":4479},[1311],[1129,4481,4483],{"className":4482,"style":1890},[1315],[1129,4484],{},[1129,4486],{"className":4487},[1352,1516],[1129,4489],{"className":4490,"style":1431},[1277],[1129,4492,1470],{"className":4493},[1596],[1129,4495],{"className":4496,"style":1431},[1277],[1129,4498,1253],{"className":4499,"style":1348},[1172,1173],[3512,4501,4503],{"id":4502},"例子二标准-laplace-分布","例子二:标准 Laplace 分布",[1091,4505,3518,4506,4534],{},[1129,4507,4509,4522],{"className":4508},[1132],[1129,4510,4512],{"className":4511},[1136],[1138,4513,4514],{"xmlns":1140},[1142,4515,4516,4520],{},[1145,4517,4518],{},[1148,4519,3533],{},[1152,4521,3533],{"encoding":1154},[1129,4523,4525],{"className":4524,"ariaHidden":1159},[1158],[1129,4526,4528,4531],{"className":4527},[1163],[1129,4529],{"className":4530,"style":1202},[1167],[1129,4532,3533],{"className":4533},[1172,1173]," 个服从标准 Laplace 分布的随机数。Laplace 分布(双指数分布)的概率密度函数为",[1091,4536,4537],{},[1129,4538,4540,4584],{"className":4539},[1132],[1129,4541,4543],{"className":4542},[1136],[1138,4544,4545],{"xmlns":1140},[1142,4546,4547,4581],{},[1145,4548,4549,4551,4553,4555,4557,4559,4565],{},[1148,4550,1635],{},[1229,4552,1250],{"stretchy":1249},[1148,4554,3006],{},[1229,4556,1256],{"stretchy":1249},[1229,4558,1231],{},[1461,4560,4561,4563],{},[1244,4562,1246],{},[1244,4564,1991],{},[1233,4566,4567,4569],{},[1148,4568,3629],{},[1145,4570,4571,4573,4577,4579],{},[1229,4572,1242],{},[1148,4574,4576],{"mathvariant":4575},"normal","∣",[1148,4578,3006],{},[1148,4580,4576],{"mathvariant":4575},[1152,4582,4583],{"encoding":1154},"f(x) = \\frac{1}{2} 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分别在两段上反解,就得到逆函数:",[1091,5406,5407],{},[1129,5408,5410,5531],{"className":5409},[1132],[1129,5411,5413],{"className":5412},[1136],[1138,5414,5415],{"xmlns":1140},[1142,5416,5417,5528],{},[1145,5418,5419,5421,5423],{},[1148,5420,1227],{},[1229,5422,1231],{},[1145,5424,5425,5427],{},[1229,5426,4761],{"fence":1159},[4763,5428,5429,5473],{"rowspacing":4765,"columnalign":4766,"columnspacing":3642},[4768,5430,5431,5451],{},[4771,5432,5433],{},[1458,5434,5435],{"scriptlevel":1377,"displaystyle":1249},[1145,5436,5437,5439,5441,5443,5445,5447,5449],{},[1148,5438,1470],{},[1229,5440,1473],{},[1229,5442,1250],{"stretchy":1249},[1244,5444,1991],{},[1148,5446,1253],{},[1229,5448,1256],{"stretchy":1249},[1229,5450,1353],{"separator":1159},[4771,5452,5453],{},[1458,5454,5455],{"scriptlevel":1377,"displaystyle":1249},[1145,5456,5457,5459,5461,5463,5465],{},[1244,5458,1377],{},[1229,5460,4803],{},[1148,5462,1253],{},[1229,5464,4803],{},[1458,5466,5467],{"scriptlevel":1377,"displaystyle":1249},[1461,5468,5469,5471],{},[1244,5470,1246],{},[1244,5472,1991],{},[4768,5474,5475,5506],{},[4771,5476,5477],{},[1458,5478,5479],{"scriptlevel":1377,"displaystyle":1249},[1145,5480,5481,5483,5485,5487,5490,5492,5494,5496,5498,5500,5502,5504],{},[1229,5482,1242],{},[1148,5484,1470],{},[1229,5486,1473],{},[1229,5488,1250],{"fence":1249,"stretchy":1159,"minsize":5489,"maxsize":5489},"1.2em",[1244,5491,1991],{},[1229,5493,1250],{"stretchy":1249},[1244,5495,1246],{},[1229,5497,1242],{},[1148,5499,1253],{},[1229,5501,1256],{"stretchy":1249},[1229,5503,1256],{"fence":1249,"stretchy":1159,"minsize":5489,"maxsize":5489},[1229,5505,1353],{"separator":1159},[4771,5507,5508],{},[1458,5509,5510],{"scriptlevel":1377,"displaystyle":1249},[1145,5511,5512,5520,5522,5524,5526],{},[1458,5513,5514],{"scriptlevel":1377,"displaystyle":1249},[1461,5515,5516,5518],{},[1244,5517,1246],{},[1244,5519,1991],{},[1229,5521,1626],{},[1148,5523,1253],{},[1229,5525,4803],{},[1244,5527,1246],{},[1152,5529,5530],{"encoding":1154},"X = \\begin{cases} \\ln(2U), & 0 \u003C U \u003C \\tfrac{1}{2} \\\\[2mm] -\\ln\\big(2(1-U)\\big), & \\tfrac{1}{2} \\le U \u003C 1 \\end{cases}",[1129,5532,5534,5552],{"className":5533,"ariaHidden":1159},[1158],[1129,5535,5537,5540,5543,5546,5549],{"className":5536},[1163],[1129,5538],{"className":5539,"style":1269},[1167],[1129,5541,1227],{"className":5542,"style":1273},[1172,1173],[1129,5544],{"className":5545,"style":1278},[1277],[1129,5547,1231],{"className":5548},[1282],[1129,5550],{"className":5551,"style":1278},[1277],[1129,5553,5555,5559],{"className":5554},[1163],[1129,5556],{"className":5557,"style":5558},[1167],"height:3.6em;vertical-align:-1.55em;",[1129,5560,5562,5649,5995],{"className":5561},[4893],[1129,5563,5565],{"className":5564},[1344],[1129,5566,5568],{"className":5567},[4900,4901],[1129,5569,5571,5640],{"className":5570},[1307,1523],[1129,5572,5574,5637],{"className":5573},[1311],[1129,5575,5578,5589,5605,5615,5626],{"className":5576,"style":5577},[1315],"height:2.05em;",[1129,5579,5581,5584],{"style":5580},"top:-2.5em;",[1129,5582],{"className":5583,"style":4918},[1323],[1129,5585,5587],{"className":5586},[4922,4923],[1129,5588,4926],{},[1129,5590,5592,5595],{"style":5591},"top:-2.492em;",[1129,5593],{"className":5594,"style":4918},[1323],[1129,5596,5598],{"style":5597},"height:0.016em;width:0.8889em;",[4937,5599,5602],{"xmlns":4939,"width":4940,"height":5600,"style":4942,"viewBox":5601,"preserveAspectRatio":4944},"0.016em","0 0 888.89 16",[4946,5603],{"d":5604},"M384 0 H504 V16 H384z M384 0 H504 V16 H384z",[1129,5606,5607,5610],{"style":4951},[1129,5608],{"className":5609,"style":4918},[1323],[1129,5611,5613],{"className":5612},[4922,4923],[1129,5614,4960],{},[1129,5616,5617,5620],{"style":4963},[1129,5618],{"className":5619,"style":4918},[1323],[1129,5621,5622],{"style":5597},[4937,5623,5624],{"xmlns":4939,"width":4940,"height":5600,"style":4942,"viewBox":5601,"preserveAspectRatio":4944},[4946,5625],{"d":5604},[1129,5627,5629,5632],{"style":5628},"top:-4.3em;",[1129,5630],{"className":5631,"style":4918},[1323],[1129,5633,5635],{"className":5634},[4922,4923],[1129,5636,4984],{},[1129,5638,1577],{"className":5639},[1576],[1129,5641,5643],{"className":5642},[1311],[1129,5644,5647],{"className":5645,"style":5646},[1315],"height:1.55em;",[1129,5648],{},[1129,5650,5652],{"className":5651},[1172],[1129,5653,5655,5769,5772],{"className":5654},[4763],[1129,5656,5658],{"className":5657},[5006],[1129,5659,5661,5760],{"className":5660},[1307,1523],[1129,5662,5664,5757],{"className":5663},[1311],[1129,5665,5668,5696],{"className":5666,"style":5667},[1315],"height:1.9745em;",[1129,5669,5671,5675],{"style":5670},"top:-3.9745em;",[1129,5672],{"className":5673,"style":5674},[1323],"height:3.008em;",[1129,5676,5678,5681,5684,5687,5690,5693],{"className":5677},[1172],[1129,5679,1470],{"className":5680},[1596],[1129,5682,1250],{"className":5683},[1344],[1129,5685,1991],{"className":5686},[1172],[1129,5688,1253],{"className":5689,"style":1348},[1172,1173],[1129,5691,1256],{"className":5692},[1352],[1129,5694,1353],{"className":5695},[1427],[1129,5697,5699,5702],{"style":5698},"top:-1.9655em;",[1129,5700],{"className":5701,"style":5674},[1323],[1129,5703,5705,5708,5711,5714,5717,5724,5727,5730,5733,5736,5739,5742,5745,5748,5754],{"className":5704},[1172],[1129,5706,1242],{"className":5707},[1172],[1129,5709],{"className":5710,"style":1431},[1277],[1129,5712,1470],{"className":5713},[1596],[1129,5715],{"className":5716,"style":1431},[1277],[1129,5718,5720],{"className":5719},[1172],[1129,5721,1250],{"className":5722},[4900,5723],"size1",[1129,5725,1991],{"className":5726},[1172],[1129,5728,1250],{"className":5729},[1344],[1129,5731,1246],{"className":5732},[1172],[1129,5734],{"className":5735,"style":1734},[1277],[1129,5737,1242],{"className":5738},[2084],[1129,5740],{"className":5741,"style":1734},[1277],[1129,5743,1253],{"className":5744,"style":1348},[1172,1173],[1129,5746,1256],{"className":5747},[1352],[1129,5749,5751],{"className":5750},[1172],[1129,5752,1256],{"className":5753},[4900,5723],[1129,5755,1353],{"className":5756},[1427],[1129,5758,1577],{"className":5759},[1576],[1129,5761,5763],{"className":5762},[1311],[1129,5764,5767],{"className":5765,"style":5766},[1315],"height:1.4745em;",[1129,5768],{},[1129,5770],{"className":5771,"style":5263},[5262],[1129,5773,5775],{"className":5774},[5006],[1129,5776,5778,5987],{"className":5777},[1307,1523],[1129,5779,5781,5984],{"className":5780},[1311],[1129,5782,5784,5884],{"className":5783,"style":5667},[1315],[1129,5785,5786,5789],{"style":5670},[1129,5787],{"className":5788,"style":5674},[1323],[1129,5790,5792,5795,5798,5801,5804,5807,5810,5813,5816],{"className":5791},[1172],[1129,5793,1377],{"className":5794},[1172],[1129,5796],{"className":5797,"style":1278},[1277],[1129,5799,4803],{"className":5800},[1282],[1129,5802],{"className":5803,"style":1278},[1277],[1129,5805,1253],{"className":5806,"style":1348},[1172,1173],[1129,5808],{"className":5809,"style":1278},[1277],[1129,5811,4803],{"className":5812},[1282],[1129,5814],{"className":5815,"style":1278},[1277],[1129,5817,5819,5822,5881],{"className":5818},[1172],[1129,5820],{"className":5821},[1344,1516],[1129,5823,5825],{"className":5824},[1461],[1129,5826,5828,5873],{"className":5827},[1307,1523],[1129,5829,5831,5870],{"className":5830},[1311],[1129,5832,5834,5848,5856],{"className":5833,"style":1530},[1315],[1129,5835,5836,5839],{"style":1533},[1129,5837],{"className":5838,"style":1537},[1323],[1129,5840,5842],{"className":5841},[1328,1329,1330,1331],[1129,5843,5845],{"className":5844},[1172,1331],[1129,5846,1991],{"className":5847},[1172,1331],[1129,5849,5850,5853],{"style":1549},[1129,5851],{"className":5852,"style":1537},[1323],[1129,5854],{"className":5855,"style":1557},[1556],[1129,5857,5858,5861],{"style":1560},[1129,5859],{"className":5860,"style":1537},[1323],[1129,5862,5864],{"className":5863},[1328,1329,1330,1331],[1129,5865,5867],{"className":5866},[1172,1331],[1129,5868,1246],{"className":5869},[1172,1331],[1129,5871,1577],{"className":5872},[1576],[1129,5874,5876],{"className":5875},[1311],[1129,5877,5879],{"className":5878,"style":1584},[1315],[1129,5880],{},[1129,5882],{"className":5883},[1352,1516],[1129,5885,5886,5889],{"style":5698},[1129,5887],{"className":5888,"style":5674},[1323],[1129,5890,5892,5960,5963,5966,5969,5972,5975,5978,5981],{"className":5891},[1172],[1129,5893,5895,5898,5957],{"className":5894},[1172],[1129,5896],{"className":5897},[1344,1516],[1129,5899,5901],{"className":5900},[1461],[1129,5902,5904,5949],{"className":5903},[1307,1523],[1129,5905,5907,5946],{"className":5906},[1311],[1129,5908,5910,5924,5932],{"className":5909,"style":1530},[1315],[1129,5911,5912,5915],{"style":1533},[1129,5913],{"className":5914,"style":1537},[1323],[1129,5916,5918],{"className":5917},[1328,1329,1330,1331],[1129,5919,5921],{"className":5920},[1172,1331],[1129,5922,1991],{"className":5923},[1172,1331],[1129,5925,5926,5929],{"style":1549},[1129,5927],{"className":5928,"style":1537},[1323],[1129,5930],{"className":5931,"style":1557},[1556],[1129,5933,5934,5937],{"style":1560},[1129,5935],{"className":5936,"style":1537},[1323],[1129,5938,5940],{"className":5939},[1328,1329,1330,1331],[1129,5941,5943],{"className":5942},[1172,1331],[1129,5944,1246],{"className":5945},[1172,1331],[1129,5947,1577],{"className":5948},[1576],[1129,5950,5952],{"className":5951},[1311],[1129,5953,5955],{"className":5954,"style":1584},[1315],[1129,5956],{},[1129,5958],{"className":5959},[1352,1516],[1129,5961],{"className":5962,"style":1278},[1277],[1129,5964,1626],{"className":5965},[1282],[1129,5967],{"className":5968,"style":1278},[1277],[1129,5970,1253],{"className":5971,"style":1348},[1172,1173],[1129,5973],{"className":5974,"style":1278},[1277],[1129,5976,4803],{"className":5977},[1282],[1129,5979],{"className":5980,"style":1278},[1277],[1129,5982,1246],{"className":5983},[1172],[1129,5985,1577],{"className":5986},[1576],[1129,5988,5990],{"className":5989},[1311],[1129,5991,5993],{"className":5992,"style":5766},[1315],[1129,5994],{},[1129,5996],{"className":5997},[1352,1516],[1091,5999,6000],{},"按这个式子把均匀随机数代进去,就得到 Laplace 分布的随机数。",[2937,6002],{},[2940,6004,6006],{"id":6005},"二拒绝接受法舍选法ⅱ","二、拒绝接受法(舍选法Ⅱ)",[1091,6008,6009,6010,6013],{},"当要生成的随机数的分布",[1101,6011,6012],{},"没有分布函数,或者分布函数的逆没有显式解","时,逆分布法就失效了,这时候用拒绝接受法。",[1091,6015,6016,6019,6020,6064,6065,6109,6110,6138],{},[1101,6017,6018],{},"适用条件",":能够找到另一个概率密度函数 ",[1129,6021,6023,6043],{"className":6022},[1132],[1129,6024,6026],{"className":6025},[1136],[1138,6027,6028],{"xmlns":1140},[1142,6029,6030,6040],{},[1145,6031,6032,6034,6036,6038],{},[1148,6033,1150],{},[1229,6035,1250],{"stretchy":1249},[1148,6037,3006],{},[1229,6039,1256],{"stretchy":1249},[1152,6041,6042],{"encoding":1154},"g(x)",[1129,6044,6046],{"className":6045,"ariaHidden":1159},[1158],[1129,6047,6049,6052,6055,6058,6061],{"className":6048},[1163],[1129,6050],{"className":6051,"style":1414},[1167],[1129,6053,1150],{"className":6054,"style":1174},[1172,1173],[1129,6056,1250],{"className":6057},[1344],[1129,6059,3006],{"className":6060},[1172,1173],[1129,6062,1256],{"className":6063},[1352],",它与目标密度 ",[1129,6066,6068,6088],{"className":6067},[1132],[1129,6069,6071],{"className":6070},[1136],[1138,6072,6073],{"xmlns":1140},[1142,6074,6075,6085],{},[1145,6076,6077,6079,6081,6083],{},[1148,6078,1635],{},[1229,6080,1250],{"stretchy":1249},[1148,6082,3006],{},[1229,6084,1256],{"stretchy":1249},[1152,6086,6087],{"encoding":1154},"f(x)",[1129,6089,6091],{"className":6090,"ariaHidden":1159},[1158],[1129,6092,6094,6097,6100,6103,6106],{"className":6093},[1163],[1129,6095],{"className":6096,"style":1414},[1167],[1129,6098,1635],{"className":6099,"style":1758},[1172,1173],[1129,6101,1250],{"className":6102},[1344],[1129,6104,3006],{"className":6105},[1172,1173],[1129,6107,1256],{"className":6108},[1352]," 有相同的定义域;同时能找到一个常数 ",[1129,6111,6113,6126],{"className":6112},[1132],[1129,6114,6116],{"className":6115},[1136],[1138,6117,6118],{"xmlns":1140},[1142,6119,6120,6124],{},[1145,6121,6122],{},[1148,6123,1190],{},[1152,6125,1190],{"encoding":1154},[1129,6127,6129],{"className":6128,"ariaHidden":1159},[1158],[1129,6130,6132,6135],{"className":6131},[1163],[1129,6133],{"className":6134,"style":1202},[1167],[1129,6136,1190],{"className":6137},[1172,1173],",使得在整个定义域上都满足",[1091,6140,6141],{},[1129,6142,6144,6178],{"className":6143},[1132],[1129,6145,6147],{"className":6146},[1136],[1138,6148,6149],{"xmlns":1140},[1142,6150,6151,6175],{},[1145,6152,6153,6155,6157,6159,6161,6163,6165,6167,6169,6171,6173],{},[1148,6154,1635],{},[1229,6156,1250],{"stretchy":1249},[1148,6158,3006],{},[1229,6160,1256],{"stretchy":1249},[1229,6162,1626],{},[1148,6164,1190],{},[1648,6166,1650],{},[1148,6168,1150],{},[1229,6170,1250],{"stretchy":1249},[1148,6172,3006],{},[1229,6174,1256],{"stretchy":1249},[1152,6176,6177],{"encoding":1154},"f(x) \\le c\\,g(x)",[1129,6179,6181,6208],{"className":6180,"ariaHidden":1159},[1158],[1129,6182,6184,6187,6190,6193,6196,6199,6202,6205],{"className":6183},[1163],[1129,6185],{"className":6186,"style":1414},[1167],[1129,6188,1635],{"className":6189,"style":1758},[1172,1173],[1129,6191,1250],{"className":6192},[1344],[1129,6194,3006],{"className":6195},[1172,1173],[1129,6197,1256],{"className":6198},[1352],[1129,6200],{"className":6201,"style":1278},[1277],[1129,6203,1626],{"className":6204},[1282],[1129,6206],{"className":6207,"style":1278},[1277],[1129,6209,6211,6214,6217,6220,6223,6226,6229],{"className":6210},[1163],[1129,6212],{"className":6213,"style":1414},[1167],[1129,6215,1190],{"className":6216},[1172,1173],[1129,6218],{"className":6219,"style":1431},[1277],[1129,6221,1150],{"className":6222,"style":1174},[1172,1173],[1129,6224,1250],{"className":6225},[1344],[1129,6227,3006],{"className":6228},[1172,1173],[1129,6230,1256],{"className":6231},[1352],[1091,6233,6234,6235,6263,6264,6267],{},"这里 ",[1129,6236,6238,6251],{"className":6237},[1132],[1129,6239,6241],{"className":6240},[1136],[1138,6242,6243],{"xmlns":1140},[1142,6244,6245,6249],{},[1145,6246,6247],{},[1148,6248,1150],{},[1152,6250,1150],{"encoding":1154},[1129,6252,6254],{"className":6253,"ariaHidden":1159},[1158],[1129,6255,6257,6260],{"className":6256},[1163],[1129,6258],{"className":6259,"style":1168},[1167],[1129,6261,1150],{"className":6262,"style":1174},[1172,1173]," 是",[1101,6265,6266],{},"试投密度(建议分布)",",属于容易直接抽样的分布(比如均匀分布、正态分布)。",[1091,6269,6270,2955],{},[1101,6271,3257],{},[3259,6273,6274,6413],{},[1098,6275,6276,6277,6305,6306,6334,6335,3343],{},"产生一个密度函数为 ",[1129,6278,6280,6293],{"className":6279},[1132],[1129,6281,6283],{"className":6282},[1136],[1138,6284,6285],{"xmlns":1140},[1142,6286,6287,6291],{},[1145,6288,6289],{},[1148,6290,1150],{},[1152,6292,1150],{"encoding":1154},[1129,6294,6296],{"className":6295,"ariaHidden":1159},[1158],[1129,6297,6299,6302],{"className":6298},[1163],[1129,6300],{"className":6301,"style":1168},[1167],[1129,6303,1150],{"className":6304,"style":1174},[1172,1173]," 的随机数 ",[1129,6307,6309,6322],{"className":6308},[1132],[1129,6310,6312],{"className":6311},[1136],[1138,6313,6314],{"xmlns":1140},[1142,6315,6316,6320],{},[1145,6317,6318],{},[1148,6319,1640],{},[1152,6321,1640],{"encoding":1154},[1129,6323,6325],{"className":6324,"ariaHidden":1159},[1158],[1129,6326,6328,6331],{"className":6327},[1163],[1129,6329],{"className":6330,"style":1269},[1167],[1129,6332,1640],{"className":6333,"style":1734},[1172,1173],",再产生一个服从均匀分布 ",[1129,6336,6338,6365],{"className":6337},[1132],[1129,6339,6341],{"className":6340},[1136],[1138,6342,6343],{"xmlns":1140},[1142,6344,6345,6363],{},[1145,6346,6347,6349,6351,6353,6355,6357,6359,6361],{},[1148,6348,1253],{},[1229,6350,1370],{},[1148,6352,1253],{},[1229,6354,1250],{"stretchy":1249},[1244,6356,1377],{},[1229,6358,1353],{"separator":1159},[1244,6360,1246],{},[1229,6362,1256],{"stretchy":1249},[1152,6364,3294],{"encoding":1154},[1129,6366,6368,6386],{"className":6367,"ariaHidden":1159},[1158],[1129,6369,6371,6374,6377,6380,6383],{"className":6370},[1163],[1129,6372],{"className":6373,"style":1269},[1167],[1129,6375,1253],{"className":6376,"style":1348},[1172,1173],[1129,6378],{"className":6379,"style":1278},[1277],[1129,6381,1370],{"className":6382},[1282],[1129,6384],{"className":6385,"style":1278},[1277],[1129,6387,6389,6392,6395,6398,6401,6404,6407,6410],{"className":6388},[1163],[1129,6390],{"className":6391,"style":1414},[1167],[1129,6393,1253],{"className":6394,"style":1348},[1172,1173],[1129,6396,1250],{"className":6397},[1344],[1129,6399,1377],{"className":6400},[1172],[1129,6402,1353],{"className":6403},[1427],[1129,6405],{"className":6406,"style":1431},[1277],[1129,6408,1246],{"className":6409},[1172],[1129,6411,1256],{"className":6412},[1352],[1098,6414,6415,6416,6585,6586,6637],{},"如果满足 ",[1129,6417,6419,6461],{"className":6418},[1132],[1129,6420,6422],{"className":6421},[1136],[1138,6423,6424],{"xmlns":1140},[1142,6425,6426,6458],{},[1145,6427,6428,6430,6432],{},[1148,6429,1253],{},[1229,6431,1626],{},[1461,6433,6434,6444],{},[1145,6435,6436,6438,6440,6442],{},[1148,6437,1635],{},[1229,6439,1250],{"stretchy":1249},[1148,6441,1640],{},[1229,6443,1256],{"stretchy":1249},[1145,6445,6446,6448,6450,6452,6454,6456],{},[1148,6447,1190],{},[1648,6449,1650],{},[1148,6451,1150],{},[1229,6453,1250],{"stretchy":1249},[1148,6455,1640],{},[1229,6457,1256],{"stretchy":1249},[1152,6459,6460],{"encoding":1154},"U \\le \\frac{f(Y)}{c\\,g(Y)}",[1129,6462,6464,6482],{"className":6463,"ariaHidden":1159},[1158],[1129,6465,6467,6470,6473,6476,6479],{"className":6466},[1163],[1129,6468],{"className":6469,"style":1671},[1167],[1129,6471,1253],{"className":6472,"style":1348},[1172,1173],[1129,6474],{"className":6475,"style":1278},[1277],[1129,6477,1626],{"className":6478},[1282],[1129,6480],{"className":6481,"style":1278},[1277],[1129,6483,6485,6489],{"className":6484},[1163],[1129,6486],{"className":6487,"style":6488},[1167],"height:1.53em;vertical-align:-0.52em;",[1129,6490,6492,6495,6582],{"className":6491},[1172],[1129,6493],{"className":6494},[1344,1516],[1129,6496,6498],{"className":6497},[1461],[1129,6499,6501,6573],{"className":6500},[1307,1523],[1129,6502,6504,6570],{"className":6503},[1311],[1129,6505,6508,6538,6546],{"className":6506,"style":6507},[1315],"height:1.01em;",[1129,6509,6510,6513],{"style":1533},[1129,6511],{"className":6512,"style":1537},[1323],[1129,6514,6516],{"className":6515},[1328,1329,1330,1331],[1129,6517,6519,6522,6526,6529,6532,6535],{"className":6518},[1172,1331],[1129,6520,1190],{"className":6521},[1172,1173,1331],[1129,6523],{"className":6524,"style":6525},[1277,1331],"margin-right:0.1952em;",[1129,6527,1150],{"className":6528,"style":1174},[1172,1173,1331],[1129,6530,1250],{"className":6531},[1344,1331],[1129,6533,1640],{"className":6534,"style":1734},[1172,1173,1331],[1129,6536,1256],{"className":6537},[1352,1331],[1129,6539,6540,6543],{"style":1549},[1129,6541],{"className":6542,"style":1537},[1323],[1129,6544],{"className":6545,"style":1557},[1556],[1129,6547,6549,6552],{"style":6548},"top:-3.485em;",[1129,6550],{"className":6551,"style":1537},[1323],[1129,6553,6555],{"className":6554},[1328,1329,1330,1331],[1129,6556,6558,6561,6564,6567],{"className":6557},[1172,1331],[1129,6559,1635],{"className":6560,"style":1758},[1172,1173,1331],[1129,6562,1250],{"className":6563},[1344,1331],[1129,6565,1640],{"className":6566,"style":1734},[1172,1173,1331],[1129,6568,1256],{"className":6569},[1352,1331],[1129,6571,1577],{"className":6572},[1576],[1129,6574,6576],{"className":6575},[1311],[1129,6577,6580],{"className":6578,"style":6579},[1315],"height:0.52em;",[1129,6581],{},[1129,6583],{"className":6584},[1352,1516],"\n那么就令 ",[1129,6587,6589,6607],{"className":6588},[1132],[1129,6590,6592],{"className":6591},[1136],[1138,6593,6594],{"xmlns":1140},[1142,6595,6596,6604],{},[1145,6597,6598,6600,6602],{},[1148,6599,1227],{},[1229,6601,1231],{},[1148,6603,1640],{},[1152,6605,6606],{"encoding":1154},"X = Y",[1129,6608,6610,6628],{"className":6609,"ariaHidden":1159},[1158],[1129,6611,6613,6616,6619,6622,6625],{"className":6612},[1163],[1129,6614],{"className":6615,"style":1269},[1167],[1129,6617,1227],{"className":6618,"style":1273},[1172,1173],[1129,6620],{"className":6621,"style":1278},[1277],[1129,6623,1231],{"className":6624},[1282],[1129,6626],{"className":6627,"style":1278},[1277],[1129,6629,6631,6634],{"className":6630},[1163],[1129,6632],{"className":6633,"style":1269},[1167],[1129,6635,1640],{"className":6636,"style":1734},[1172,1173],"(接受);否则丢弃,返回上一步继续迭代。",[1091,6639,6640,6643,6644,6672,6673,6702,6703,6731,6732,6774,6775,1603],{},[1101,6641,6642],{},"推导思路",":令接受条件成立的那个事件,可以证明\"被接受的 ",[1129,6645,6647,6660],{"className":6646},[1132],[1129,6648,6650],{"className":6649},[1136],[1138,6651,6652],{"xmlns":1140},[1142,6653,6654,6658],{},[1145,6655,6656],{},[1148,6657,1640],{},[1152,6659,1640],{"encoding":1154},[1129,6661,6663],{"className":6662,"ariaHidden":1159},[1158],[1129,6664,6666,6669],{"className":6665},[1163],[1129,6667],{"className":6668,"style":1269},[1167],[1129,6670,1640],{"className":6671,"style":1734},[1172,1173],"\"的条件分布恰好就是目标分布 ",[1129,6674,6676,6689],{"className":6675},[1132],[1129,6677,6679],{"className":6678},[1136],[1138,6680,6681],{"xmlns":1140},[1142,6682,6683,6687],{},[1145,6684,6685],{},[1148,6686,1635],{},[1152,6688,1635],{"encoding":1154},[1129,6690,6692],{"className":6691,"ariaHidden":1159},[1158],[1129,6693,6695,6699],{"className":6694},[1163],[1129,6696],{"className":6697,"style":6698},[1167],"height:0.8889em;vertical-align:-0.1944em;",[1129,6700,1635],{"className":6701,"style":1758},[1172,1173],"。具体地,取任意区间,计算\"",[1129,6704,6706,6719],{"className":6705},[1132],[1129,6707,6709],{"className":6708},[1136],[1138,6710,6711],{"xmlns":1140},[1142,6712,6713,6717],{},[1145,6714,6715],{},[1148,6716,1640],{},[1152,6718,1640],{"encoding":1154},[1129,6720,6722],{"className":6721,"ariaHidden":1159},[1158],[1129,6723,6725,6728],{"className":6724},[1163],[1129,6726],{"className":6727,"style":1269},[1167],[1129,6729,1640],{"className":6730,"style":1734},[1172,1173]," 落在该区间且被接受\"的概率,会发现它正比于 ",[1129,6733,6735,6752],{"className":6734},[1132],[1129,6736,6738],{"className":6737},[1136],[1138,6739,6740],{"xmlns":1140},[1142,6741,6742,6749],{},[1145,6743,6744,6747],{},[1229,6745,6746],{},"∫",[1148,6748,1635],{},[1152,6750,6751],{"encoding":1154},"\\int f",[1129,6753,6755],{"className":6754,"ariaHidden":1159},[1158],[1129,6756,6758,6762,6768,6771],{"className":6757},[1163],[1129,6759],{"className":6760,"style":6761},[1167],"height:1.1111em;vertical-align:-0.3061em;",[1129,6763,6746],{"className":6764,"style":6767},[1596,6765,6766],"op-symbol","small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[1129,6769],{"className":6770,"style":1431},[1277],[1129,6772,1635],{"className":6773,"style":1758},[1172,1173],",归一化之后就是 ",[1129,6776,6778,6791],{"className":6777},[1132],[1129,6779,6781],{"className":6780},[1136],[1138,6782,6783],{"xmlns":1140},[1142,6784,6785,6789],{},[1145,6786,6787],{},[1148,6788,1635],{},[1152,6790,1635],{"encoding":1154},[1129,6792,6794],{"className":6793,"ariaHidden":1159},[1158],[1129,6795,6797,6800],{"className":6796},[1163],[1129,6798],{"className":6799,"style":6698},[1167],[1129,6801,1635],{"className":6802,"style":1758},[1172,1173],[1091,6804,6805],{},[1129,6806,6808,6888],{"className":6807},[1132],[1129,6809,6811],{"className":6810},[1136],[1138,6812,6813],{"xmlns":1140},[1142,6814,6815,6885],{},[1145,6816,6817,6820,6822,6825,6827,6829,6831,6834,6836,6838,6864,6866,6869,6871,6873,6875,6877,6879],{},[1148,6818,6819],{},"P",[1229,6821,1250],{"stretchy":1249},[1648,6823,6824],{},"接受",[1229,6826,4576],{},[1148,6828,1640],{},[1229,6830,1231],{},[1148,6832,6833],{},"y",[1229,6835,1256],{"stretchy":1249},[1229,6837,1231],{},[1461,6839,6840,6850],{},[1145,6841,6842,6844,6846,6848],{},[1148,6843,1635],{},[1229,6845,1250],{"stretchy":1249},[1148,6847,6833],{},[1229,6849,1256],{"stretchy":1249},[1145,6851,6852,6854,6856,6858,6860,6862],{},[1148,6853,1190],{},[1648,6855,1650],{},[1148,6857,1150],{},[1229,6859,1250],{"stretchy":1249},[1148,6861,6833],{},[1229,6863,1256],{"stretchy":1249},[1229,6865,1353],{"separator":1159},[1277,6867],{"width":6868},"2em",[1148,6870,6819],{},[1229,6872,1250],{"stretchy":1249},[1648,6874,6824],{},[1229,6876,1256],{"stretchy":1249},[1229,6878,1231],{},[1461,6880,6881,6883],{},[1244,6882,1246],{},[1148,6884,1190],{},[1152,6886,6887],{"encoding":1154},"P(\\text{接受} \\mid Y=y) = \\frac{f(y)}{c\\,g(y)}, \\qquad P(\\text{接受}) = \\frac{1}{c}",[1129,6889,6891,6919,6937,6958,7090],{"className":6890,"ariaHidden":1159},[1158],[1129,6892,6894,6897,6900,6903,6910,6913,6916],{"className":6893},[1163],[1129,6895],{"className":6896,"style":1414},[1167],[1129,6898,6819],{"className":6899,"style":1299},[1172,1173],[1129,6901,1250],{"className":6902},[1344],[1129,6904,6906],{"className":6905},[1172,3585],[1129,6907,6824],{"className":6908},[1172,6909],"cjk_fallback",[1129,6911],{"className":6912,"style":1278},[1277],[1129,6914,4576],{"className":6915},[1282],[1129,6917],{"className":6918,"style":1278},[1277],[1129,6920,6922,6925,6928,6931,6934],{"className":6921},[1163],[1129,6923],{"className":6924,"style":1269},[1167],[1129,6926,1640],{"className":6927,"style":1734},[1172,1173],[1129,6929],{"className":6930,"style":1278},[1277],[1129,6932,1231],{"className":6933},[1282],[1129,6935],{"className":6936,"style":1278},[1277],[1129,6938,6940,6943,6946,6949,6952,6955],{"className":6939},[1163],[1129,6941],{"className":6942,"style":1414},[1167],[1129,6944,6833],{"className":6945,"style":1174},[1172,1173],[1129,6947,1256],{"className":6948},[1352],[1129,6950],{"className":6951,"style":1278},[1277],[1129,6953,1231],{"className":6954},[1282],[1129,6956],{"className":6957,"style":1278},[1277],[1129,6959,6961,6964,7056,7059,7063,7066,7069,7072,7078,7081,7084,7087],{"className":6960},[1163],[1129,6962],{"className":6963,"style":6488},[1167],[1129,6965,6967,6970,7053],{"className":6966},[1172],[1129,6968],{"className":6969},[1344,1516],[1129,6971,6973],{"className":6972},[1461],[1129,6974,6976,7045],{"className":6975},[1307,1523],[1129,6977,6979,7042],{"className":6978},[1311],[1129,6980,6982,7011,7019],{"className":6981,"style":6507},[1315],[1129,6983,6984,6987],{"style":1533},[1129,6985],{"className":6986,"style":1537},[1323],[1129,6988,6990],{"className":6989},[1328,1329,1330,1331],[1129,6991,6993,6996,6999,7002,7005,7008],{"className":6992},[1172,1331],[1129,6994,1190],{"className":6995},[1172,1173,1331],[1129,6997],{"className":6998,"style":6525},[1277,1331],[1129,7000,1150],{"className":7001,"style":1174},[1172,1173,1331],[1129,7003,1250],{"className":7004},[1344,1331],[1129,7006,6833],{"className":7007,"style":1174},[1172,1173,1331],[1129,7009,1256],{"className":7010},[1352,1331],[1129,7012,7013,7016],{"style":1549},[1129,7014],{"className":7015,"style":1537},[1323],[1129,7017],{"className":7018,"style":1557},[1556],[1129,7020,7021,7024],{"style":6548},[1129,7022],{"className":7023,"style":1537},[1323],[1129,7025,7027],{"className":7026},[1328,1329,1330,1331],[1129,7028,7030,7033,7036,7039],{"className":7029},[1172,1331],[1129,7031,1635],{"className":7032,"style":1758},[1172,1173,1331],[1129,7034,1250],{"className":7035},[1344,1331],[1129,7037,6833],{"className":7038,"style":1174},[1172,1173,1331],[1129,7040,1256],{"className":7041},[1352,1331],[1129,7043,1577],{"className":7044},[1576],[1129,7046,7048],{"className":7047},[1311],[1129,7049,7051],{"className":7050,"style":6579},[1315],[1129,7052],{},[1129,7054],{"className":7055},[1352,1516],[1129,7057,1353],{"className":7058},[1427],[1129,7060],{"className":7061,"style":7062},[1277],"margin-right:2em;",[1129,7064],{"className":7065,"style":1431},[1277],[1129,7067,6819],{"className":7068,"style":1299},[1172,1173],[1129,7070,1250],{"className":7071},[1344],[1129,7073,7075],{"className":7074},[1172,3585],[1129,7076,6824],{"className":7077},[1172,6909],[1129,7079,1256],{"className":7080},[1352],[1129,7082],{"className":7083,"style":1278},[1277],[1129,7085,1231],{"className":7086},[1282],[1129,7088],{"className":7089,"style":1278},[1277],[1129,7091,7093,7096],{"className":7092},[1163],[1129,7094],{"className":7095,"style":1506},[1167],[1129,7097,7099,7102,7161],{"className":7098},[1172],[1129,7100],{"className":7101},[1344,1516],[1129,7103,7105],{"className":7104},[1461],[1129,7106,7108,7153],{"className":7107},[1307,1523],[1129,7109,7111,7150],{"className":7110},[1311],[1129,7112,7114,7128,7136],{"className":7113,"style":1530},[1315],[1129,7115,7116,7119],{"style":1533},[1129,7117],{"className":7118,"style":1537},[1323],[1129,7120,7122],{"className":7121},[1328,1329,1330,1331],[1129,7123,7125],{"className":7124},[1172,1331],[1129,7126,1190],{"className":7127},[1172,1173,1331],[1129,7129,7130,7133],{"style":1549},[1129,7131],{"className":7132,"style":1537},[1323],[1129,7134],{"className":7135,"style":1557},[1556],[1129,7137,7138,7141],{"style":1560},[1129,7139],{"className":7140,"style":1537},[1323],[1129,7142,7144],{"className":7143},[1328,1329,1330,1331],[1129,7145,7147],{"className":7146},[1172,1331],[1129,7148,1246],{"className":7149},[1172,1331],[1129,7151,1577],{"className":7152},[1576],[1129,7154,7156],{"className":7155},[1311],[1129,7157,7159],{"className":7158,"style":1584},[1315],[1129,7160],{},[1129,7162],{"className":7163},[1352,1516],[1091,7165,7166,7167,7170,7171,7265,7266,7294,7295,7323],{},"拒绝接受算法的效率由",[1101,7168,7169],{},"接受率","决定,而接受率正好是 ",[1129,7172,7174,7194],{"className":7173},[1132],[1129,7175,7177],{"className":7176},[1136],[1138,7178,7179],{"xmlns":1140},[1142,7180,7181,7191],{},[1145,7182,7183],{},[1458,7184,7185],{"scriptlevel":1377,"displaystyle":1159},[1461,7186,7187,7189],{},[1244,7188,1246],{},[1148,7190,1190],{},[1152,7192,7193],{"encoding":1154},"\\dfrac{1}{c}",[1129,7195,7197],{"className":7196,"ariaHidden":1159},[1158],[1129,7198,7200,7203],{"className":7199},[1163],[1129,7201],{"className":7202,"style":1831},[1167],[1129,7204,7206,7209,7262],{"className":7205},[1172],[1129,7207],{"className":7208},[1344,1516],[1129,7210,7212],{"className":7211},[1461],[1129,7213,7215,7254],{"className":7214},[1307,1523],[1129,7216,7218,7251],{"className":7217},[1311],[1129,7219,7221,7232,7240],{"className":7220,"style":1850},[1315],[1129,7222,7223,7226],{"style":1712},[1129,7224],{"className":7225,"style":1537},[1323],[1129,7227,7229],{"className":7228},[1172],[1129,7230,1190],{"className":7231},[1172,1173],[1129,7233,7234,7237],{"style":1549},[1129,7235],{"className":7236,"style":1537},[1323],[1129,7238],{"className":7239,"style":1557},[1556],[1129,7241,7242,7245],{"style":1748},[1129,7243],{"className":7244,"style":1537},[1323],[1129,7246,7248],{"className":7247},[1172],[1129,7249,1246],{"className":7250},[1172],[1129,7252,1577],{"className":7253},[1576],[1129,7255,7257],{"className":7256},[1311],[1129,7258,7260],{"className":7259,"style":1890},[1315],[1129,7261],{},[1129,7263],{"className":7264},[1352,1516],"。也就是说,常数 ",[1129,7267,7269,7282],{"className":7268},[1132],[1129,7270,7272],{"className":7271},[1136],[1138,7273,7274],{"xmlns":1140},[1142,7275,7276,7280],{},[1145,7277,7278],{},[1148,7279,1190],{},[1152,7281,1190],{"encoding":1154},[1129,7283,7285],{"className":7284,"ariaHidden":1159},[1158],[1129,7286,7288,7291],{"className":7287},[1163],[1129,7289],{"className":7290,"style":1202},[1167],[1129,7292,1190],{"className":7293},[1172,1173]," 越小(越接近 1),接受率越高,算法效率越高;",[1129,7296,7298,7311],{"className":7297},[1132],[1129,7299,7301],{"className":7300},[1136],[1138,7302,7303],{"xmlns":1140},[1142,7304,7305,7309],{},[1145,7306,7307],{},[1148,7308,1190],{},[1152,7310,1190],{"encoding":1154},[1129,7312,7314],{"className":7313,"ariaHidden":1159},[1158],[1129,7315,7317,7320],{"className":7316},[1163],[1129,7318],{"className":7319,"style":1202},[1167],[1129,7321,1190],{"className":7322},[1172,1173]," 越大,被丢弃的样本越多。",[2937,7325],{},[2940,7327,7329],{"id":7328},"三舍选法ⅰ","三、舍选法Ⅰ",[1091,7331,7332],{},"舍选法Ⅰ是拒绝接受法在一种简单情形下的特例",[1091,7334,7335,7337,7338,7341,7342,7396,7397,7440,7441,7470,7471,7499,7500,1603],{},[1101,7336,6018],{},":要生成的随机数的分布取值于一个",[1101,7339,7340],{},"有限区间"," ",[1129,7343,7345,7369],{"className":7344},[1132],[1129,7346,7348],{"className":7347},[1136],[1138,7349,7350],{"xmlns":1140},[1142,7351,7352,7366],{},[1145,7353,7354,7356,7359,7361,7364],{},[1229,7355,3077],{"stretchy":1249},[1148,7357,7358],{},"a",[1229,7360,1353],{"separator":1159},[1148,7362,7363],{},"b",[1229,7365,3086],{"stretchy":1249},[1152,7367,7368],{"encoding":1154},"[a,b]",[1129,7370,7372],{"className":7371,"ariaHidden":1159},[1158],[1129,7373,7375,7378,7381,7384,7387,7390,7393],{"className":7374},[1163],[1129,7376],{"className":7377,"style":1414},[1167],[1129,7379,3077],{"className":7380},[1344],[1129,7382,7358],{"className":7383},[1172,1173],[1129,7385,1353],{"className":7386},[1427],[1129,7388],{"className":7389,"style":1431},[1277],[1129,7391,7363],{"className":7392},[1172,1173],[1129,7394,3086],{"className":7395},[1352],",并且它的密度函数 ",[1129,7398,7400,7419],{"className":7399},[1132],[1129,7401,7403],{"className":7402},[1136],[1138,7404,7405],{"xmlns":1140},[1142,7406,7407,7417],{},[1145,7408,7409,7411,7413,7415],{},[1148,7410,1635],{},[1229,7412,1250],{"stretchy":1249},[1148,7414,3006],{},[1229,7416,1256],{"stretchy":1249},[1152,7418,6087],{"encoding":1154},[1129,7420,7422],{"className":7421,"ariaHidden":1159},[1158],[1129,7423,7425,7428,7431,7434,7437],{"className":7424},[1163],[1129,7426],{"className":7427,"style":1414},[1167],[1129,7429,1635],{"className":7430,"style":1758},[1172,1173],[1129,7432,1250],{"className":7433},[1344],[1129,7435,3006],{"className":7436},[1172,1173],[1129,7438,1256],{"className":7439},[1352]," 有上界 ",[1129,7442,7444,7458],{"className":7443},[1132],[1129,7445,7447],{"className":7446},[1136],[1138,7448,7449],{"xmlns":1140},[1142,7450,7451,7456],{},[1145,7452,7453],{},[1148,7454,7455],{},"M",[1152,7457,7455],{"encoding":1154},[1129,7459,7461],{"className":7460,"ariaHidden":1159},[1158],[1129,7462,7464,7467],{"className":7463},[1163],[1129,7465],{"className":7466,"style":1269},[1167],[1129,7468,7455],{"className":7469,"style":1348},[1172,1173],",即对所有 ",[1129,7472,7474,7487],{"className":7473},[1132],[1129,7475,7477],{"className":7476},[1136],[1138,7478,7479],{"xmlns":1140},[1142,7480,7481,7485],{},[1145,7482,7483],{},[1148,7484,3006],{},[1152,7486,3006],{"encoding":1154},[1129,7488,7490],{"className":7489,"ariaHidden":1159},[1158],[1129,7491,7493,7496],{"className":7492},[1163],[1129,7494],{"className":7495,"style":1202},[1167],[1129,7497,3006],{"className":7498},[1172,1173]," 都有 ",[1129,7501,7503,7527],{"className":7502},[1132],[1129,7504,7506],{"className":7505},[1136],[1138,7507,7508],{"xmlns":1140},[1142,7509,7510,7524],{},[1145,7511,7512,7514,7516,7518,7520,7522],{},[1148,7513,1635],{},[1229,7515,1250],{"stretchy":1249},[1148,7517,3006],{},[1229,7519,1256],{"stretchy":1249},[1229,7521,1626],{},[1148,7523,7455],{},[1152,7525,7526],{"encoding":1154},"f(x) \\le M",[1129,7528,7530,7557],{"className":7529,"ariaHidden":1159},[1158],[1129,7531,7533,7536,7539,7542,7545,7548,7551,7554],{"className":7532},[1163],[1129,7534],{"className":7535,"style":1414},[1167],[1129,7537,1635],{"className":7538,"style":1758},[1172,1173],[1129,7540,1250],{"className":7541},[1344],[1129,7543,3006],{"className":7544},[1172,1173],[1129,7546,1256],{"className":7547},[1352],[1129,7549],{"className":7550,"style":1278},[1277],[1129,7552,1626],{"className":7553},[1282],[1129,7555],{"className":7556,"style":1278},[1277],[1129,7558,7560,7563],{"className":7559},[1163],[1129,7561],{"className":7562,"style":1269},[1167],[1129,7564,7455],{"className":7565,"style":1348},[1172,1173],[1091,7567,7568,2955],{},[1101,7569,3257],{},[3259,7571,7572,7820],{},[1098,7573,7574,7575,7698,7699,7819],{},"在区间上生成 ",[1129,7576,7578,7610],{"className":7577},[1132],[1129,7579,7581],{"className":7580},[1136],[1138,7582,7583],{"xmlns":1140},[1142,7584,7585,7607],{},[1145,7586,7587,7593,7595,7597,7599,7601,7603,7605],{},[2563,7588,7589,7591],{},[1148,7590,1227],{},[1244,7592,1246],{},[1229,7594,1370],{},[1148,7596,1253],{},[1229,7598,1250],{"stretchy":1249},[1148,7600,7358],{},[1229,7602,1353],{"separator":1159},[1148,7604,7363],{},[1229,7606,1256],{"stretchy":1249},[1152,7608,7609],{"encoding":1154},"X_1 \\sim U(a,b)",[1129,7611,7613,7671],{"className":7612,"ariaHidden":1159},[1158],[1129,7614,7616,7620,7662,7665,7668],{"className":7615},[1163],[1129,7617],{"className":7618,"style":7619},[1167],"height:0.8333em;vertical-align:-0.15em;",[1129,7621,7623,7626],{"className":7622},[1172],[1129,7624,1227],{"className":7625,"style":1273},[1172,1173],[1129,7627,7629],{"className":7628},[1303],[1129,7630,7632,7654],{"className":7631},[1307,1523],[1129,7633,7635,7651],{"className":7634},[1311],[1129,7636,7639],{"className":7637,"style":7638},[1315],"height:0.3011em;",[1129,7640,7642,7645],{"style":7641},"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;",[1129,7643],{"className":7644,"style":1324},[1323],[1129,7646,7648],{"className":7647},[1328,1329,1330,1331],[1129,7649,1246],{"className":7650},[1172,1331],[1129,7652,1577],{"className":7653},[1576],[1129,7655,7657],{"className":7656},[1311],[1129,7658,7660],{"className":7659,"style":2624},[1315],[1129,7661],{},[1129,7663],{"className":7664,"style":1278},[1277],[1129,7666,1370],{"className":7667},[1282],[1129,7669],{"className":7670,"style":1278},[1277],[1129,7672,7674,7677,7680,7683,7686,7689,7692,7695],{"className":7673},[1163],[1129,7675],{"className":7676,"style":1414},[1167],[1129,7678,1253],{"className":7679,"style":1348},[1172,1173],[1129,7681,1250],{"className":7682},[1344],[1129,7684,7358],{"className":7685},[1172,1173],[1129,7687,1353],{"className":7688},[1427],[1129,7690],{"className":7691,"style":1431},[1277],[1129,7693,7363],{"className":7694},[1172,1173],[1129,7696,1256],{"className":7697},[1352],",再生成 ",[1129,7700,7702,7734],{"className":7701},[1132],[1129,7703,7705],{"className":7704},[1136],[1138,7706,7707],{"xmlns":1140},[1142,7708,7709,7731],{},[1145,7710,7711,7717,7719,7721,7723,7725,7727,7729],{},[2563,7712,7713,7715],{},[1148,7714,1227],{},[1244,7716,1991],{},[1229,7718,1370],{},[1148,7720,1253],{},[1229,7722,1250],{"stretchy":1249},[1244,7724,1377],{},[1229,7726,1353],{"separator":1159},[1148,7728,7455],{},[1229,7730,1256],{"stretchy":1249},[1152,7732,7733],{"encoding":1154},"X_2 \\sim U(0, M)",[1129,7735,7737,7792],{"className":7736,"ariaHidden":1159},[1158],[1129,7738,7740,7743,7783,7786,7789],{"className":7739},[1163],[1129,7741],{"className":7742,"style":7619},[1167],[1129,7744,7746,7749],{"className":7745},[1172],[1129,7747,1227],{"className":7748,"style":1273},[1172,1173],[1129,7750,7752],{"className":7751},[1303],[1129,7753,7755,7775],{"className":7754},[1307,1523],[1129,7756,7758,7772],{"className":7757},[1311],[1129,7759,7761],{"className":7760,"style":7638},[1315],[1129,7762,7763,7766],{"style":7641},[1129,7764],{"className":7765,"style":1324},[1323],[1129,7767,7769],{"className":7768},[1328,1329,1330,1331],[1129,7770,1991],{"className":7771},[1172,1331],[1129,7773,1577],{"className":7774},[1576],[1129,7776,7778],{"className":7777},[1311],[1129,7779,7781],{"className":7780,"style":2624},[1315],[1129,7782],{},[1129,7784],{"className":7785,"style":1278},[1277],[1129,7787,1370],{"className":7788},[1282],[1129,7790],{"className":7791,"style":1278},[1277],[1129,7793,7795,7798,7801,7804,7807,7810,7813,7816],{"className":7794},[1163],[1129,7796],{"className":7797,"style":1414},[1167],[1129,7799,1253],{"className":7800,"style":1348},[1172,1173],[1129,7802,1250],{"className":7803},[1344],[1129,7805,1377],{"className":7806},[1172],[1129,7808,1353],{"className":7809},[1427],[1129,7811],{"className":7812,"style":1431},[1277],[1129,7814,7455],{"className":7815,"style":1348},[1172,1173],[1129,7817,1256],{"className":7818},[1352],";",[1098,7821,7822,7823,7971,7972,8064],{},"如果 ",[1129,7824,7826,7858],{"className":7825},[1132],[1129,7827,7829],{"className":7828},[1136],[1138,7830,7831],{"xmlns":1140},[1142,7832,7833,7855],{},[1145,7834,7835,7841,7843,7845,7847,7853],{},[2563,7836,7837,7839],{},[1148,7838,1227],{},[1244,7840,1991],{},[1229,7842,1626],{},[1148,7844,1635],{},[1229,7846,1250],{"stretchy":1249},[2563,7848,7849,7851],{},[1148,7850,1227],{},[1244,7852,1246],{},[1229,7854,1256],{"stretchy":1249},[1152,7856,7857],{"encoding":1154},"X_2 \\le f(X_1)",[1129,7859,7861,7916],{"className":7860,"ariaHidden":1159},[1158],[1129,7862,7864,7867,7907,7910,7913],{"className":7863},[1163],[1129,7865],{"className":7866,"style":7619},[1167],[1129,7868,7870,7873],{"className":7869},[1172],[1129,7871,1227],{"className":7872,"style":1273},[1172,1173],[1129,7874,7876],{"className":7875},[1303],[1129,7877,7879,7899],{"className":7878},[1307,1523],[1129,7880,7882,7896],{"className":7881},[1311],[1129,7883,7885],{"className":7884,"style":7638},[1315],[1129,7886,7887,7890],{"style":7641},[1129,7888],{"className":7889,"style":1324},[1323],[1129,7891,7893],{"className":7892},[1328,1329,1330,1331],[1129,7894,1991],{"className":7895},[1172,1331],[1129,7897,1577],{"className":7898},[1576],[1129,7900,7902],{"className":7901},[1311],[1129,7903,7905],{"className":7904,"style":2624},[1315],[1129,7906],{},[1129,7908],{"className":7909,"style":1278},[1277],[1129,7911,1626],{"className":7912},[1282],[1129,7914],{"className":7915,"style":1278},[1277],[1129,7917,7919,7922,7925,7928,7968],{"className":7918},[1163],[1129,7920],{"className":7921,"style":1414},[1167],[1129,7923,1635],{"className":7924,"style":1758},[1172,1173],[1129,7926,1250],{"className":7927},[1344],[1129,7929,7931,7934],{"className":7930},[1172],[1129,7932,1227],{"className":7933,"style":1273},[1172,1173],[1129,7935,7937],{"className":7936},[1303],[1129,7938,7940,7960],{"className":7939},[1307,1523],[1129,7941,7943,7957],{"className":7942},[1311],[1129,7944,7946],{"className":7945,"style":7638},[1315],[1129,7947,7948,7951],{"style":7641},[1129,7949],{"className":7950,"style":1324},[1323],[1129,7952,7954],{"className":7953},[1328,1329,1330,1331],[1129,7955,1246],{"className":7956},[1172,1331],[1129,7958,1577],{"className":7959},[1576],[1129,7961,7963],{"className":7962},[1311],[1129,7964,7966],{"className":7965,"style":2624},[1315],[1129,7967],{},[1129,7969,1256],{"className":7970},[1352],",就接受,令 ",[1129,7973,7975,7997],{"className":7974},[1132],[1129,7976,7978],{"className":7977},[1136],[1138,7979,7980],{"xmlns":1140},[1142,7981,7982,7994],{},[1145,7983,7984,7986,7988],{},[1148,7985,1227],{},[1229,7987,1231],{},[2563,7989,7990,7992],{},[1148,7991,1227],{},[1244,7993,1246],{},[1152,7995,7996],{"encoding":1154},"X = X_1",[1129,7998,8000,8018],{"className":7999,"ariaHidden":1159},[1158],[1129,8001,8003,8006,8009,8012,8015],{"className":8002},[1163],[1129,8004],{"className":8005,"style":1269},[1167],[1129,8007,1227],{"className":8008,"style":1273},[1172,1173],[1129,8010],{"className":8011,"style":1278},[1277],[1129,8013,1231],{"className":8014},[1282],[1129,8016],{"className":8017,"style":1278},[1277],[1129,8019,8021,8024],{"className":8020},[1163],[1129,8022],{"className":8023,"style":7619},[1167],[1129,8025,8027,8030],{"className":8026},[1172],[1129,8028,1227],{"className":8029,"style":1273},[1172,1173],[1129,8031,8033],{"className":8032},[1303],[1129,8034,8036,8056],{"className":8035},[1307,1523],[1129,8037,8039,8053],{"className":8038},[1311],[1129,8040,8042],{"className":8041,"style":7638},[1315],[1129,8043,8044,8047],{"style":7641},[1129,8045],{"className":8046,"style":1324},[1323],[1129,8048,8050],{"className":8049},[1328,1329,1330,1331],[1129,8051,1246],{"className":8052},[1172,1331],[1129,8054,1577],{"className":8055},[1576],[1129,8057,8059],{"className":8058},[1311],[1129,8060,8062],{"className":8061,"style":2624},[1315],[1129,8063],{},";否则返回步骤 1 重来。",[1091,8066,8067,8068,8166,8167,8195],{},"这实际上就是在矩形框 ",[1129,8069,8071,8106],{"className":8070},[1132],[1129,8072,8074],{"className":8073},[1136],[1138,8075,8076],{"xmlns":1140},[1142,8077,8078,8103],{},[1145,8079,8080,8082,8084,8086,8088,8090,8093,8095,8097,8099,8101],{},[1229,8081,3077],{"stretchy":1249},[1148,8083,7358],{},[1229,8085,1353],{"separator":1159},[1148,8087,7363],{},[1229,8089,3086],{"stretchy":1249},[1229,8091,8092],{},"×",[1229,8094,3077],{"stretchy":1249},[1244,8096,1377],{},[1229,8098,1353],{"separator":1159},[1148,8100,7455],{},[1229,8102,3086],{"stretchy":1249},[1152,8104,8105],{"encoding":1154},"[a,b] \\times [0,M]",[1129,8107,8109,8142],{"className":8108,"ariaHidden":1159},[1158],[1129,8110,8112,8115,8118,8121,8124,8127,8130,8133,8136,8139],{"className":8111},[1163],[1129,8113],{"className":8114,"style":1414},[1167],[1129,8116,3077],{"className":8117},[1344],[1129,8119,7358],{"className":8120},[1172,1173],[1129,8122,1353],{"className":8123},[1427],[1129,8125],{"className":8126,"style":1431},[1277],[1129,8128,7363],{"className":8129},[1172,1173],[1129,8131,3086],{"className":8132},[1352],[1129,8134],{"className":8135,"style":1734},[1277],[1129,8137,8092],{"className":8138},[2084],[1129,8140],{"className":8141,"style":1734},[1277],[1129,8143,8145,8148,8151,8154,8157,8160,8163],{"className":8144},[1163],[1129,8146],{"className":8147,"style":1414},[1167],[1129,8149,3077],{"className":8150},[1344],[1129,8152,1377],{"className":8153},[1172],[1129,8155,1353],{"className":8156},[1427],[1129,8158],{"className":8159,"style":1431},[1277],[1129,8161,7455],{"className":8162,"style":1348},[1172,1173],[1129,8164,3086],{"className":8165},[1352]," 里\"打点\",落在密度曲线 ",[1129,8168,8170,8183],{"className":8169},[1132],[1129,8171,8173],{"className":8172},[1136],[1138,8174,8175],{"xmlns":1140},[1142,8176,8177,8181],{},[1145,8178,8179],{},[1148,8180,1635],{},[1152,8182,1635],{"encoding":1154},[1129,8184,8186],{"className":8185,"ariaHidden":1159},[1158],[1129,8187,8189,8192],{"className":8188},[1163],[1129,8190],{"className":8191,"style":6698},[1167],[1129,8193,1635],{"className":8194,"style":1758},[1172,1173]," 下方的点就保留、其横坐标即为所求随机数。它也可以套进拒绝接受法的框架来看:",[3259,8197,8198,8350],{},[1098,8199,8200,8201,8271,8272,7819],{},"产生随机数 ",[1129,8202,8204,8222],{"className":8203},[1132],[1129,8205,8207],{"className":8206},[1136],[1138,8208,8209],{"xmlns":1140},[1142,8210,8211,8219],{},[1145,8212,8213],{},[2563,8214,8215,8217],{},[1148,8216,1227],{},[1244,8218,1246],{},[1152,8220,8221],{"encoding":1154},"X_1",[1129,8223,8225],{"className":8224,"ariaHidden":1159},[1158],[1129,8226,8228,8231],{"className":8227},[1163],[1129,8229],{"className":8230,"style":7619},[1167],[1129,8232,8234,8237],{"className":8233},[1172],[1129,8235,1227],{"className":8236,"style":1273},[1172,1173],[1129,8238,8240],{"className":8239},[1303],[1129,8241,8243,8263],{"className":8242},[1307,1523],[1129,8244,8246,8260],{"className":8245},[1311],[1129,8247,8249],{"className":8248,"style":7638},[1315],[1129,8250,8251,8254],{"style":7641},[1129,8252],{"className":8253,"style":1324},[1323],[1129,8255,8257],{"className":8256},[1328,1329,1330,1331],[1129,8258,1246],{"className":8259},[1172,1331],[1129,8261,1577],{"className":8262},[1576],[1129,8264,8266],{"className":8265},[1311],[1129,8267,8269],{"className":8268,"style":2624},[1315],[1129,8270],{},"(取自均匀分布)以及 ",[1129,8273,8275,8302],{"className":8274},[1132],[1129,8276,8278],{"className":8277},[1136],[1138,8279,8280],{"xmlns":1140},[1142,8281,8282,8300],{},[1145,8283,8284,8286,8288,8290,8292,8294,8296,8298],{},[1148,8285,1253],{},[1229,8287,1370],{},[1148,8289,1253],{},[1229,8291,1250],{"stretchy":1249},[1244,8293,1377],{},[1229,8295,1353],{"separator":1159},[1244,8297,1246],{},[1229,8299,1256],{"stretchy":1249},[1152,8301,3294],{"encoding":1154},[1129,8303,8305,8323],{"className":8304,"ariaHidden":1159},[1158],[1129,8306,8308,8311,8314,8317,8320],{"className":8307},[1163],[1129,8309],{"className":8310,"style":1269},[1167],[1129,8312,1253],{"className":8313,"style":1348},[1172,1173],[1129,8315],{"className":8316,"style":1278},[1277],[1129,8318,1370],{"className":8319},[1282],[1129,8321],{"className":8322,"style":1278},[1277],[1129,8324,8326,8329,8332,8335,8338,8341,8344,8347],{"className":8325},[1163],[1129,8327],{"className":8328,"style":1414},[1167],[1129,8330,1253],{"className":8331,"style":1348},[1172,1173],[1129,8333,1250],{"className":8334},[1344],[1129,8336,1377],{"className":8337},[1172],[1129,8339,1353],{"className":8340},[1427],[1129,8342],{"className":8343,"style":1431},[1277],[1129,8345,1246],{"className":8346},[1172],[1129,8348,1256],{"className":8349},[1352],[1098,8351,7822,8352,8527,8528,8619],{},[1129,8353,8355,8391],{"className":8354},[1132],[1129,8356,8358],{"className":8357},[1136],[1138,8359,8360],{"xmlns":1140},[1142,8361,8362,8388],{},[1145,8363,8364,8366,8368],{},[1148,8365,1253],{},[1229,8367,1626],{},[1458,8369,8370],{"scriptlevel":1377,"displaystyle":1159},[1461,8371,8372,8386],{},[1145,8373,8374,8376,8378,8384],{},[1148,8375,1635],{},[1229,8377,1250],{"stretchy":1249},[2563,8379,8380,8382],{},[1148,8381,1227],{},[1244,8383,1246],{},[1229,8385,1256],{"stretchy":1249},[1148,8387,7455],{},[1152,8389,8390],{"encoding":1154},"U \\le \\dfrac{f(X_1)}{M}",[1129,8392,8394,8412],{"className":8393,"ariaHidden":1159},[1158],[1129,8395,8397,8400,8403,8406,8409],{"className":8396},[1163],[1129,8398],{"className":8399,"style":1671},[1167],[1129,8401,1253],{"className":8402,"style":1348},[1172,1173],[1129,8404],{"className":8405,"style":1278},[1277],[1129,8407,1626],{"className":8408},[1282],[1129,8410],{"className":8411,"style":1278},[1277],[1129,8413,8415,8419],{"className":8414},[1163],[1129,8416],{"className":8417,"style":8418},[1167],"height:2.113em;vertical-align:-0.686em;",[1129,8420,8422,8425,8524],{"className":8421},[1172],[1129,8423],{"className":8424},[1344,1516],[1129,8426,8428],{"className":8427},[1461],[1129,8429,8431,8516],{"className":8430},[1307,1523],[1129,8432,8434,8513],{"className":8433},[1311],[1129,8435,8437,8448,8456],{"className":8436,"style":1709},[1315],[1129,8438,8439,8442],{"style":1712},[1129,8440],{"className":8441,"style":1537},[1323],[1129,8443,8445],{"className":8444},[1172],[1129,8446,7455],{"className":8447,"style":1348},[1172,1173],[1129,8449,8450,8453],{"style":1549},[1129,8451],{"className":8452,"style":1537},[1323],[1129,8454],{"className":8455,"style":1557},[1556],[1129,8457,8458,8461],{"style":1748},[1129,8459],{"className":8460,"style":1537},[1323],[1129,8462,8464,8467,8470,8510],{"className":8463},[1172],[1129,8465,1635],{"className":8466,"style":1758},[1172,1173],[1129,8468,1250],{"className":8469},[1344],[1129,8471,8473,8476],{"className":8472},[1172],[1129,8474,1227],{"className":8475,"style":1273},[1172,1173],[1129,8477,8479],{"className":8478},[1303],[1129,8480,8482,8502],{"className":8481},[1307,1523],[1129,8483,8485,8499],{"className":8484},[1311],[1129,8486,8488],{"className":8487,"style":7638},[1315],[1129,8489,8490,8493],{"style":7641},[1129,8491],{"className":8492,"style":1324},[1323],[1129,8494,8496],{"className":8495},[1328,1329,1330,1331],[1129,8497,1246],{"className":8498},[1172,1331],[1129,8500,1577],{"className":8501},[1576],[1129,8503,8505],{"className":8504},[1311],[1129,8506,8508],{"className":8507,"style":2624},[1315],[1129,8509],{},[1129,8511,1256],{"className":8512},[1352],[1129,8514,1577],{"className":8515},[1576],[1129,8517,8519],{"className":8518},[1311],[1129,8520,8522],{"className":8521,"style":1890},[1315],[1129,8523],{},[1129,8525],{"className":8526},[1352,1516],",则令 ",[1129,8529,8531,8552],{"className":8530},[1132],[1129,8532,8534],{"className":8533},[1136],[1138,8535,8536],{"xmlns":1140},[1142,8537,8538,8550],{},[1145,8539,8540,8542,8544],{},[1148,8541,1227],{},[1229,8543,1231],{},[2563,8545,8546,8548],{},[1148,8547,1227],{},[1244,8549,1246],{},[1152,8551,7996],{"encoding":1154},[1129,8553,8555,8573],{"className":8554,"ariaHidden":1159},[1158],[1129,8556,8558,8561,8564,8567,8570],{"className":8557},[1163],[1129,8559],{"className":8560,"style":1269},[1167],[1129,8562,1227],{"className":8563,"style":1273},[1172,1173],[1129,8565],{"className":8566,"style":1278},[1277],[1129,8568,1231],{"className":8569},[1282],[1129,8571],{"className":8572,"style":1278},[1277],[1129,8574,8576,8579],{"className":8575},[1163],[1129,8577],{"className":8578,"style":7619},[1167],[1129,8580,8582,8585],{"className":8581},[1172],[1129,8583,1227],{"className":8584,"style":1273},[1172,1173],[1129,8586,8588],{"className":8587},[1303],[1129,8589,8591,8611],{"className":8590},[1307,1523],[1129,8592,8594,8608],{"className":8593},[1311],[1129,8595,8597],{"className":8596,"style":7638},[1315],[1129,8598,8599,8602],{"style":7641},[1129,8600],{"className":8601,"style":1324},[1323],[1129,8603,8605],{"className":8604},[1328,1329,1330,1331],[1129,8606,1246],{"className":8607},[1172,1331],[1129,8609,1577],{"className":8610},[1576],[1129,8612,8614],{"className":8613},[1311],[1129,8615,8617],{"className":8616,"style":2624},[1315],[1129,8618],{},";否则返回上一步继续迭代。",[1091,8621,8622,8623,8737],{},"两种写法本质是同一件事,只是把 ",[1129,8624,8626,8652],{"className":8625},[1132],[1129,8627,8629],{"className":8628},[1136],[1138,8630,8631],{"xmlns":1140},[1142,8632,8633,8649],{},[1145,8634,8635,8641,8643,8645,8647],{},[2563,8636,8637,8639],{},[1148,8638,1227],{},[1244,8640,1991],{},[1229,8642,1231],{},[1148,8644,7455],{},[1229,8646,1969],{},[1148,8648,1253],{},[1152,8650,8651],{"encoding":1154},"X_2 = M\\cdot U",[1129,8653,8655,8710,8728],{"className":8654,"ariaHidden":1159},[1158],[1129,8656,8658,8661,8701,8704,8707],{"className":8657},[1163],[1129,8659],{"className":8660,"style":7619},[1167],[1129,8662,8664,8667],{"className":8663},[1172],[1129,8665,1227],{"className":8666,"style":1273},[1172,1173],[1129,8668,8670],{"className":8669},[1303],[1129,8671,8673,8693],{"className":8672},[1307,1523],[1129,8674,8676,8690],{"className":8675},[1311],[1129,8677,8679],{"className":8678,"style":7638},[1315],[1129,8680,8681,8684],{"style":7641},[1129,8682],{"className":8683,"style":1324},[1323],[1129,8685,8687],{"className":8686},[1328,1329,1330,1331],[1129,8688,1991],{"className":8689},[1172,1331],[1129,8691,1577],{"className":8692},[1576],[1129,8694,8696],{"className":8695},[1311],[1129,8697,8699],{"className":8698,"style":2624},[1315],[1129,8700],{},[1129,8702],{"className":8703,"style":1278},[1277],[1129,8705,1231],{"className":8706},[1282],[1129,8708],{"className":8709,"style":1278},[1277],[1129,8711,8713,8716,8719,8722,8725],{"className":8712},[1163],[1129,8714],{"className":8715,"style":1269},[1167],[1129,8717,7455],{"className":8718,"style":1348},[1172,1173],[1129,8720],{"className":8721,"style":1734},[1277],[1129,8723,1969],{"className":8724},[2084],[1129,8726],{"className":8727,"style":1734},[1277],[1129,8729,8731,8734],{"className":8730},[1163],[1129,8732],{"className":8733,"style":1269},[1167],[1129,8735,1253],{"className":8736,"style":1348},[1172,1173]," 换了个记法。",[2937,8739],{},[2940,8741,8743],{"id":8742},"四最大期望算法em-算法","四、最大期望算法(EM 算法)",[1091,8745,8746,8749,8750,8753],{},[1101,8747,8748],{},"EM(Expectation-Maximization)"," 算法用来求含 ",[1101,8751,8752],{},"隐变量"," 的概率模型的参数极大似然估计。当似然函数因为存在隐变量而难以直接极大化时,EM 通过\"E 步补隐变量的期望、M 步再极大化\"两步交替迭代,逐步逼近最优解。",[1091,8755,8756,2955],{},[1101,8757,3257],{},[3259,8759,8760,8841,9857,10300],{},[1098,8761,8762,8765,8766,8840],{},[1101,8763,8764],{},"选初值",":选择参数的初值 ",[1129,8767,8769,8793],{"className":8768},[1132],[1129,8770,8772],{"className":8771},[1136],[1138,8773,8774],{"xmlns":1140},[1142,8775,8776,8790],{},[1145,8777,8778],{},[1233,8779,8780,8782],{},[1148,8781,1978],{},[1145,8783,8784,8786,8788],{},[1229,8785,1250],{"stretchy":1249},[1244,8787,1377],{},[1229,8789,1256],{"stretchy":1249},[1152,8791,8792],{"encoding":1154},"\\theta^{(0)}",[1129,8794,8796],{"className":8795,"ariaHidden":1159},[1158],[1129,8797,8799,8802],{"className":8798},[1163],[1129,8800],{"className":8801,"style":2019},[1167],[1129,8803,8805,8808],{"className":8804},[1172],[1129,8806,1978],{"className":8807,"style":2141},[1172,1173],[1129,8809,8811],{"className":8810},[1303],[1129,8812,8814],{"className":8813},[1307],[1129,8815,8817],{"className":8816},[1311],[1129,8818,8820],{"className":8819,"style":2019},[1315],[1129,8821,8822,8825],{"style":1319},[1129,8823],{"className":8824,"style":1324},[1323],[1129,8826,8828],{"className":8827},[1328,1329,1330,1331],[1129,8829,8831,8834,8837],{"className":8830},[1172,1331],[1129,8832,1250],{"className":8833},[1344,1331],[1129,8835,1377],{"className":8836},[1172,1331],[1129,8838,1256],{"className":8839},[1352,1331],",开始迭代;",[1098,8842,8843,8846,8847,8921,8922,8951,8952,8955,8956,9008,9009,9011,9597,9599,9600,9724,9725,9753,9754,9827,9828,9856],{},[1101,8844,8845],{},"E 步",":记 ",[1129,8848,8850,8874],{"className":8849},[1132],[1129,8851,8853],{"className":8852},[1136],[1138,8854,8855],{"xmlns":1140},[1142,8856,8857,8871],{},[1145,8858,8859],{},[1233,8860,8861,8863],{},[1148,8862,1978],{},[1145,8864,8865,8867,8869],{},[1229,8866,1250],{"stretchy":1249},[1148,8868,1959],{},[1229,8870,1256],{"stretchy":1249},[1152,8872,8873],{"encoding":1154},"\\theta^{(i)}",[1129,8875,8877],{"className":8876,"ariaHidden":1159},[1158],[1129,8878,8880,8883],{"className":8879},[1163],[1129,8881],{"className":8882,"style":2019},[1167],[1129,8884,8886,8889],{"className":8885},[1172],[1129,8887,1978],{"className":8888,"style":2141},[1172,1173],[1129,8890,8892],{"className":8891},[1303],[1129,8893,8895],{"className":8894},[1307],[1129,8896,8898],{"className":8897},[1311],[1129,8899,8901],{"className":8900,"style":2019},[1315],[1129,8902,8903,8906],{"style":1319},[1129,8904],{"className":8905,"style":1324},[1323],[1129,8907,8909],{"className":8908},[1328,1329,1330,1331],[1129,8910,8912,8915,8918],{"className":8911},[1172,1331],[1129,8913,1250],{"className":8914},[1344,1331],[1129,8916,1959],{"className":8917},[1172,1173,1331],[1129,8919,1256],{"className":8920},[1352,1331]," 为第 ",[1129,8923,8925,8938],{"className":8924},[1132],[1129,8926,8928],{"className":8927},[1136],[1138,8929,8930],{"xmlns":1140},[1142,8931,8932,8936],{},[1145,8933,8934],{},[1148,8935,1959],{},[1152,8937,1959],{"encoding":1154},[1129,8939,8941],{"className":8940,"ariaHidden":1159},[1158],[1129,8942,8944,8948],{"className":8943},[1163],[1129,8945],{"className":8946,"style":8947},[1167],"height:0.6595em;",[1129,8949,1959],{"className":8950},[1172,1173]," 次迭代得到的参数估计值。",[8953,8954],"br",{},"在第 ",[1129,8957,8959,8977],{"className":8958},[1132],[1129,8960,8962],{"className":8961},[1136],[1138,8963,8964],{"xmlns":1140},[1142,8965,8966,8974],{},[1145,8967,8968,8970,8972],{},[1148,8969,1959],{},[1229,8971,1994],{},[1244,8973,1246],{},[1152,8975,8976],{"encoding":1154},"i+1",[1129,8978,8980,8999],{"className":8979,"ariaHidden":1159},[1158],[1129,8981,8983,8987,8990,8993,8996],{"className":8982},[1163],[1129,8984],{"className":8985,"style":8986},[1167],"height:0.7429em;vertical-align:-0.0833em;",[1129,8988,1959],{"className":8989},[1172,1173],[1129,8991],{"className":8992,"style":1734},[1277],[1129,8994,1994],{"className":8995},[2084],[1129,8997],{"className":8998,"style":1734},[1277],[1129,9000,9002,9005],{"className":9001},[1163],[1129,9003],{"className":9004,"style":2074},[1167],[1129,9006,1246],{"className":9007},[1172]," 次迭代的 E 步,计算 Q 函数",[8953,9010],{},[1129,9012,9014,9161],{"className":9013},[1132],[1129,9015,9017],{"className":9016},[1136],[1138,9018,9019],{"xmlns":1140},[1142,9020,9021,9158],{},[1145,9022,9023,9026,9028,9030,9032,9044,9046,9048,9076,9078,9081,9083,9085,9087,9089,9091,9093,9095,9097,9099,9101,9103,9110,9112,9114,9116,9118,9120,9122,9124,9126,9128,9130,9132,9134,9136,9138,9140,9142,9144,9156],{},[1148,9024,9025],{},"Q",[1229,9027,1250],{"stretchy":1249},[1148,9029,1978],{},[1229,9031,1353],{"separator":1159},[1233,9033,9034,9036],{},[1148,9035,1978],{},[1145,9037,9038,9040,9042],{},[1229,9039,1250],{"stretchy":1249},[1148,9041,1959],{},[1229,9043,1256],{"stretchy":1249},[1229,9045,1256],{"stretchy":1249},[1229,9047,1231],{},[2563,9049,9050,9053],{},[1148,9051,9052],{},"E",[1145,9054,9055,9058,9060,9062,9064],{},[1148,9056,9057],{},"Z",[1229,9059,4576],{},[1148,9061,1640],{},[1229,9063,1353],{"separator":1159},[1233,9065,9066,9068],{},[1148,9067,1978],{},[1145,9069,9070,9072,9074],{},[1229,9071,1250],{"stretchy":1249},[1148,9073,1959],{},[1229,9075,1256],{"stretchy":1249},[1229,9077,3077],{"fence":1249,"stretchy":1159,"minsize":5489,"maxsize":5489},[1148,9079,9080],{},"log",[1229,9082,1473],{},[1148,9084,6819],{},[1229,9086,1250],{"stretchy":1249},[1148,9088,1640],{},[1229,9090,1353],{"separator":1159},[1148,9092,9057],{},[1229,9094,4576],{},[1148,9096,1978],{},[1229,9098,1256],{"stretchy":1249},[1229,9100,3086],{"fence":1249,"stretchy":1159,"minsize":5489,"maxsize":5489},[1229,9102,1231],{},[2563,9104,9105,9108],{},[1229,9106,9107],{},"∑",[1148,9109,9057],{},[1148,9111,9080],{},[1229,9113,1473],{},[1148,9115,6819],{},[1229,9117,1250],{"stretchy":1249},[1148,9119,1640],{},[1229,9121,1353],{"separator":1159},[1148,9123,9057],{},[1229,9125,4576],{},[1148,9127,1978],{},[1229,9129,1256],{"stretchy":1249},[1648,9131,1650],{},[1148,9133,6819],{},[1229,9135,1250],{"stretchy":1249},[1148,9137,9057],{},[1229,9139,4576],{},[1148,9141,1640],{},[1229,9143,1353],{"separator":1159},[1233,9145,9146,9148],{},[1148,9147,1978],{},[1145,9149,9150,9152,9154],{},[1229,9151,1250],{"stretchy":1249},[1148,9153,1959],{},[1229,9155,1256],{"stretchy":1249},[1229,9157,1256],{"stretchy":1249},[1152,9159,9160],{"encoding":1154},"Q(\\theta, \\theta^{(i)}) = E_{Z\\mid Y,\\theta^{(i)}}\\big[\\log P(Y,Z \\mid \\theta)\\big] = \\sum_{Z} \\log P(Y,Z\\mid\\theta)\\, P(Z\\mid Y,\\theta^{(i)})",[1129,9162,9164,9236,9388,9416,9508,9541],{"className":9163,"ariaHidden":1159},[1158],[1129,9165,9167,9171,9174,9177,9180,9183,9186,9224,9227,9230,9233],{"className":9166},[1163],[1129,9168],{"className":9169,"style":9170},[1167],"height:1.138em;vertical-align:-0.25em;",[1129,9172,9025],{"className":9173},[1172,1173],[1129,9175,1250],{"className":9176},[1344],[1129,9178,1978],{"className":9179,"style":2141},[1172,1173],[1129,9181,1353],{"className":9182},[1427],[1129,9184],{"className":9185,"style":1431},[1277],[1129,9187,9189,9192],{"className":9188},[1172],[1129,9190,1978],{"className":9191,"style":2141},[1172,1173],[1129,9193,9195],{"className":9194},[1303],[1129,9196,9198],{"className":9197},[1307],[1129,9199,9201],{"className":9200},[1311],[1129,9202,9204],{"className":9203,"style":2019},[1315],[1129,9205,9206,9209],{"style":1319},[1129,9207],{"className":9208,"style":1324},[1323],[1129,9210,9212],{"className":9211},[1328,1329,1330,1331],[1129,9213,9215,9218,9221],{"className":9214},[1172,1331],[1129,9216,1250],{"className":9217},[1344,1331],[1129,9219,1959],{"className":9220},[1172,1173,1331],[1129,9222,1256],{"className":9223},[1352,1331],[1129,9225,1256],{"className":9226},[1352],[1129,9228],{"className":9229,"style":1278},[1277],[1129,9231,1231],{"className":9232},[1282],[1129,9234],{"className":9235,"style":1278},[1277],[1129,9237,9239,9243,9342,9348,9351,9358,9361,9364,9367,9370,9373,9376,9379,9382,9385],{"className":9238},[1163],[1129,9240],{"className":9241,"style":9242},[1167],"height:1.2556em;vertical-align:-0.4056em;",[1129,9244,9246,9250],{"className":9245},[1172],[1129,9247,9052],{"className":9248,"style":9249},[1172,1173],"margin-right:0.0576em;",[1129,9251,9253],{"className":9252},[1303],[1129,9254,9256,9333],{"className":9255},[1307,1523],[1129,9257,9259,9330],{"className":9258},[1311],[1129,9260,9263],{"className":9261,"style":9262},[1315],"height:0.3448em;",[1129,9264,9266,9269],{"style":9265},"top:-2.4694em;margin-left:-0.0576em;margin-right:0.05em;",[1129,9267],{"className":9268,"style":1324},[1323],[1129,9270,9272],{"className":9271},[1328,1329,1330,1331],[1129,9273,9275,9279,9282,9285,9288],{"className":9274},[1172,1331],[1129,9276,9057],{"className":9277,"style":9278},[1172,1173,1331],"margin-right:0.0715em;",[1129,9280,4576],{"className":9281},[1282,1331],[1129,9283,1640],{"className":9284,"style":1734},[1172,1173,1331],[1129,9286,1353],{"className":9287},[1427,1331],[1129,9289,9291,9294],{"className":9290},[1172,1331],[1129,9292,1978],{"className":9293,"style":2141},[1172,1173,1331],[1129,9295,9297],{"className":9296},[1303],[1129,9298,9300],{"className":9299},[1307],[1129,9301,9303],{"className":9302},[1311],[1129,9304,9307],{"className":9305,"style":9306},[1315],"height:0.822em;",[1129,9308,9310,9314],{"style":9309},"top:-2.822em;margin-right:0.0714em;",[1129,9311],{"className":9312,"style":9313},[1323],"height:2.5357em;",[1129,9315,9318],{"className":9316},[1328,9317,5723,1331],"reset-size3",[1129,9319,9321,9324,9327],{"className":9320},[1172,1331],[1129,9322,1250],{"className":9323},[1344,1331],[1129,9325,1959],{"className":9326},[1172,1173,1331],[1129,9328,1256],{"className":9329},[1352,1331],[1129,9331,1577],{"className":9332},[1576],[1129,9334,9336],{"className":9335},[1311],[1129,9337,9340],{"className":9338,"style":9339},[1315],"height:0.4056em;",[1129,9341],{},[1129,9343,9345],{"className":9344},[1172],[1129,9346,3077],{"className":9347},[4900,5723],[1129,9349],{"className":9350,"style":1431},[1277],[1129,9352,9354,9355],{"className":9353},[1596],"lo",[1129,9356,1150],{"style":9357},"margin-right:0.0139em;",[1129,9359],{"className":9360,"style":1431},[1277],[1129,9362,6819],{"className":9363,"style":1299},[1172,1173],[1129,9365,1250],{"className":9366},[1344],[1129,9368,1640],{"className":9369,"style":1734},[1172,1173],[1129,9371,1353],{"className":9372},[1427],[1129,9374],{"className":9375,"style":1431},[1277],[1129,9377,9057],{"className":9378,"style":9278},[1172,1173],[1129,9380],{"className":9381,"style":1278},[1277],[1129,9383,4576],{"className":9384},[1282],[1129,9386],{"className":9387,"style":1278},[1277],[1129,9389,9391,9395,9398,9401,9407,9410,9413],{"className":9390},[1163],[1129,9392],{"className":9393,"style":9394},[1167],"height:1.2em;vertical-align:-0.35em;",[1129,9396,1978],{"className":9397,"style":2141},[1172,1173],[1129,9399,1256],{"className":9400},[1352],[1129,9402,9404],{"className":9403},[1172],[1129,9405,3086],{"className":9406},[4900,5723],[1129,9408],{"className":9409,"style":1278},[1277],[1129,9411,1231],{"className":9412},[1282],[1129,9414],{"className":9415,"style":1278},[1277],[1129,9417,9419,9423,9470,9473,9478,9481,9484,9487,9490,9493,9496,9499,9502,9505],{"className":9418},[1163],[1129,9420],{"className":9421,"style":9422},[1167],"height:1.0497em;vertical-align:-0.2997em;",[1129,9424,9426,9430],{"className":9425},[1596],[1129,9427,9107],{"className":9428,"style":9429},[1596,6765,6766],"position:relative;top:0em;",[112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",[1129,9601,9603,9641],{"className":9602},[1132],[1129,9604,9606],{"className":9605},[1136],[1138,9607,9608],{"xmlns":1140},[1142,9609,9610,9638],{},[1145,9611,9612,9614,9616,9618,9620,9622,9624,9636],{},[1148,9613,6819],{},[1229,9615,1250],{"stretchy":1249},[1148,9617,9057],{},[1229,9619,4576],{},[1148,9621,1640],{},[1229,9623,1353],{"separator":1159},[1233,9625,9626,9628],{},[1148,9627,1978],{},[1145,9629,9630,9632,9634],{},[1229,9631,1250],{"stretchy":1249},[1148,9633,1959],{},[1229,9635,1256],{"stretchy":1249},[1229,9637,1256],{"stretchy":1249},[1152,9639,9640],{"encoding":1154},"P(Z\\mid Y,\\theta^{(i)})",[1129,9642,9644,9668],{"className":9643,"ariaHidden":1159},[1158],[1129,9645,9647,9650,9653,9656,9659,9662,9665],{"className":9646},[1163],[1129,9648],{"className":9649,"style":1414},[1167],[1129,9651,6819],{"className":9652,"style":1299},[1172,1173],[1129,9654,1250],{"className":9655},[1344],[1129,9657,9057],{"className":9658,"style":9278},[1172,1173],[1129,9660],{"className":9661,"style":1278},[1277],[1129,9663,4576],{"className":9664},[1282],[1129,9666],{"className":9667,"style":1278},[1277],[1129,9669,9671,9674,9677,9680,9683,9721],{"className":9670},[1163],[1129,9672],{"className":9673,"style":9170},[1167],[1129,9675,1640],{"className":9676,"style":1734},[1172,1173],[1129,9678,1353],{"className":9679},[1427],[1129,9681],{"className":9682,"style":1431},[1277],[1129,9684,9686,9689],{"className":9685},[1172],[1129,9687,1978],{"className":9688,"style":2141},[1172,1173],[1129,9690,9692],{"className":9691},[1303],[1129,9693,9695],{"className":9694},[1307],[1129,9696,9698],{"className":9697},[1311],[1129,9699,9701],{"className":9700,"style":2019},[1315],[1129,9702,9703,9706],{"style":1319},[1129,9704],{"className":9705,"style":1324},[1323],[1129,9707,9709],{"className":9708},[1328,1329,1330,1331],[1129,9710,9712,9715,9718],{"className":9711},[1172,1331],[1129,9713,1250],{"className":9714},[1344,1331],[1129,9716,1959],{"className":9717},[1172,1173,1331],[1129,9719,1256],{"className":9720},[1352,1331],[1129,9722,1256],{"className":9723},[1352]," 是在给定观测数据 ",[1129,9726,9728,9741],{"className":9727},[1132],[1129,9729,9731],{"className":9730},[1136],[1138,9732,9733],{"xmlns":1140},[1142,9734,9735,9739],{},[1145,9736,9737],{},[1148,9738,1640],{},[1152,9740,1640],{"encoding":1154},[1129,9742,9744],{"className":9743,"ariaHidden":1159},[1158],[1129,9745,9747,9750],{"className":9746},[1163],[1129,9748],{"className":9749,"style":1269},[1167],[1129,9751,1640],{"className":9752,"style":1734},[1172,1173]," 和当前估计值 ",[1129,9755,9757,9780],{"className":9756},[1132],[1129,9758,9760],{"className":9759},[1136],[1138,9761,9762],{"xmlns":1140},[1142,9763,9764,9778],{},[1145,9765,9766],{},[1233,9767,9768,9770],{},[1148,9769,1978],{},[1145,9771,9772,9774,9776],{},[1229,9773,1250],{"stretchy":1249},[1148,9775,1959],{},[1229,9777,1256],{"stretchy":1249},[1152,9779,8873],{"encoding":1154},[1129,9781,9783],{"className":9782,"ariaHidden":1159},[1158],[1129,9784,9786,9789],{"className":9785},[1163],[1129,9787],{"className":9788,"style":2019},[1167],[1129,9790,9792,9795],{"className":9791},[1172],[1129,9793,1978],{"className":9794,"style":2141},[1172,1173],[1129,9796,9798],{"className":9797},[1303],[1129,9799,9801],{"className":9800},[1307],[1129,9802,9804],{"className":9803},[1311],[1129,9805,9807],{"className":9806,"style":2019},[1315],[1129,9808,9809,9812],{"style":1319},[1129,9810],{"className":9811,"style":1324},[1323],[1129,9813,9815],{"className":9814},[1328,1329,1330,1331],[1129,9816,9818,9821,9824],{"className":9817},[1172,1331],[1129,9819,1250],{"className":9820},[1344,1331],[1129,9822,1959],{"className":9823},[1172,1173,1331],[1129,9825,1256],{"className":9826},[1352,1331]," 下,隐变量 ",[1129,9829,9831,9844],{"className":9830},[1132],[1129,9832,9834],{"className":9833},[1136],[1138,9835,9836],{"xmlns":1140},[1142,9837,9838,9842],{},[1145,9839,9840],{},[1148,9841,9057],{},[1152,9843,9057],{"encoding":1154},[1129,9845,9847],{"className":9846,"ariaHidden":1159},[1158],[1129,9848,9850,9853],{"className":9849},[1163],[1129,9851],{"className":9852,"style":1269},[1167],[1129,9854,9057],{"className":9855,"style":9278},[1172,1173]," 的条件概率分布;",[1098,9858,9859,9862,9863,9965,9966,9995,9996,10046,10047,10049],{},[1101,9860,9861],{},"M 步",":求使 ",[1129,9864,9866,9900],{"className":9865},[1132],[1129,9867,9869],{"className":9868},[1136],[1138,9870,9871],{"xmlns":1140},[1142,9872,9873,9897],{},[1145,9874,9875,9877,9879,9881,9883,9895],{},[1148,9876,9025],{},[1229,9878,1250],{"stretchy":1249},[1148,9880,1978],{},[1229,9882,1353],{"separator":1159},[1233,9884,9885,9887],{},[1148,9886,1978],{},[1145,9888,9889,9891,9893],{},[1229,9890,1250],{"stretchy":1249},[1148,9892,1959],{},[1229,9894,1256],{"stretchy":1249},[1229,9896,1256],{"stretchy":1249},[1152,9898,9899],{"encoding":1154},"Q(\\theta,\\theta^{(i)})",[1129,9901,9903],{"className":9902,"ariaHidden":1159},[1158],[1129,9904,9906,9909,9912,9915,9918,9921,9924,9962],{"className":9905},[1163],[1129,9907],{"className":9908,"style":9170},[1167],[1129,9910,9025],{"className":9911},[1172,1173],[1129,9913,1250],{"className":9914},[1344],[1129,9916,1978],{"className":9917,"style":2141},[1172,1173],[1129,9919,1353],{"className":9920},[1427],[1129,9922],{"className":9923,"style":1431},[1277],[1129,9925,9927,9930],{"className":9926},[1172],[1129,9928,1978],{"className":9929,"style":2141},[1172,1173],[1129,9931,9933],{"className":9932},[1303],[1129,9934,9936],{"className":9935},[1307],[1129,9937,9939],{"className":9938},[1311],[1129,9940,9942],{"className":9941,"style":2019},[1315],[1129,9943,9944,9947],{"style":1319},[1129,9945],{"className":9946,"style":1324},[1323],[1129,9948,9950],{"className":9949},[1328,1329,1330,1331],[1129,9951,9953,9956,9959],{"className":9952},[1172,1331],[1129,9954,1250],{"className":9955},[1344,1331],[1129,9957,1959],{"className":9958},[1172,1173,1331],[1129,9960,1256],{"className":9961},[1352,1331],[1129,9963,1256],{"className":9964},[1352]," 极大化的 ",[1129,9967,9969,9983],{"className":9968},[1132],[1129,9970,9972],{"className":9971},[1136],[1138,9973,9974],{"xmlns":1140},[1142,9975,9976,9980],{},[1145,9977,9978],{},[1148,9979,1978],{},[1152,9981,9982],{"encoding":1154},"\\theta",[1129,9984,9986],{"className":9985,"ariaHidden":1159},[1158],[1129,9987,9989,9992],{"className":9988},[1163],[1129,9990],{"className":9991,"style":2850},[1167],[1129,9993,1978],{"className":9994,"style":2141},[1172,1173],",把它作为第 ",[1129,9997,9999,10016],{"className":9998},[1132],[1129,10000,10002],{"className":10001},[1136],[1138,10003,10004],{"xmlns":1140},[1142,10005,10006,10014],{},[1145,10007,10008,10010,10012],{},[1148,10009,1959],{},[1229,10011,1994],{},[1244,10013,1246],{},[1152,10015,8976],{"encoding":1154},[1129,10017,10019,10037],{"className":10018,"ariaHidden":1159},[1158],[1129,10020,10022,10025,10028,10031,10034],{"className":10021},[1163],[1129,10023],{"className":10024,"style":8986},[1167],[1129,10026,1959],{"className":10027},[1172,1173],[1129,10029],{"className":10030,"style":1734},[1277],[1129,10032,1994],{"className":10033},[2084],[1129,10035],{"className":10036,"style":1734},[1277],[1129,10038,10040,10043],{"className":10039},[1163],[1129,10041],{"className":10042,"style":2074},[1167],[1129,10044,1246],{"className":10045},[1172]," 次迭代的参数估计值",[8953,10048],{},[1129,10050,10052,10120],{"className":10051},[1132],[1129,10053,10055],{"className":10054},[1136],[1138,10056,10057],{"xmlns":1140},[1142,10058,10059,10117],{},[1145,10060,10061,10077,10079,10082,10084,10095,10097,10099,10101,10103,10115],{},[1233,10062,10063,10065],{},[1148,10064,1978],{},[1145,10066,10067,10069,10071,10073,10075],{},[1229,10068,1250],{"stretchy":1249},[1148,10070,1959],{},[1229,10072,1994],{},[1244,10074,1246],{},[1229,10076,1256],{"stretchy":1249},[1229,10078,1231],{},[1148,10080,10081],{},"arg",[1229,10083,1473],{},[2563,10085,10086,10093],{},[1145,10087,10088,10091],{},[1148,10089,10090],{},"max",[1229,10092,1473],{},[1148,10094,1978],{},[1148,10096,9025],{},[1229,10098,1250],{"stretchy":1249},[1148,10100,1978],{},[1229,10102,1353],{"separator":1159},[1233,10104,10105,10107],{},[1148,10106,1978],{},[1145,10108,10109,10111,10113],{},[1229,10110,1250],{"stretchy":1249},[1148,10112,1959],{},[1229,10114,1256],{"stretchy":1249},[1229,10116,1256],{"stretchy":1249},[1152,10118,10119],{"encoding":1154},"\\theta^{(i+1)} = \\arg\\max_{\\theta} Q(\\theta, \\theta^{(i)})",[1129,10121,10123,10182],{"className":10122,"ariaHidden":1159},[1158],[1129,10124,10126,10129,10173,10176,10179],{"className":10125},[1163],[1129,10127],{"className":10128,"style":2019},[1167],[1129,10130,10132,10135],{"className":10131},[1172],[1129,10133,1978],{"className":10134,"style":2141},[1172,1173],[1129,10136,10138],{"className":10137},[1303],[1129,10139,10141],{"className":10140},[1307],[1129,10142,10144],{"className":10143},[1311],[1129,10145,10147],{"className":10146,"style":2019},[1315],[1129,10148,10149,10152],{"style":1319},[1129,10150],{"className":10151,"style":1324},[1323],[1129,10153,10155],{"className":10154},[1328,1329,1330,1331],[1129,10156,10158,10161,10164,10167,10170],{"className":10157},[1172,1331],[1129,10159,1250],{"className":10160},[1344,1331],[1129,10162,1959],{"className":10163},[1172,1173,1331],[1129,10165,1994],{"className":10166},[2084,1331],[1129,10168,1246],{"className":10169},[1172,1331],[1129,10171,1256],{"className":10172},[1352,1331],[1129,10174],{"className":10175,"style":1278},[1277],[1129,10177,1231],{"className":10178},[1282],[1129,10180],{"className":10181,"style":1278},[1277],[1129,10183,10185,10188,10194,10197,10241,10244,10247,10250,10253,10256,10259,10297],{"className":10184},[1163],[1129,10186],{"className":10187,"style":9170},[1167],[1129,10189,10191,10192],{"className":10190},[1596],"ar",[1129,10193,1150],{"style":9357},[1129,10195],{"className":10196,"style":1431},[1277],[1129,10198,10200,10203],{"className":10199},[1596],[1129,10201,10090],{"className":10202},[1596],[1129,10204,10206],{"className":10205},[1303],[1129,10207,10209,10233],{"className":10208},[1307,1523],[1129,10210,10212,10230],{"className":10211},[1311],[1129,10213,10215],{"className":10214,"style":2601},[1315],[1129,10216,10218,10221],{"style":10217},"top:-2.55em;margin-right:0.05em;",[1129,10219],{"className":10220,"style":1324},[1323],[1129,10222,10224],{"className":10223},[1328,1329,1330,1331],[1129,10225,10227],{"className":10226},[1172,1331],[1129,10228,1978],{"className":10229,"style":2141},[1172,1173,1331],[1129,10231,1577],{"className":10232},[1576],[1129,10234,10236],{"className":10235},[1311],[1129,10237,10239],{"className":10238,"style":2624},[1315],[1129,10240],{},[1129,10242],{"className":10243,"style":1431},[1277],[1129,10245,9025],{"className":10246},[1172,1173],[1129,10248,1250],{"className":10249},[1344],[1129,10251,1978],{"className":10252,"style":2141},[1172,1173],[1129,10254,1353],{"className":10255},[1427],[1129,10257],{"className":10258,"style":1431},[1277],[1129,10260,10262,10265],{"className":10261},[1172],[1129,10263,1978],{"className":10264,"style":2141},[1172,1173],[1129,10266,10268],{"className":10267},[1303],[1129,10269,10271],{"className":10270},[1307],[1129,10272,10274],{"className":10273},[1311],[1129,10275,10277],{"className":10276,"style":2019},[1315],[1129,10278,10279,10282],{"style":1319},[1129,10280],{"className":10281,"style":1324},[1323],[1129,10283,10285],{"className":10284},[1328,1329,1330,1331],[1129,10286,10288,10291,10294],{"className":10287},[1172,1331],[1129,10289,1250],{"className":10290},[1344,1331],[1129,10292,1959],{"className":10293},[1172,1173,1331],[1129,10295,1256],{"className":10296},[1352,1331],[1129,10298,1256],{"className":10299},[1352],[1098,10301,10302,10305],{},[1101,10303,10304],{},"迭代",":重复第 2、3 步,直至收敛(参数或对数似然的变化足够小)。",[3512,10307,10309],{"id":10308},"例子一遗传模型genetic-linkage-model","例子一:遗传模型(genetic linkage model)",[1091,10311,10312],{},"设一次实验可能出现四个结果,发生概率分别为",[1091,10314,10315],{},[1129,10316,10318,10401],{"className":10317},[1132],[1129,10319,10321],{"className":10320},[1136],[1138,10322,10323],{"xmlns":1140},[1142,10324,10325,10398],{},[1145,10326,10327,10333,10335,10342,10344,10346,10358,10360,10362,10374,10376,10378,10384,10386,10388,10390,10392,10394,10396],{},[1461,10328,10329,10331],{},[1244,10330,1246],{},[1244,10332,1991],{},[1229,10334,1994],{},[1461,10336,10337,10339],{},[1148,10338,1978],{},[1244,10340,10341],{},"4",[1229,10343,1353],{"separator":1159},[1277,10345],{"width":3642},[1461,10347,10348,10356],{},[1145,10349,10350,10352,10354],{},[1244,10351,1246],{},[1229,10353,1242],{},[1148,10355,1978],{},[1244,10357,10341],{},[1229,10359,1353],{"separator":1159},[1277,10361],{"width":3642},[1461,10363,10364,10372],{},[1145,10365,10366,10368,10370],{},[1244,10367,1246],{},[1229,10369,1242],{},[1148,10371,1978],{},[1244,10373,10341],{},[1229,10375,1353],{"separator":1159},[1277,10377],{"width":3642},[1461,10379,10380,10382],{},[1148,10381,1978],{},[1244,10383,10341],{},[1229,10385,1353],{"separator":1159},[1277,10387],{"width":6868},[1244,10389,1377],{},[1229,10391,1626],{},[1148,10393,1978],{},[1229,10395,1626],{},[1244,10397,1246],{},[1152,10399,10400],{"encoding":1154},"\\frac{1}{2} + \\frac{\\theta}{4},\\quad \\frac{1-\\theta}{4},\\quad \\frac{1-\\theta}{4},\\quad \\frac{\\theta}{4}, \\qquad 0 \\le \\theta \\le 1",[1129,10402,10404,10487,10827,10846],{"className":10403,"ariaHidden":1159},[1158],[1129,10405,10407,10410,10478,10481,10484],{"className":10406},[1163],[1129,10408],{"className":10409,"style":1506},[1167],[1129,10411,10413,10416,10475],{"className":10412},[1172],[1129,10414],{"className":10415},[1344,1516],[1129,10417,10419],{"className":10418},[1461],[1129,10420,10422,10467],{"className":10421},[1307,1523],[1129,10423,10425,10464],{"className":10424},[1311],[1129,10426,10428,10442,10450],{"className":10427,"style":1530},[1315],[1129,10429,10430,10433],{"style":1533},[1129,10431],{"className":10432,"style":1537},[1323],[1129,10434,10436],{"className":10435},[1328,1329,1330,1331],[1129,10437,10439],{"className":10438},[1172,1331],[1129,10440,1991],{"className":10441},[1172,1331],[1129,10443,10444,10447],{"style":1549},[1129,10445],{"className":10446,"style":1537},[1323],[1129,10448],{"className":10449,"style":1557},[1556],[1129,10451,10452,10455],{"style":1560},[1129,10453],{"className":10454,"style":1537},[1323],[1129,10456,10458],{"className":10457},[1328,1329,1330,1331],[1129,10459,10461],{"className":10460},[1172,1331],[1129,10462,1246],{"className":10463},[1172,1331],[1129,10465,1577],{"className":10466},[1576],[1129,10468,10470],{"className":10469},[1311],[1129,10471,10473],{"className":10472,"style":1584},[1315],[1129,10474],{},[1129,10476],{"className":10477},[1352,1516],[1129,10479],{"className":10480,"style":1734},[1277],[1129,10482,1994],{"className":10483},[2084],[1129,10485],{"className":10486,"style":1734},[1277],[1129,10488,10490,10494,10563,10566,10569,10572,10646,10649,10652,10655,10729,10732,10735,10738,10806,10809,10812,10815,10818,10821,10824],{"className":10489},[1163],[1129,10491],{"className":10492,"style":10493},[1167],"height:1.2251em;vertical-align:-0.345em;",[1129,10495,10497,10500,10560],{"className":10496},[1172],[1129,10498],{"className":10499},[1344,1516],[1129,10501,10503],{"className":10502},[1461],[1129,10504,10506,10552],{"className":10505},[1307,1523],[1129,10507,10509,10549],{"className":10508},[1311],[1129,10510,10513,10527,10535],{"className":10511,"style":10512},[1315],"height:0.8801em;",[1129,10514,10515,10518],{"style":1533},[1129,10516],{"className":10517,"style":1537},[1323],[1129,10519,10521],{"className":10520},[1328,1329,1330,1331],[1129,10522,10524],{"className":10523},[1172,1331],[1129,10525,10341],{"className":10526},[1172,1331],[1129,10528,10529,10532],{"style":1549},[1129,10530],{"className":10531,"style":1537},[1323],[1129,10533],{"className":10534,"style":1557},[1556],[1129,10536,10537,10540],{"style":1560},[1129,10538],{"className":10539,"style":1537},[1323],[1129,10541,10543],{"className":10542},[1328,1329,1330,1331],[1129,10544,10546],{"className":10545},[1172,1331],[1129,10547,1978],{"className":10548,"style":2141},[1172,1173,1331],[1129,10550,1577],{"className":10551},[1576],[1129,10553,10555],{"className":10554},[1311],[1129,10556,10558],{"className":10557,"style":1584},[1315],[1129,10559],{},[1129,10561],{"className":10562},[1352,1516],[1129,10564,1353],{"className":10565},[1427],[1129,10567],{"className":10568,"style":3770},[1277],[1129,10570],{"className":10571,"style":1431},[1277],[1129,10573,10575,10578,10643],{"className":10574},[1172],[1129,10576],{"className":10577},[1344,1516],[1129,10579,10581],{"className":10580},[1461],[1129,10582,10584,10635],{"className":10583},[1307,1523],[1129,10585,10587,10632],{"className":10586},[1311],[1129,10588,10590,10604,10612],{"className":10589,"style":10512},[1315],[1129,10591,10592,10595],{"style":1533},[1129,10593],{"className":10594,"style":1537},[1323],[1129,10596,10598],{"className":10597},[1328,1329,1330,1331],[1129,10599,10601],{"className":10600},[1172,1331],[1129,10602,10341],{"className":10603},[1172,1331],[1129,10605,10606,10609],{"style":1549},[1129,10607],{"className":10608,"style":1537},[1323],[1129,10610],{"className":10611,"style":1557},[1556],[1129,10613,10614,10617],{"style":1560},[1129,10615],{"className":10616,"style":1537},[1323],[1129,10618,10620],{"className":10619},[1328,1329,1330,1331],[1129,10621,10623,10626,10629],{"className":10622},[1172,1331],[1129,10624,1246],{"className":10625},[1172,1331],[1129,10627,1242],{"className":10628},[2084,1331],[1129,10630,1978],{"className":10631,"style":2141},[1172,1173,1331],[1129,10633,1577],{"className":10634},[1576],[1129,10636,10638],{"className":10637},[1311],[1129,10639,10641],{"className":10640,"style":1584},[1315],[1129,10642],{},[1129,10644],{"className":10645},[1352,1516],[1129,10647,1353],{"className":10648},[1427],[1129,10650],{"className":10651,"style":3770},[1277],[1129,10653],{"className":10654,"style":1431},[1277],[1129,10656,10658,10661,10726],{"className":10657},[1172],[1129,10659],{"className":10660},[1344,1516],[1129,10662,10664],{"className":10663},[1461],[1129,10665,10667,10718],{"className":10666},[1307,1523],[1129,10668,10670,10715],{"className":10669},[1311],[1129,10671,10673,10687,10695],{"className":10672,"style":10512},[1315],[1129,10674,10675,10678],{"style":1533},[1129,10676],{"className":10677,"style":1537},[1323],[1129,10679,10681],{"className":10680},[1328,1329,1330,1331],[1129,10682,10684],{"className":10683},[1172,1331],[1129,10685,10341],{"className":10686},[1172,1331],[1129,10688,10689,10692],{"style":1549},[1129,10690],{"className":10691,"style":1537},[1323],[1129,10693],{"className":10694,"style":1557},[1556],[1129,10696,10697,10700],{"style":1560},[1129,10698],{"className":10699,"style":1537},[1323],[1129,10701,10703],{"className":10702},[1328,1329,1330,1331],[1129,10704,10706,10709,10712],{"className":10705},[1172,1331],[1129,10707,1246],{"className":10708},[1172,1331],[1129,10710,1242],{"className":10711},[2084,1331],[1129,10713,1978],{"className":10714,"style":2141},[1172,1173,1331],[1129,10716,1577],{"className":10717},[1576],[1129,10719,10721],{"className":10720},[1311],[1129,10722,10724],{"className":10723,"style":1584},[1315],[1129,10725],{},[1129,10727],{"className":10728},[1352,1516],[1129,10730,1353],{"className":10731},[1427],[1129,10733],{"className":10734,"style":3770},[1277],[1129,10736],{"className":10737,"style":1431},[1277],[1129,10739,10741,10744,10803],{"className":10740},[1172],[1129,10742],{"className":10743},[1344,1516],[1129,10745,10747],{"className":10746},[1461],[1129,10748,10750,10795],{"className":10749},[1307,1523],[1129,10751,10753,10792],{"className":10752},[1311],[1129,10754,10756,10770,10778],{"className":10755,"style":10512},[1315],[1129,10757,10758,10761],{"style":1533},[1129,10759],{"className":10760,"style":1537},[1323],[1129,10762,10764],{"className":10763},[1328,1329,1330,1331],[1129,10765,10767],{"className":10766},[1172,1331],[1129,10768,10341],{"className":10769},[1172,1331],[1129,10771,10772,10775],{"style":1549},[1129,10773],{"className":10774,"style":1537},[1323],[1129,10776],{"className":10777,"style":1557},[1556],[1129,10779,10780,10783],{"style":1560},[1129,10781],{"className":10782,"style":1537},[1323],[1129,10784,10786],{"className":10785},[1328,1329,1330,1331],[1129,10787,10789],{"className":10788},[1172,1331],[1129,10790,1978],{"className":10791,"style":2141},[1172,1173,1331],[1129,10793,1577],{"className":10794},[1576],[1129,10796,10798],{"className":10797},[1311],[1129,10799,10801],{"className":10800,"style":1584},[1315],[1129,10802],{},[1129,10804],{"className":10805},[1352,1516],[1129,10807,1353],{"className":10808},[1427],[1129,10810],{"className":10811,"style":7062},[1277],[1129,10813],{"className":10814,"style":1431},[1277],[1129,10816,1377],{"className":10817},[1172],[1129,10819],{"className":10820,"style":1278},[1277],[1129,10822,1626],{"className":10823},[1282],[1129,10825],{"className":10826,"style":1278},[1277],[1129,10828,10830,10834,10837,10840,10843],{"className":10829},[1163],[1129,10831],{"className":10832,"style":10833},[1167],"height:0.8304em;vertical-align:-0.136em;",[1129,10835,1978],{"className":10836,"style":2141},[1172,1173],[1129,10838],{"className":10839,"style":1278},[1277],[1129,10841,1626],{"className":10842},[1282],[1129,10844],{"className":10845,"style":1278},[1277],[1129,10847,10849,10852],{"className":10848},[1163],[1129,10850],{"className":10851,"style":2074},[1167],[1129,10853,1246],{"className":10854},[1172],[1091,10856,10857,10858,10861,10862,10890],{},"现在进行了 197 次试验,四种结果的发生次数分别为 ",[1101,10859,10860],{},"125、18、20、34","。要求出分布中参数 ",[1129,10863,10865,10878],{"className":10864},[1132],[1129,10866,10868],{"className":10867},[1136],[1138,10869,10870],{"xmlns":1140},[1142,10871,10872,10876],{},[1145,10873,10874],{},[1148,10875,1978],{},[1152,10877,9982],{"encoding":1154},[1129,10879,10881],{"className":10880,"ariaHidden":1159},[1158],[1129,10882,10884,10887],{"className":10883},[1163],[1129,10885],{"className":10886,"style":2850},[1167],[1129,10888,1978],{"className":10889,"style":2141},[1172,1173]," 的一个好的估计。",[1091,10892,10893,10896,10897,11090,11091,11191,11192,11292,11293,11191,11408,11436,11437,11191,11536,11635,11636,11664],{},[1101,10894,10895],{},"引入隐变量",":第一类结果的概率 ",[1129,10898,10900,10930],{"className":10899},[1132],[1129,10901,10903],{"className":10902},[1136],[1138,10904,10905],{"xmlns":1140},[1142,10906,10907,10927],{},[1145,10908,10909,10917,10919],{},[1458,10910,10911],{"scriptlevel":1377,"displaystyle":1249},[1461,10912,10913,10915],{},[1244,10914,1246],{},[1244,10916,1991],{},[1229,10918,1994],{},[1458,10920,10921],{"scriptlevel":1377,"displaystyle":1249},[1461,10922,10923,10925],{},[1148,10924,1978],{},[1244,10926,10341],{},[1152,10928,10929],{"encoding":1154},"\\tfrac{1}{2} + \\tfrac{\\theta}{4}",[1129,10931,10933,11016],{"className":10932,"ariaHidden":1159},[1158],[1129,10934,10936,10939,11007,11010,11013],{"className":10935},[1163],[1129,10937],{"className":10938,"style":1506},[1167],[1129,10940,10942,10945,11004],{"className":10941},[1172],[1129,10943],{"className":10944},[1344,1516],[1129,10946,10948],{"className":10947},[1461],[1129,10949,10951,10996],{"className":10950},[1307,1523],[1129,10952,10954,10993],{"className":10953},[1311],[1129,10955,10957,10971,10979],{"className":10956,"style":1530},[1315],[1129,10958,10959,10962],{"style":1533},[1129,10960],{"className":10961,"style":1537},[1323],[1129,10963,10965],{"className":10964},[1328,1329,1330,1331],[1129,10966,10968],{"className":10967},[1172,1331],[1129,10969,1991],{"className":10970},[1172,1331],[1129,10972,10973,10976],{"style":1549},[1129,10974],{"className":10975,"style":1537},[1323],[1129,10977],{"className":10978,"style":1557},[1556],[1129,10980,10981,10984],{"style":1560},[1129,10982],{"className":10983,"style":1537},[1323],[1129,10985,10987],{"className":10986},[1328,1329,1330,1331],[1129,10988,10990],{"className":10989},[1172,1331],[1129,10991,1246],{"className":10992},[1172,1331],[1129,10994,1577],{"className":10995},[1576],[1129,10997,10999],{"className":10998},[1311],[1129,11000,11002],{"className":11001,"style":1584},[1315],[1129,11003],{},[1129,11005],{"className":11006},[1352,1516],[1129,11008],{"className":11009,"style":1734},[1277],[1129,11011,1994],{"className":11012},[2084],[1129,11014],{"className":11015,"style":1734},[1277],[1129,11017,11019,11022],{"className":11018},[1163],[1129,11020],{"className":11021,"style":10493},[1167],[1129,11023,11025,11028,11087],{"className":11024},[1172],[1129,11026],{"className":11027},[1344,1516],[1129,11029,11031],{"className":11030},[1461],[1129,11032,11034,11079],{"className":11033},[1307,1523],[1129,11035,11037,11076],{"className":11036},[1311],[1129,11038,11040,11054,11062],{"className":11039,"style":10512},[1315],[1129,11041,11042,11045],{"style":1533},[1129,11043],{"className":11044,"style":1537},[1323],[1129,11046,11048],{"className":11047},[1328,1329,1330,1331],[1129,11049,11051],{"className":11050},[1172,1331],[1129,11052,10341],{"className":11053},[1172,1331],[1129,11055,11056,11059],{"style":1549},[1129,11057],{"className":11058,"style":1537},[1323],[1129,11060],{"className":11061,"style":1557},[1556],[1129,11063,11064,11067],{"style":1560},[1129,11065],{"className":11066,"style":1537},[1323],[1129,11068,11070],{"className":11069},[1328,1329,1330,1331],[1129,11071,11073],{"className":11072},[1172,1331],[1129,11074,1978],{"className":11075,"style":2141},[1172,1173,1331],[1129,11077,1577],{"className":11078},[1576],[1129,11080,11082],{"className":11081},[1311],[1129,11083,11085],{"className":11084,"style":1584},[1315],[1129,11086],{},[1129,11088],{"className":11089},[1352,1516]," 可以拆成 ",[1129,11092,11094,11114],{"className":11093},[1132],[1129,11095,11097],{"className":11096},[1136],[1138,11098,11099],{"xmlns":1140},[1142,11100,11101,11111],{},[1145,11102,11103],{},[1458,11104,11105],{"scriptlevel":1377,"displaystyle":1249},[1461,11106,11107,11109],{},[1244,11108,1246],{},[1244,11110,1991],{},[1152,11112,11113],{"encoding":1154},"\\tfrac{1}{2}",[1129,11115,11117],{"className":11116,"ariaHidden":1159},[1158],[1129,11118,11120,11123],{"className":11119},[1163],[1129,11121],{"className":11122,"style":1506},[1167],[1129,11124,11126,11129,11188],{"className":11125},[1172],[1129,11127],{"className":11128},[1344,1516],[1129,11130,11132],{"className":11131},[1461],[1129,11133,11135,11180],{"className":11134},[1307,1523],[1129,11136,11138,11177],{"className":11137},[1311],[1129,11139,11141,11155,11163],{"className":11140,"style":1530},[1315],[1129,11142,11143,11146],{"style":1533},[1129,11144],{"className":11145,"style":1537},[1323],[1129,11147,11149],{"className":11148},[1328,1329,1330,1331],[1129,11150,11152],{"className":11151},[1172,1331],[1129,11153,1991],{"className":11154},[1172,1331],[1129,11156,11157,11160],{"style":1549},[1129,11158],{"className":11159,"style":1537},[1323],[1129,11161],{"className":11162,"style":1557},[1556],[1129,11164,11165,11168],{"style":1560},[1129,11166],{"className":11167,"style":1537},[1323],[1129,11169,11171],{"className":11170},[1328,1329,1330,1331],[1129,11172,11174],{"className":11173},[1172,1331],[1129,11175,1246],{"className":11176},[1172,1331],[1129,11178,1577],{"className":11179},[1576],[1129,11181,11183],{"className":11182},[1311],[1129,11184,11186],{"className":11185,"style":1584},[1315],[1129,11187],{},[1129,11189],{"className":11190},[1352,1516]," 和 ",[1129,11193,11195,11215],{"className":11194},[1132],[1129,11196,11198],{"className":11197},[1136],[1138,11199,11200],{"xmlns":1140},[1142,11201,11202,11212],{},[1145,11203,11204],{},[1458,11205,11206],{"scriptlevel":1377,"displaystyle":1249},[1461,11207,11208,11210],{},[1148,11209,1978],{},[1244,11211,10341],{},[1152,11213,11214],{"encoding":1154},"\\tfrac{\\theta}{4}",[1129,11216,11218],{"className":11217,"ariaHidden":1159},[1158],[1129,11219,11221,11224],{"className":11220},[1163],[1129,11222],{"className":11223,"style":10493},[1167],[1129,11225,11227,11230,11289],{"className":11226},[1172],[1129,11228],{"className":11229},[1344,1516],[1129,11231,11233],{"className":11232},[1461],[1129,11234,11236,11281],{"className":11235},[1307,1523],[1129,11237,11239,11278],{"className":11238},[1311],[1129,11240,11242,11256,11264],{"className":11241,"style":10512},[1315],[1129,11243,11244,11247],{"style":1533},[1129,11245],{"className":11246,"style":1537},[1323],[1129,11248,11250],{"className":11249},[1328,1329,1330,1331],[1129,11251,11253],{"className":11252},[1172,1331],[1129,11254,10341],{"className":11255},[1172,1331],[1129,11257,11258,11261],{"style":1549},[1129,11259],{"className":11260,"style":1537},[1323],[1129,11262],{"className":11263,"style":1557},[1556],[1129,11265,11266,11269],{"style":1560},[1129,11267],{"className":11268,"style":1537},[1323],[1129,11270,11272],{"className":11271},[1328,1329,1330,1331],[1129,11273,11275],{"className":11274},[1172,1331],[1129,11276,1978],{"className":11277,"style":2141},[1172,1173,1331],[1129,11279,1577],{"className":11280},[1576],[1129,11282,11284],{"className":11283},[1311],[1129,11285,11287],{"className":11286,"style":1584},[1315],[1129,11288],{},[1129,11290],{"className":11291},[1352,1516]," 两部分,于是把观测到的 125 拆成两块 ",[1129,11294,11296,11322],{"className":11295},[1132],[1129,11297,11299],{"className":11298},[1136],[1138,11300,11301],{"xmlns":1140},[1142,11302,11303,11319],{},[1145,11304,11305,11311,11313,11315,11317],{},[2563,11306,11307,11309],{},[1148,11308,6833],{},[1244,11310,1246],{},[1229,11312,1231],{},[1244,11314,1966],{},[1229,11316,1242],{},[1148,11318,1952],{},[1152,11320,11321],{"encoding":1154},"y_1 = 125 - z",[1129,11323,11325,11381,11399],{"className":11324,"ariaHidden":1159},[1158],[1129,11326,11328,11331,11372,11375,11378],{"className":11327},[1163],[1129,11329],{"className":11330,"style":1168},[1167],[1129,11332,11334,11337],{"className":11333},[1172],[1129,11335,6833],{"className":11336,"style":1174},[1172,1173],[1129,11338,11340],{"className":11339},[1303],[1129,11341,11343,11364],{"className":11342},[1307,1523],[1129,11344,11346,11361],{"className":11345},[1311],[1129,11347,11349],{"className":11348,"style":7638},[1315],[1129,11350,11352,11355],{"style":11351},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1129,11353],{"className":11354,"style":1324},[1323],[1129,11356,11358],{"className":11357},[1328,1329,1330,1331],[1129,11359,1246],{"className":11360},[1172,1331],[1129,11362,1577],{"className":11363},[1576],[1129,11365,11367],{"className":11366},[1311],[1129,11368,11370],{"className":11369,"style":2624},[1315],[1129,11371],{},[1129,11373],{"className":11374,"style":1278},[1277],[1129,11376,1231],{"className":11377},[1282],[1129,11379],{"className":11380,"style":1278},[1277],[1129,11382,11384,11387,11390,11393,11396],{"className":11383},[1163],[1129,11385],{"className":11386,"style":3801},[1167],[1129,11388,1966],{"className":11389},[1172],[1129,11391],{"className":11392,"style":1734},[1277],[1129,11394,1242],{"className":11395},[2084],[1129,11397],{"className":11398,"style":1734},[1277],[1129,11400,11402,11405],{"className":11401},[1163],[1129,11403],{"className":11404,"style":1202},[1167],[1129,11406,1952],{"className":11407,"style":2026},[1172,1173],[1129,11409,11411,11424],{"className":11410},[1132],[1129,11412,11414],{"className":11413},[1136],[1138,11415,11416],{"xmlns":1140},[1142,11417,11418,11422],{},[1145,11419,11420],{},[1148,11421,1952],{},[1152,11423,1952],{"encoding":1154},[1129,11425,11427],{"className":11426,"ariaHidden":1159},[1158],[1129,11428,11430,11433],{"className":11429},[1163],[1129,11431],{"className":11432,"style":1202},[1167],[1129,11434,1952],{"className":11435,"style":2026},[1172,1173],",对应概率分别为 ",[1129,11438,11440,11459],{"className":11439},[1132],[1129,11441,11443],{"className":11442},[1136],[1138,11444,11445],{"xmlns":1140},[1142,11446,11447,11457],{},[1145,11448,11449],{},[1458,11450,11451],{"scriptlevel":1377,"displaystyle":1249},[1461,11452,11453,11455],{},[1244,11454,1246],{},[1244,11456,1991],{},[1152,11458,11113],{"encoding":1154},[1129,11460,11462],{"className":11461,"ariaHidden":1159},[1158],[1129,11463,11465,11468],{"className":11464},[1163],[1129,11466],{"className":11467,"style":1506},[1167],[1129,11469,11471,11474,11533],{"className":11470},[1172],[1129,11472],{"className":11473},[1344,1516],[1129,11475,11477],{"className":11476},[1461],[1129,11478,11480,11525],{"className":11479},[1307,1523],[1129,11481,11483,11522],{"className":11482},[1311],[1129,11484,11486,11500,11508],{"className":11485,"style":1530},[1315],[1129,11487,11488,11491],{"style":1533},[1129,11489],{"className":11490,"style":1537},[1323],[1129,11492,11494],{"className":11493},[1328,1329,1330,1331],[1129,11495,11497],{"className":11496},[1172,1331],[1129,11498,1991],{"className":11499},[1172,1331],[1129,11501,11502,11505],{"style":1549},[1129,11503],{"className":11504,"style":1537},[1323],[1129,11506],{"className":11507,"style":1557},[1556],[1129,11509,11510,11513],{"style":1560},[1129,11511],{"className":11512,"style":1537},[1323],[1129,11514,11516],{"className":11515},[1328,1329,1330,1331],[1129,11517,11519],{"className":11518},[1172,1331],[1129,11520,1246],{"className":11521},[1172,1331],[1129,11523,1577],{"className":11524},[1576],[1129,11526,11528],{"className":11527},[1311],[1129,11529,11531],{"className":11530,"style":1584},[1315],[1129,11532],{},[1129,11534],{"className":11535},[1352,1516],[1129,11537,11539,11558],{"className":11538},[1132],[1129,11540,11542],{"className":11541},[1136],[1138,11543,11544],{"xmlns":1140},[1142,11545,11546,11556],{},[1145,11547,11548],{},[1458,11549,11550],{"scriptlevel":1377,"displaystyle":1249},[1461,11551,11552,11554],{},[1148,11553,1978],{},[1244,11555,10341],{},[1152,11557,11214],{"encoding":1154},[1129,11559,11561],{"className":11560,"ariaHidden":1159},[1158],[1129,11562,11564,11567],{"className":11563},[1163],[1129,11565],{"className":11566,"style":10493},[1167],[1129,11568,11570,11573,11632],{"className":11569},[1172],[1129,11571],{"className":11572},[1344,1516],[1129,11574,11576],{"className":11575},[1461],[1129,11577,11579,11624],{"className":11578},[1307,1523],[1129,11580,11582,11621],{"className":11581},[1311],[1129,11583,11585,11599,11607],{"className":11584,"style":10512},[1315],[1129,11586,11587,11590],{"style":1533},[1129,11588],{"className":11589,"style":1537},[1323],[1129,11591,11593],{"className":11592},[1328,1329,1330,1331],[1129,11594,11596],{"className":11595},[1172,1331],[1129,11597,10341],{"className":11598},[1172,1331],[1129,11600,11601,11604],{"style":1549},[1129,11602],{"className":11603,"style":1537},[1323],[1129,11605],{"className":11606,"style":1557},[1556],[1129,11608,11609,11612],{"style":1560},[1129,11610],{"className":11611,"style":1537},[1323],[1129,11613,11615],{"className":11614},[1328,1329,1330,1331],[1129,11616,11618],{"className":11617},[1172,1331],[1129,11619,1978],{"className":11620,"style":2141},[1172,1173,1331],[1129,11622,1577],{"className":11623},[1576],[1129,11625,11627],{"className":11626},[1311],[1129,11628,11630],{"className":11629,"style":1584},[1315],[1129,11631],{},[1129,11633],{"className":11634},[1352,1516],",其中 ",[1129,11637,11639,11652],{"className":11638},[1132],[1129,11640,11642],{"className":11641},[1136],[1138,11643,11644],{"xmlns":1140},[1142,11645,11646,11650],{},[1145,11647,11648],{},[1148,11649,1952],{},[1152,11651,1952],{"encoding":1154},[1129,11653,11655],{"className":11654,"ariaHidden":1159},[1158],[1129,11656,11658,11661],{"className":11657},[1163],[1129,11659],{"className":11660,"style":1202},[1167],[1129,11662,1952],{"className":11663,"style":2026},[1172,1173]," 就是看不到的隐变量。",[1091,11666,11667,11670,11671,1256],{},[1101,11668,11669],{},"完全似然函数","可以写成(带隐变量 ",[1129,11672,11674,11687],{"className":11673},[1132],[1129,11675,11677],{"className":11676},[1136],[1138,11678,11679],{"xmlns":1140},[1142,11680,11681,11685],{},[1145,11682,11683],{},[1148,11684,1952],{},[1152,11686,1952],{"encoding":1154},[1129,11688,11690],{"className":11689,"ariaHidden":1159},[1158],[1129,11691,11693,11696],{"className":11692},[1163],[1129,11694],{"className":11695,"style":1202},[1167],[1129,11697,1952],{"className":11698,"style":2026},[1172,1173],[1091,11700,11701],{},[1129,11702,11704,11828],{"className":11703},[1132],[1129,11705,11707],{"className":11706},[1136],[1138,11708,11709],{"xmlns":1140},[1142,11710,11711,11825],{},[1145,11712,11713,11716,11718,11720,11722,11725,11747,11763,11786,11809],{},[1148,11714,11715],{},"L",[1229,11717,1250],{"stretchy":1249},[1148,11719,1978],{},[1229,11721,1256],{"stretchy":1249},[1229,11723,11724],{},"∝",[1233,11726,11727,11739],{},[1145,11728,11729,11731,11737],{},[1229,11730,1250],{"fence":1159},[1461,11732,11733,11735],{},[1244,11734,1246],{},[1244,11736,1991],{},[1229,11738,1256],{"fence":1159},[1145,11740,11741,11743,11745],{},[1244,11742,1966],{},[1229,11744,1242],{},[1148,11746,1952],{},[1233,11748,11749,11761],{},[1145,11750,11751,11753,11759],{},[1229,11752,1250],{"fence":1159},[1461,11754,11755,11757],{},[1148,11756,1978],{},[1244,11758,10341],{},[1229,11760,1256],{"fence":1159},[1148,11762,1952],{},[1233,11764,11765,11783],{},[1145,11766,11767,11769,11781],{},[1229,11768,1250],{"fence":1159},[1461,11770,11771,11779],{},[1145,11772,11773,11775,11777],{},[1244,11774,1246],{},[1229,11776,1242],{},[1148,11778,1978],{},[1244,11780,10341],{},[1229,11782,1256],{"fence":1159},[1244,11784,11785],{},"18",[1233,11787,11788,11806],{},[1145,11789,11790,11792,11804],{},[1229,11791,1250],{"fence":1159},[1461,11793,11794,11802],{},[1145,11795,11796,11798,11800],{},[1244,11797,1246],{},[1229,11799,1242],{},[1148,11801,1978],{},[1244,11803,10341],{},[1229,11805,1256],{"fence":1159},[1244,11807,11808],{},"20",[1233,11810,11811,11823],{},[1145,11812,11813,11815,11821],{},[1229,11814,1250],{"fence":1159},[1461,11816,11817,11819],{},[1148,11818,1978],{},[1244,11820,10341],{},[1229,11822,1256],{"fence":1159},[1244,11824,2297],{},[1152,11826,11827],{"encoding":1154},"L(\\theta) \\propto 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",[1129,13694,13696,13709],{"className":13695},[1132],[1129,13697,13699],{"className":13698},[1136],[1138,13700,13701],{"xmlns":1140},[1142,13702,13703,13707],{},[1145,13704,13705],{},[1148,13706,9025],{},[1152,13708,9025],{"encoding":1154},[1129,13710,13712],{"className":13711,"ariaHidden":1159},[1158],[1129,13713,13715,13719],{"className":13714},[1163],[1129,13716],{"className":13717,"style":13718},[1167],"height:0.8778em;vertical-align:-0.1944em;",[1129,13720,9025],{"className":13721},[1172,1173],"(即上面对数似然把 ",[1129,13724,13726,13739],{"className":13725},[1132],[1129,13727,13729],{"className":13728},[1136],[1138,13730,13731],{"xmlns":1140},[1142,13732,13733,13737],{},[1145,13734,13735],{},[1148,13736,1952],{},[1152,13738,1952],{"encoding":1154},[1129,13740,13742],{"className":13741,"ariaHidden":1159},[1158],[1129,13743,13745,13748],{"className":13744},[1163],[1129,13746],{"className":13747,"style":1202},[1167],[1129,13749,1952],{"className":13750,"style":2026},[1172,1173]," 换成 ",[1129,13753,13755,13779],{"className":13754},[1132],[1129,13756,13758],{"className":13757},[1136],[1138,13759,13760],{"xmlns":1140},[1142,13761,13762,13776],{},[1145,13763,13764],{},[1233,13765,13766,13768],{},[1148,13767,1952],{},[1145,13769,13770,13772,13774],{},[1229,13771,1250],{"stretchy":1249},[1148,13773,1959],{},[1229,13775,1256],{"stretchy":1249},[1152,13777,13778],{"encoding":1154},"z^{(i)}",[1129,13780,13782],{"className":13781,"ariaHidden":1159},[1158],[1129,13783,13785,13788],{"className":13784},[1163],[1129,13786],{"className":13787,"style":2019},[1167],[1129,13789,13791,13794],{"className":13790},[1172],[1129,13792,1952],{"className":13793,"style":2026},[1172,1173],[1129,13795,13797],{"className":13796},[1303],[1129,13798,13800],{"className":13799},[1307],[1129,13801,13803],{"className":13802},[1311],[1129,13804,13806],{"className":13805,"style":2019},[1315],[1129,13807,13808,13811],{"style":1319},[1129,13809],{"className":13810,"style":1324},[1323],[1129,13812,13814],{"className":13813},[1328,1329,1330,1331],[1129,13815,13817,13820,13823],{"className":13816},[1172,1331],[1129,13818,1250],{"className":13819},[1344,1331],[1129,13821,1959],{"className":13822},[1172,1173,1331],[1129,13824,1256],{"className":13825},[1352,1331],")求 ",[1129,13828,13830,13843],{"className":13829},[1132],[1129,13831,13833],{"className":13832},[1136],[1138,13834,13835],{"xmlns":1140},[1142,13836,13837,13841],{},[1145,13838,13839],{},[1148,13840,1978],{},[1152,13842,9982],{"encoding":1154},[1129,13844,13846],{"className":13845,"ariaHidden":1159},[1158],[1129,13847,13849,13852],{"className":13848},[1163],[1129,13850],{"className":13851,"style":2850},[1167],[1129,13853,1978],{"className":13854,"style":2141},[1172,1173]," 的偏导并令其为 0",[1091,13857,13858],{},[1129,13859,13861,13976],{"className":13860},[1132],[1129,13862,13864],{"className":13863},[1136],[1138,13865,13866],{"xmlns":1140},[1142,13867,13868,13973],{},[1145,13869,13870,13881,13884,13886,13898,13900,13902,13904,13906,13908,13910,13912,13915,13917,13919,13921,13923,13925,13927,13929,13931,13933,13955,13957,13969,13971],{},[1461,13871,13872,13875],{},[1148,13873,13874],{"mathvariant":4575},"∂",[1145,13876,13877,13879],{},[1148,13878,13874],{"mathvariant":4575},[1148,13880,1978],{},[1229,13882,3077],{"fence":1249,"stretchy":1159,"minsize":13883,"maxsize":13883},"1.8em",[1229,13885,1250],{"stretchy":1249},[1233,13887,13888,13890],{},[1148,13889,1952],{},[1145,13891,13892,13894,13896],{},[1229,13893,1250],{"stretchy":1249},[1148,13895,1959],{},[1229,13897,1256],{"stretchy":1249},[1229,13899,1994],{},[1244,13901,2297],{},[1229,13903,1256],{"stretchy":1249},[1148,13905,9080],{},[1229,13907,1473],{},[1148,13909,1978],{},[1229,13911,1994],{},[1244,13913,13914],{},"38",[1148,13916,9080],{},[1229,13918,1473],{},[1229,13920,1250],{"stretchy":1249},[1244,13922,1246],{},[1229,13924,1242],{},[1148,13926,1978],{},[1229,13928,1256],{"stretchy":1249},[1229,13930,3086],{"fence":1249,"stretchy":1159,"minsize":13883,"maxsize":13883},[1229,13932,1231],{},[1461,13934,13935,13953],{},[1145,13936,13937,13949,13951],{},[1233,13938,13939,13941],{},[1148,13940,1952],{},[1145,13942,13943,13945,13947],{},[1229,13944,1250],{"stretchy":1249},[1148,13946,1959],{},[1229,13948,1256],{"stretchy":1249},[1229,13950,1994],{},[1244,13952,2297],{},[1148,13954,1978],{},[1229,13956,1242],{},[1461,13958,13959,13961],{},[1244,13960,13914],{},[1145,13962,13963,13965,13967],{},[1244,13964,1246],{},[1229,13966,1242],{},[1148,13968,1978],{},[1229,13970,1231],{},[1244,13972,1377],{},[1152,13974,13975],{"encoding":1154},"\\frac{\\partial}{\\partial\\theta}\\Big[(z^{(i)}+34)\\log\\theta + 38\\log(1-\\theta)\\Big] = \\frac{z^{(i)}+34}{\\theta} - \\frac{38}{1-\\theta} = 0",[1129,13977,13979,14114,14149,14181,14208,14333,14424],{"className":13978,"ariaHidden":1159},[1158],[1129,13980,13982,13986,14057,14064,14067,14105,14108,14111],{"className":13981},[1163],[1129,13983],{"className":13984,"style":13985},[1167],"height:1.8em;vertical-align:-0.65em;",[1129,13987,13989,13992,14054],{"className":13988},[1172],[1129,13990],{"className":13991},[1344,1516],[1129,13993,13995],{"className":13994},[1461],[1129,13996,13998,14046],{"className":13997},[1307,1523],[1129,13999,14001,14043],{"className":14000},[1311],[1129,14002,14004,14021,14029],{"className":14003,"style":10512},[1315],[1129,14005,14006,14009],{"style":1533},[1129,14007],{"className":14008,"style":1537},[1323],[1129,14010,14012],{"className":14011},[1328,1329,1330,1331],[1129,14013,14015,14018],{"className":14014},[1172,1331],[1129,14016,13874],{"className":14017,"style":2860},[1172,1331],[1129,14019,1978],{"className":14020,"style":2141},[1172,1173,1331],[1129,14022,14023,14026],{"style":1549},[1129,14024],{"className":14025,"style":1537},[1323],[1129,14027],{"className":14028,"style":1557},[1556],[1129,14030,14031,14034],{"style":1560},[1129,14032],{"className":14033,"style":1537},[1323],[1129,14035,14037],{"className":14036},[1328,1329,1330,1331],[1129,14038,14040],{"className":14039},[1172,1331],[1129,14041,13874],{"className":14042,"style":2860},[1172,1331],[1129,14044,1577],{"className":14045},[1576],[1129,14047,14049],{"className":14048},[1311],[1129,14050,14052],{"className":14051,"style":1584},[1315],[1129,14053],{},[1129,14055],{"className":14056},[1352,1516],[1129,14058,14060],{"className":14059},[1172],[1129,14061,3077],{"className":14062},[4900,14063],"size2",[1129,14065,1250],{"className":14066},[1344],[1129,14068,14070,14073],{"className":14069},[1172],[1129,14071,1952],{"className":14072,"style":2026},[1172,1173],[1129,14074,14076],{"className":14075},[1303],[1129,14077,14079],{"className":14078},[1307],[1129,14080,14082],{"className":14081},[1311],[1129,14083,14085],{"className":14084,"style":2019},[1315],[1129,14086,14087,14090],{"style":1319},[1129,14088],{"className":14089,"style":1324},[1323],[1129,14091,14093],{"className":14092},[1328,1329,1330,1331],[1129,14094,14096,14099,14102],{"className":14095},[1172,1331],[1129,14097,1250],{"className":14098},[1344,1331],[1129,14100,1959],{"className":14101},[1172,1173,1331],[1129,14103,1256],{"className":14104},[1352,1331],[1129,14106],{"className":14107,"style":1734},[1277],[1129,14109,1994],{"className":14110},[2084],[1129,14112],{"className":14113,"style":1734},[1277],[1129,14115,14117,14120,14123,14126,14129,14134,14137,14140,14143,14146],{"className":14116},[1163],[1129,14118],{"className":14119,"style":1414},[1167],[1129,14121,2297],{"className":14122},[1172],[1129,14124,1256],{"className":14125},[1352],[1129,14127],{"className":14128,"style":1431},[1277],[1129,14130,9354,14132],{"className":14131},[1596],[1129,14133,1150],{"style":9357},[1129,14135],{"className":14136,"style":1431},[1277],[1129,14138,1978],{"className":14139,"style":2141},[1172,1173],[1129,14141],{"className":14142,"style":1734},[1277],[1129,14144,1994],{"className":14145},[2084],[1129,14147],{"className":14148,"style":1734},[1277],[1129,14150,14152,14155,14158,14161,14166,14169,14172,14175,14178],{"className":14151},[1163],[1129,14153],{"className":14154,"style":1414},[1167],[1129,14156,13914],{"className":14157},[1172],[1129,14159],{"className":14160,"style":1431},[1277],[1129,14162,9354,14164],{"className":14163},[1596],[1129,14165,1150],{"style":9357},[1129,14167,1250],{"className":14168},[1344],[1129,14170,1246],{"className":14171},[1172],[1129,14173],{"className":14174,"style":1734},[1277],[1129,14176,1242],{"className":14177},[2084],[1129,14179],{"className":14180,"style":1734},[1277],[1129,14182,14184,14187,14190,14193,14199,14202,14205],{"className":14183},[1163],[1129,14185],{"className":14186,"style":13985},[1167],[1129,14188,1978],{"className":14189,"style":2141},[1172,1173],[1129,14191,1256],{"className":14192},[1352],[1129,14194,14196],{"className":14195},[1172],[1129,14197,3086],{"className":14198},[4900,14063],[1129,14200],{"className":14201,"style":1278},[1277],[1129,14203,1231],{"className":14204},[1282],[1129,14206],{"className":14207,"style":1278},[1277],[1129,14209,14211,14215,14324,14327,14330],{"className":14210},[1163],[1129,14212],{"className":14213,"style":14214},[1167],"height:1.4157em;vertical-align:-0.345em;",[1129,14216,14218,14221,14321],{"className":14217},[1172],[1129,14219],{"className":14220},[1344,1516],[1129,14222,14224],{"className":14223},[1461],[1129,14225,14227,14313],{"className":14226},[1307,1523],[1129,14228,14230,14310],{"className":14229},[1311],[1129,14231,14233,14247,14255],{"className":14232,"style":13281},[1315],[1129,14234,14235,14238],{"style":1533},[1129,14236],{"className":14237,"style":1537},[1323],[1129,14239,14241],{"className":14240},[1328,1329,1330,1331],[1129,14242,14244],{"className":14243},[1172,1331],[1129,14245,1978],{"className":14246,"style":2141},[1172,1173,1331],[1129,14248,14249,14252],{"style":1549},[1129,14250],{"className":14251,"style":1537},[1323],[1129,14253],{"className":14254,"style":1557},[1556],[1129,14256,14257,14260],{"style":1560},[1129,14258],{"className":14259,"style":1537},[1323],[1129,14261,14263],{"className":14262},[1328,1329,1330,1331],[1129,14264,14266,14304,14307],{"className":14265},[1172,1331],[1129,14267,14269,14272],{"className":14268},[1172,1331],[1129,14270,1952],{"className":14271,"style":2026},[1172,1173,1331],[1129,14273,14275],{"className":14274},[1303],[1129,14276,14278],{"className":14277},[1307],[1129,14279,14281],{"className":14280},[1311],[1129,14282,14284],{"className":14283,"style":13333},[1315],[1129,14285,14286,14289],{"style":13336},[1129,14287],{"className":14288,"style":9313},[1323],[1129,14290,14292],{"className":14291},[1328,9317,5723,1331],[1129,14293,14295,14298,14301],{"className":14294},[1172,1331],[1129,14296,1250],{"className":14297},[1344,1331],[1129,14299,1959],{"className":14300},[1172,1173,1331],[1129,14302,1256],{"className":14303},[1352,1331],[1129,14305,1994],{"className":14306},[2084,1331],[1129,14308,2297],{"className":14309},[1172,1331],[1129,14311,1577],{"className":14312},[1576],[1129,14314,14316],{"className":14315},[1311],[1129,14317,14319],{"className":14318,"style":1584},[1315],[1129,14320],{},[1129,14322],{"className":14323},[1352,1516],[1129,14325],{"className":14326,"style":1734},[1277],[1129,14328,1242],{"className":14329},[2084],[1129,14331],{"className":14332,"style":1734},[1277],[1129,14334,14336,14340,14415,14418,14421],{"className":14335},[1163],[1129,14337],{"className":14338,"style":14339},[1167],"height:1.2484em;vertical-align:-0.4033em;",[1129,14341,14343,14346,14412],{"className":14342},[1172],[1129,14344],{"className":14345},[1344,1516],[1129,14347,14349],{"className":14348},[1461],[1129,14350,14352,14403],{"className":14351},[1307,1523],[1129,14353,14355,14400],{"className":14354},[1311],[1129,14356,14358,14378,14386],{"className":14357,"style":1530},[1315],[1129,14359,14360,14363],{"style":1533},[1129,14361],{"className":14362,"style":1537},[1323],[1129,14364,14366],{"className":14365},[1328,1329,1330,1331],[1129,14367,14369,14372,14375],{"className":14368},[1172,1331],[1129,14370,1246],{"className":14371},[1172,1331],[1129,14373,1242],{"className":14374},[2084,1331],[1129,14376,1978],{"className":14377,"style":2141},[1172,1173,1331],[1129,14379,14380,14383],{"style":1549},[1129,14381],{"className":14382,"style":1537},[1323],[1129,14384],{"className":14385,"style":1557},[1556],[1129,14387,14388,14391],{"style":1560},[1129,14389],{"className":14390,"style":1537},[1323],[1129,14392,14394],{"className":14393},[1328,1329,1330,1331],[1129,14395,14397],{"className":14396},[1172,1331],[1129,14398,13914],{"className":14399},[1172,1331],[1129,14401,1577],{"className":14402},[1576],[1129,14404,14406],{"className":14405},[1311],[1129,14407,14410],{"className":14408,"style":14409},[1315],"height:0.4033em;",[1129,14411],{},[1129,14413],{"className":14414},[1352,1516],[1129,14416],{"className":14417,"style":1278},[1277],[1129,14419,1231],{"className":14420},[1282],[1129,14422],{"className":14423,"style":1278},[1277],[1129,14425,14427,14430],{"className":14426},[1163],[1129,14428],{"className":14429,"style":2074},[1167],[1129,14431,1377],{"className":14432},[1172],[1091,14434,14435],{},"解得迭代公式",[1091,14437,14438],{},[1129,14439,14441,14553],{"className":14440},[1132],[1129,14442,14444],{"className":14443},[1136],[1138,14445,14446],{"xmlns":1140},[1142,14447,14448,14550],{},[1145,14449,14450,14466,14468,14510,14512],{},[1233,14451,14452,14454],{},[1148,14453,1978],{},[1145,14455,14456,14458,14460,14462,14464],{},[1229,14457,1250],{"stretchy":1249},[1148,14459,1959],{},[1229,14461,1994],{},[1244,14463,1246],{},[1229,14465,1256],{"stretchy":1249},[1229,14467,1231],{},[1461,14469,14470,14488],{},[1145,14471,14472,14484,14486],{},[1233,14473,14474,14476],{},[1148,14475,1952],{},[1145,14477,14478,14480,14482],{},[1229,14479,1250],{"stretchy":1249},[1148,14481,1959],{},[1229,14483,1256],{"stretchy":1249},[1229,14485,1994],{},[1244,14487,2297],{},[1145,14489,14490,14502,14504,14506,14508],{},[1233,14491,14492,14494],{},[1148,14493,1952],{},[1145,14495,14496,14498,14500],{},[1229,14497,1250],{"stretchy":1249},[1148,14499,1959],{},[1229,14501,1256],{"stretchy":1249},[1229,14503,1994],{},[1244,14505,2297],{},[1229,14507,1994],{},[1244,14509,13914],{},[1229,14511,1231],{},[1461,14513,14514,14532],{},[1145,14515,14516,14528,14530],{},[1233,14517,14518,14520],{},[1148,14519,1952],{},[1145,14521,14522,14524,14526],{},[1229,14523,1250],{"stretchy":1249},[1148,14525,1959],{},[1229,14527,1256],{"stretchy":1249},[1229,14529,1994],{},[1244,14531,2297],{},[1145,14533,14534,14546,14548],{},[1233,14535,14536,14538],{},[1148,14537,1952],{},[1145,14539,14540,14542,14544],{},[1229,14541,1250],{"stretchy":1249},[1148,14543,1959],{},[1229,14545,1256],{"stretchy":1249},[1229,14547,1994],{},[1244,14549,2316],{},[1152,14551,14552],{"encoding":1154},"\\theta^{(i+1)} = \\frac{z^{(i)} + 34}{z^{(i)} + 34 + 38} = \\frac{z^{(i)} + 34}{z^{(i)} + 72}",[1129,14554,14556,14615,14786],{"className":14555,"ariaHidden":1159},[1158],[1129,14557,14559,14562,14606,14609,14612],{"className":14558},[1163],[1129,14560],{"className":14561,"style":2019},[1167],[1129,14563,14565,14568],{"className":14564},[1172],[1129,14566,1978],{"className":14567,"style":2141},[1172,1173],[1129,14569,14571],{"className":14570},[1303],[1129,14572,14574],{"className":14573},[1307],[1129,14575,14577],{"className":14576},[1311],[1129,14578,14580],{"className":14579,"style":2019},[1315],[1129,14581,14582,14585],{"style":1319},[1129,14583],{"className":14584,"style":1324},[1323],[1129,14586,14588],{"className":14587},[1328,1329,1330,1331],[1129,14589,14591,14594,14597,14600,14603],{"className":14590},[1172,1331],[1129,14592,1250],{"className":14593},[1344,1331],[1129,14595,1959],{"className":14596},[1172,1173,1331],[1129,14598,1994],{"className":14599},[2084,1331],[1129,14601,1246],{"className":14602},[1172,1331],[1129,14604,1256],{"className":14605},[1352,1331],[1129,14607],{"className":14608,"style":1278},[1277],[1129,14610,1231],{"className":14611},[1282],[1129,14613],{"className":14614,"style":1278},[1277],[1129,14616,14618,14621,14777,14780,14783],{"className":14617},[1163],[1129,14619],{"className":14620,"style":13541},[1167],[1129,14622,14624,14627,14774],{"className":14623},[1172],[1129,14625],{"className":14626},[1344,1516],[1129,14628,14630],{"className":14629},[1461],[1129,14631,14633,14766],{"className":14632},[1307,1523],[1129,14634,14636,14763],{"className":14635},[1311],[1129,14637,14639,14700,14708],{"className":14638,"style":13281},[1315],[1129,14640,14641,14644],{"style":13562},[1129,14642],{"className":14643,"style":1537},[1323],[1129,14645,14647],{"className":14646},[1328,1329,1330,1331],[1129,14648,14650,14688,14691,14694,14697],{"className":14649},[1172,1331],[1129,14651,14653,14656],{"className":14652},[1172,1331],[1129,14654,1952],{"className":14655,"style":2026},[1172,1173,1331],[1129,14657,14659],{"className":14658},[1303],[1129,14660,14662],{"className":14661},[1307],[1129,14663,14665],{"className":14664},[1311],[1129,14666,14668],{"className":14667,"style":9306},[1315],[1129,14669,14670,14673],{"style":9309},[1129,14671],{"className":14672,"style":9313},[1323],[1129,14674,14676],{"className":14675},[1328,9317,5723,1331],[1129,14677,14679,14682,14685],{"className":14678},[1172,1331],[1129,14680,1250],{"className":14681},[1344,1331],[1129,14683,1959],{"className":14684},[1172,1173,1331],[1129,14686,1256],{"className":14687},[1352,1331],[1129,14689,1994],{"className":14690},[2084,1331],[1129,14692,2297],{"className":14693},[1172,1331],[1129,14695,1994],{"className":14696},[2084,1331],[1129,14698,13914],{"className":14699},[1172,1331],[1129,14701,14702,14705],{"style":1549},[1129,14703],{"className":14704,"style":1537},[1323],[1129,14706],{"className":14707,"style":1557},[1556],[1129,14709,14710,14713],{"style":1560},[1129,14711],{"className":14712,"style":1537},[1323],[1129,14714,14716],{"className":14715},[1328,1329,1330,1331],[1129,14717,14719,14757,14760],{"className":14718},[1172,1331],[1129,14720,14722,14725],{"className":14721},[1172,1331],[1129,14723,1952],{"className":14724,"style":2026},[1172,1173,1331],[1129,14726,14728],{"className":14727},[1303],[1129,14729,14731],{"className":14730},[1307],[1129,14732,14734],{"className":14733},[1311],[1129,14735,14737],{"className":14736,"style":13333},[1315],[1129,14738,14739,14742],{"style":13336},[1129,14740],{"className":14741,"style":9313},[1323],[1129,14743,14745],{"className":14744},[1328,9317,5723,1331],[1129,14746,14748,14751,14754],{"className":14747},[1172,1331],[1129,14749,1250],{"className":14750},[1344,1331],[1129,14752,1959],{"className":14753},[1172,1173,1331],[1129,14755,1256],{"className":14756},[1352,1331],[1129,14758,1994],{"className":14759},[2084,1331],[1129,14761,2297],{"className":14762},[1172,1331],[1129,14764,1577],{"className":14765},[1576],[1129,14767,14769],{"className":14768},[1311],[1129,14770,14772],{"className":14771,"style":13682},[1315],[1129,14773],{},[1129,14775],{"className":14776},[1352,1516],[1129,14778],{"className":14779,"style":1278},[1277],[1129,14781,1231],{"className":14782},[1282],[1129,14784],{"className":14785,"style":1278},[1277],[1129,14787,14789,14792],{"className":14788},[1163],[1129,14790],{"className":14791,"style":13541},[1167],[1129,14793,14795,14798,14939],{"className":14794},[1172],[1129,14796],{"className":14797},[1344,1516],[1129,14799,14801],{"className":14800},[1461],[1129,14802,14804,14931],{"className":14803},[1307,1523],[1129,14805,14807,14928],{"className":14806},[1311],[1129,14808,14810,14865,14873],{"className":14809,"style":13281},[1315],[1129,14811,14812,14815],{"style":13562},[1129,14813],{"className":14814,"style":1537},[1323],[1129,14816,14818],{"className":14817},[1328,1329,1330,1331],[1129,14819,14821,14859,14862],{"className":14820},[1172,1331],[1129,14822,14824,14827],{"className":14823},[1172,1331],[1129,14825,1952],{"className":14826,"style":2026},[1172,1173,1331],[1129,14828,14830],{"className":14829},[1303],[1129,14831,14833],{"className":14832},[1307],[1129,14834,14836],{"className":14835},[1311],[1129,14837,14839],{"className":14838,"style":9306},[1315],[1129,14840,14841,14844],{"style":9309},[1129,14842],{"className":14843,"style":9313},[1323],[1129,14845,14847],{"className":14846},[1328,9317,5723,1331],[1129,14848,14850,14853,14856],{"className":14849},[1172,1331],[1129,14851,1250],{"className":14852},[1344,1331],[1129,14854,1959],{"className":14855},[1172,1173,1331],[1129,14857,1256],{"className":14858},[1352,1331],[1129,14860,1994],{"className":14861},[2084,1331],[1129,14863,2316],{"className":14864},[1172,1331],[1129,14866,14867,14870],{"style":1549},[1129,14868],{"className":14869,"style":1537},[1323],[1129,14871],{"className":14872,"style":1557},[1556],[1129,14874,14875,14878],{"style":1560},[1129,14876],{"className":14877,"style":1537},[1323],[1129,14879,14881],{"className":14880},[1328,1329,1330,1331],[1129,14882,14884,14922,14925],{"className":14883},[1172,1331],[1129,14885,14887,14890],{"className":14886},[1172,1331],[1129,14888,1952],{"className":14889,"style":2026},[1172,1173,1331],[1129,14891,14893],{"className":14892},[1303],[1129,14894,14896],{"className":14895},[1307],[1129,14897,14899],{"className":14898},[1311],[1129,14900,14902],{"className":14901,"style":13333},[1315],[1129,14903,14904,14907],{"style":13336},[1129,14905],{"className":14906,"style":9313},[1323],[1129,14908,14910],{"className":14909},[1328,9317,5723,1331],[1129,14911,14913,14916,14919],{"className":14912},[1172,1331],[1129,14914,1250],{"className":14915},[1344,1331],[1129,14917,1959],{"className":14918},[1172,1173,1331],[1129,14920,1256],{"className":14921},[1352,1331],[1129,14923,1994],{"className":14924},[2084,1331],[1129,14926,2297],{"className":14927},[1172,1331],[1129,14929,1577],{"className":14930},[1576],[1129,14932,14934],{"className":14933},[1311],[1129,14935,14937],{"className":14936,"style":13682},[1315],[1129,14938],{},[1129,14940],{"className":14941},[1352,1516],[1091,14943,14944,14945,14973],{},"反复用这两步迭代,",[1129,14946,14948,14961],{"className":14947},[1132],[1129,14949,14951],{"className":14950},[1136],[1138,14952,14953],{"xmlns":1140},[1142,14954,14955,14959],{},[1145,14956,14957],{},[1148,14958,1978],{},[1152,14960,9982],{"encoding":1154},[1129,14962,14964],{"className":14963,"ariaHidden":1159},[1158],[1129,14965,14967,14970],{"className":14966},[1163],[1129,14968],{"className":14969,"style":2850},[1167],[1129,14971,1978],{"className":14972,"style":2141},[1172,1173]," 就会收敛到极大似然估计。",[3512,14975,14977],{"id":14976},"例子二混合高斯模型gaussian-mixture-model-gmm","例子二:混合高斯模型(Gaussian Mixture Model, GMM)",[1091,14979,14980,14981,15178],{},"假设观测数据 ",[1129,14982,14984,15024],{"className":14983},[1132],[1129,14985,14987],{"className":14986},[1136],[1138,14988,14989],{"xmlns":1140},[1142,14990,14991,15021],{},[1145,14992,14993,14999,15001,15007,15009,15012,15014],{},[2563,14994,14995,14997],{},[1148,14996,6833],{},[1244,14998,1246],{},[1229,15000,1353],{"separator":1159},[2563,15002,15003,15005],{},[1148,15004,6833],{},[1244,15006,1991],{},[1229,15008,1353],{"separator":1159},[1229,15010,15011],{},"…",[1229,15013,1353],{"separator":1159},[2563,15015,15016,15018],{},[1148,15017,6833],{},[1148,15019,15020],{},"N",[1152,15022,15023],{"encoding":1154},"y_1, y_2, \\dots, y_N",[1129,15025,15027],{"className":15026,"ariaHidden":1159},[1158],[1129,15028,15030,15033,15073,15076,15079,15119,15122,15125,15128,15131,15134,15137],{"className":15029},[1163],[1129,15031],{"className":15032,"style":1168},[1167],[1129,15034,15036,15039],{"className":15035},[1172],[1129,15037,6833],{"className":15038,"style":1174},[1172,1173],[1129,15040,15042],{"className":15041},[1303],[1129,15043,15045,15065],{"className":15044},[1307,1523],[1129,15046,15048,15062],{"className":15047},[1311],[1129,15049,15051],{"className":15050,"style":7638},[1315],[1129,15052,15053,15056],{"style":11351},[1129,15054],{"className":15055,"style":1324},[1323],[1129,15057,15059],{"className":15058},[1328,1329,1330,1331],[1129,15060,1246],{"className":15061},[1172,1331],[1129,15063,1577],{"className":15064},[1576],[1129,15066,15068],{"className":15067},[1311],[1129,15069,15071],{"className":15070,"style":2624},[1315],[1129,15072],{},[1129,15074,1353],{"className":15075},[1427],[1129,15077],{"className":15078,"style":1431},[1277],[1129,15080,15082,15085],{"className":15081},[1172],[1129,15083,6833],{"className":15084,"style":1174},[1172,1173],[1129,15086,15088],{"className":15087},[1303],[1129,15089,15091,15111],{"className":15090},[1307,1523],[1129,15092,15094,15108],{"className":15093},[1311],[1129,15095,15097],{"className":15096,"style":7638},[1315],[1129,15098,15099,15102],{"style":11351},[1129,15100],{"className":15101,"style":1324},[1323],[1129,15103,15105],{"className":15104},[1328,1329,1330,1331],[1129,15106,1991],{"className":15107},[1172,1331],[1129,15109,1577],{"className":15110},[1576],[1129,15112,15114],{"className":15113},[1311],[1129,15115,15117],{"className":15116,"style":2624},[1315],[1129,15118],{},[1129,15120,1353],{"className":15121},[1427],[1129,15123],{"className":15124,"style":1431},[1277],[1129,15126,15011],{"className":15127},[4893],[1129,15129],{"className":15130,"style":1431},[1277],[1129,15132,1353],{"className":15133},[1427],[1129,15135],{"className":15136,"style":1431},[1277],[1129,15138,15140,15143],{"className":15139},[1172],[1129,15141,6833],{"className":15142,"style":1174},[1172,1173],[1129,15144,15146],{"className":15145},[1303],[1129,15147,15149,15170],{"className":15148},[1307,1523],[1129,15150,15152,15167],{"className":15151},[1311],[1129,15153,15156],{"className":15154,"style":15155},[1315],"height:0.3283em;",[1129,15157,15158,15161],{"style":11351},[1129,15159],{"className":15160,"style":1324},[1323],[1129,15162,15164],{"className":15163},[1328,1329,1330,1331],[1129,15165,15020],{"className":15166,"style":1348},[1172,1173,1331],[1129,15168,1577],{"className":15169},[1576],[1129,15171,15173],{"className":15172},[1311],[1129,15174,15176],{"className":15175,"style":2624},[1315],[1129,15177],{}," 由高斯混合模型生成:",[1091,15180,15181],{},[1129,15182,15184,15260],{"className":15183},[1132],[1129,15185,15187],{"className":15186},[1136],[1138,15188,15189],{"xmlns":1140},[1142,15190,15191,15257],{},[1145,15192,15193,15195,15197,15199,15201,15203,15205,15207,15222,15228,15230,15233,15235,15237,15239,15245,15247,15255],{},[1148,15194,6819],{},[1229,15196,1250],{"stretchy":1249},[1148,15198,6833],{},[1229,15200,4576],{},[1148,15202,1978],{},[1229,15204,1256],{"stretchy":1249},[1229,15206,1231],{},[2641,15208,15209,15211,15219],{},[1229,15210,9107],{},[1145,15212,15213,15215,15217],{},[1148,15214,2570],{},[1229,15216,1231],{},[1244,15218,1246],{},[1148,15220,15221],{},"K",[2563,15223,15224,15226],{},[1148,15225,2732],{},[1148,15227,2570],{},[1648,15229,1650],{},[1148,15231,15232],{},"ϕ",[1229,15234,1250],{"stretchy":1249},[1148,15236,6833],{},[1229,15238,4576],{},[2563,15240,15241,15243],{},[1148,15242,2567],{},[1148,15244,2570],{},[1229,15246,1353],{"separator":1159},[2641,15248,15249,15251,15253],{},[1148,15250,2645],{},[1148,15252,2570],{},[1244,15254,1991],{},[1229,15256,1256],{"stretchy":1249},[1152,15258,15259],{"encoding":1154},"P(y\\mid\\theta) = \\sum_{k=1}^{K} \\alpha_k\\, \\phi(y\\mid\\mu_k,\\sigma_k^2)",[1129,15261,15263,15287,15308,15444],{"className":15262,"ariaHidden":1159},[1158],[1129,15264,15266,15269,15272,15275,15278,15281,15284],{"className":15265},[1163],[1129,15267],{"className":15268,"style":1414},[1167],[1129,15270,6819],{"className":15271,"style":1299},[1172,1173],[1129,15273,1250],{"className":15274},[1344],[1129,15276,6833],{"className":15277,"style":1174},[1172,1173],[1129,15279],{"className":15280,"style":1278},[1277],[1129,15282,4576],{"className":15283},[1282],[1129,15285],{"className":15286,"style":1278},[1277],[1129,15288,15290,15293,15296,15299,15302,15305],{"className":15289},[1163],[1129,15291],{"className":15292,"style":1414},[1167],[1129,15294,1978],{"className":15295,"style":2141},[1172,1173],[1129,15297,1256],{"className":15298},[1352],[1129,15300],{"className":15301,"style":1278},[1277],[1129,15303,1231],{"className":15304},[1282],[1129,15306],{"className":15307,"style":1278},[1277],[1129,15309,15311,15315,15380,15383,15423,15426,15429,15432,15435,15438,15441],{"className":15310},[1163],[1129,15312],{"className":15313,"style":15314},[1167],"height:1.2809em;vertical-align:-0.2997em;",[1129,15316,15318,15321],{"className":15317},[1596],[1129,15319,9107],{"className":15320,"style":9429},[1596,6765,6766],[1129,15322,15324],{"className":15323},[1303],[1129,15325,15327,15372],{"className":15326},[1307,1523],[1129,15328,15330,15369],{"className":15329},[1311],[1129,15331,15334,15354],{"className":15332,"style":15333},[1315],"height:0.9812em;",[1129,15335,15336,15339],{"style":9445},[1129,15337],{"className":15338,"style":1324},[1323],[1129,15340,15342],{"className":15341},[1328,1329,1330,1331],[1129,15343,15345,15348,15351],{"className":15344},[1172,1331],[1129,15346,2570],{"className":15347,"style":2614},[1172,1173,1331],[1129,15349,1231],{"className":15350},[1282,1331],[1129,15352,1246],{"className":15353},[1172,1331],[1129,15355,15357,15360],{"style":15356},"top:-3.2029em;margin-right:0.05em;",[1129,15358],{"className":15359,"style":1324},[1323],[1129,15361,15363],{"className":15362},[1328,1329,1330,1331],[1129,15364,15366],{"className":15365},[1172,1331],[1129,15367,15221],{"className":15368,"style":9278},[1172,1173,1331],[1129,15370,1577],{"className":15371},[1576],[1129,15373,15375],{"className":15374},[1311],[1129,15376,15378],{"className":15377,"style":9467},[1315],[1129,15379],{},[1129,15381],{"className":15382,"style":1431},[1277],[1129,15384,15386,15389],{"className":15385},[1172],[1129,15387,2732],{"className":15388,"style":2754},[1172,1173],[1129,15390,15392],{"className":15391},[1303],[1129,15393,15395,15415],{"className":15394},[1307,1523],[1129,15396,15398,15412],{"className":15397},[1311],[1129,15399,15401],{"className":15400,"style":2601},[1315],[1129,15402,15403,15406],{"style":2769},[1129,15404],{"className":15405,"style":1324},[1323],[1129,15407,15409],{"className":15408},[1328,1329,1330,1331],[1129,15410,2570],{"className":15411,"style":2614},[1172,1173,1331],[1129,15413,1577],{"className":15414},[1576],[1129,15416,15418],{"className":15417},[1311],[1129,15419,15421],{"className":15420,"style":2624},[1315],[1129,15422],{},[1129,15424],{"className":15425,"style":1431},[1277],[1129,15427,15232],{"className":15428},[1172,1173],[1129,15430,1250],{"className":15431},[1344],[1129,15433,6833],{"className":15434,"style":1174},[1172,1173],[1129,15436],{"className":15437,"style":1278},[1277],[1129,15439,4576],{"className":15440},[1282],[1129,15442],{"className":15443,"style":1278},[1277],[1129,15445,15447,15450,15490,15493,15496,15547],{"className":15446},[1163],[1129,15448],{"className":15449,"style":2662},[1167],[1129,15451,15453,15456],{"className":15452},[1172],[1129,15454,2567],{"className":15455},[1172,1173],[1129,15457,15459],{"className":15458},[1303],[1129,15460,15462,15482],{"className":15461},[1307,1523],[1129,15463,15465,15479],{"className":15464},[1311],[1129,15466,15468],{"className":15467,"style":2601},[1315],[1129,15469,15470,15473],{"style":2604},[1129,15471],{"className":15472,"style":1324},[1323],[1129,15474,15476],{"className":15475},[1328,1329,1330,1331],[1129,15477,2570],{"className":15478,"style":2614},[1172,1173,1331],[1129,15480,1577],{"className":15481},[1576],[1129,15483,15485],{"className":15484},[1311],[1129,15486,15488],{"className":15487,"style":2624},[1315],[1129,15489],{},[1129,15491,1353],{"className":15492},[1427],[1129,15494],{"className":15495,"style":1431},[1277],[1129,15497,15499,15502],{"className":15498},[1172],[1129,15500,2645],{"className":15501,"style":1174},[1172,1173],[1129,15503,15505],{"className":15504},[1303],[1129,15506,15508,15539],{"className":15507},[1307,1523],[1129,15509,15511,15536],{"className":15510},[1311],[1129,15512,15514,15525],{"className":15513,"style":1316},[1315],[1129,15515,15516,15519],{"style":2683},[1129,15517],{"className":15518,"style":1324},[1323],[1129,15520,15522],{"className":15521},[1328,1329,1330,1331],[1129,15523,2570],{"className":15524,"style":2614},[1172,1173,1331],[1129,15526,15527,15530],{"style":1319},[1129,15528],{"className":15529,"style":1324},[1323],[1129,15531,15533],{"className":15532},[1328,1329,1330,1331],[1129,15534,1991],{"className":15535},[1172,1331],[1129,15537,1577],{"className":15538},[1576],[1129,15540,15542],{"className":15541},[1311],[1129,15543,15545],{"className":15544,"style":2713},[1315],[1129,15546],{},[1129,15548,1256],{"className":15549},[1352],[1091,15551,9599,15552,15621,15622,15650,15651,2627,15744,7819,15886,15621,16060,16088,16089,1603],{},[1129,15553,15555,15572],{"className":15554},[1132],[1129,15556,15558],{"className":15557},[1136],[1138,15559,15560],{"xmlns":1140},[1142,15561,15562,15570],{},[1145,15563,15564],{},[2563,15565,15566,15568],{},[1148,15567,2732],{},[1148,15569,2570],{},[1152,15571,2737],{"encoding":1154},[1129,15573,15575],{"className":15574,"ariaHidden":1159},[1158],[1129,15576,15578,15581],{"className":15577},[1163],[1129,15579],{"className":15580,"style":2747},[1167],[1129,15582,15584,15587],{"className":15583},[1172],[1129,15585,2732],{"className":15586,"style":2754},[1172,1173],[1129,15588,15590],{"className":15589},[1303],[1129,15591,15593,15613],{"className":15592},[1307,1523],[1129,15594,15596,15610],{"className":15595},[1311],[1129,15597,15599],{"className":15598,"style":2601},[1315],[1129,15600,15601,15604],{"style":2769},[1129,15602],{"className":15603,"style":1324},[1323],[1129,15605,15607],{"className":15606},[1328,1329,1330,1331],[1129,15608,2570],{"className":15609,"style":2614},[1172,1173,1331],[1129,15611,1577],{"className":15612},[1576],[1129,15614,15616],{"className":15615},[1311],[1129,15617,15619],{"className":15618,"style":2624},[1315],[1129,15620],{}," 是第 ",[1129,15623,15625,15638],{"className":15624},[1132],[1129,15626,15628],{"className":15627},[1136],[1138,15629,15630],{"xmlns":1140},[1142,15631,15632,15636],{},[1145,15633,15634],{},[1148,15635,2570],{},[1152,15637,2570],{"encoding":1154},[1129,15639,15641],{"className":15640,"ariaHidden":1159},[1158],[1129,15642,15644,15647],{"className":15643},[1163],[1129,15645],{"className":15646,"style":2850},[1167],[1129,15648,2570],{"className":15649,"style":2614},[1172,1173]," 个分模型的混合系数,满足 ",[1129,15652,15654,15676],{"className":15653},[1132],[1129,15655,15657],{"className":15656},[1136],[1138,15658,15659],{"xmlns":1140},[1142,15660,15661,15673],{},[1145,15662,15663,15669,15671],{},[2563,15664,15665,15667],{},[1148,15666,2732],{},[1148,15668,2570],{},[1229,15670,3677],{},[1244,15672,1377],{},[1152,15674,15675],{"encoding":1154},"\\alpha_k \\ge 0",[1129,15677,15679,15735],{"className":15678,"ariaHidden":1159},[1158],[1129,15680,15682,15686,15726,15729,15732],{"className":15681},[1163],[1129,15683],{"className":15684,"style":15685},[1167],"height:0.786em;vertical-align:-0.15em;",[1129,15687,15689,15692],{"className":15688},[1172],[1129,15690,2732],{"className":15691,"style":2754},[1172,1173],[1129,15693,15695],{"className":15694},[1303],[1129,15696,15698,15718],{"className":15697},[1307,1523],[1129,15699,15701,15715],{"className":15700},[1311],[1129,15702,15704],{"className":15703,"style":2601},[1315],[1129,15705,15706,15709],{"style":2769},[1129,15707],{"className":15708,"style":1324},[1323],[1129,15710,15712],{"className":15711},[1328,1329,1330,1331],[1129,15713,2570],{"className":15714,"style":2614},[1172,1173,1331],[1129,15716,1577],{"className":15717},[1576],[1129,15719,15721],{"className":15720},[1311],[1129,15722,15724],{"className":15723,"style":2624},[1315],[1129,15725],{},[1129,15727],{"className":15728,"style":1278},[1277],[1129,15730,3677],{"className":15731},[1282],[1129,15733],{"className":15734,"style":1278},[1277],[1129,15736,15738,15741],{"className":15737},[1163],[1129,15739],{"className":15740,"style":2074},[1167],[1129,15742,1377],{"className":15743},[1172],[1129,15745,15747,15775],{"className":15746},[1132],[1129,15748,15750],{"className":15749},[1136],[1138,15751,15752],{"xmlns":1140},[1142,15753,15754,15772],{},[1145,15755,15756,15762,15768,15770],{},[2563,15757,15758,15760],{},[1229,15759,9107],{},[1148,15761,2570],{},[2563,15763,15764,15766],{},[1148,15765,2732],{},[1148,15767,2570],{},[1229,15769,1231],{},[1244,15771,1246],{},[1152,15773,15774],{"encoding":1154},"\\sum_k \\alpha_k = 1",[1129,15776,15778,15877],{"className":15777,"ariaHidden":1159},[1158],[1129,15779,15781,15784,15825,15828,15868,15871,15874],{"className":15780},[1163],[1129,15782],{"className":15783,"style":9422},[1167],[1129,15785,15787,15790],{"className":15786},[1596],[1129,15788,9107],{"className":15789,"style":9429},[1596,6765,6766],[1129,15791,15793],{"className":15792},[1303],[1129,15794,15796,15817],{"className":15795},[1307,1523],[1129,15797,15799,15814],{"className":15798},[1311],[1129,15800,15803],{"className":15801,"style":15802},[1315],"height:0.1864em;",[1129,15804,15805,15808],{"style":9445},[1129,15806],{"className":15807,"style":1324},[1323],[1129,15809,15811],{"className":15810},[1328,1329,1330,1331],[1129,15812,2570],{"className":15813,"style":2614},[1172,1173,1331],[1129,15815,1577],{"className":15816},[1576],[1129,15818,15820],{"className":15819},[1311],[1129,15821,15823],{"className":15822,"style":9467},[1315],[1129,15824],{},[1129,15826],{"className":15827,"style":1431},[1277],[1129,15829,15831,15834],{"className":15830},[1172],[1129,15832,2732],{"className":15833,"style":2754},[1172,1173],[1129,15835,15837],{"className":15836},[1303],[1129,15838,15840,15860],{"className":15839},[1307,1523],[1129,15841,15843,15857],{"className":15842},[1311],[1129,15844,15846],{"className":15845,"style":2601},[1315],[1129,15847,15848,15851],{"style":2769},[1129,15849],{"className":15850,"style":1324},[1323],[1129,15852,15854],{"className":15853},[1328,1329,1330,1331],[1129,15855,2570],{"className":15856,"style":2614},[1172,1173,1331],[1129,15858,1577],{"className":15859},[1576],[1129,15861,15863],{"className":15862},[1311],[1129,15864,15866],{"className":15865,"style":2624},[1315],[1129,15867],{},[1129,15869],{"className":15870,"style":1278},[1277],[1129,15872,1231],{"className":15873},[1282],[1129,15875],{"className":15876,"style":1278},[1277],[1129,15878,15880,15883],{"className":15879},[1163],[1129,15881],{"className":15882,"style":2074},[1167],[1129,15884,1246],{"className":15885},[1172],[1129,15887,15889,15927],{"className":15888},[1132],[1129,15890,15892],{"className":15891},[1136],[1138,15893,15894],{"xmlns":1140},[1142,15895,15896,15924],{},[1145,15897,15898,15900,15902,15904,15906,15912,15914,15922],{},[1148,15899,15232],{},[1229,15901,1250],{"stretchy":1249},[1148,15903,6833],{},[1229,15905,4576],{},[2563,15907,15908,15910],{},[1148,15909,2567],{},[1148,15911,2570],{},[1229,15913,1353],{"separator":1159},[2641,15915,15916,15918,15920],{},[1148,15917,2645],{},[1148,15919,2570],{},[1244,15921,1991],{},[1229,15923,1256],{"stretchy":1249},[1152,15925,15926],{"encoding":1154},"\\phi(y\\mid\\mu_k,\\sigma_k^2)",[1129,15928,15930,15954],{"className":15929,"ariaHidden":1159},[1158],[1129,15931,15933,15936,15939,15942,15945,15948,15951],{"className":15932},[1163],[1129,15934],{"className":15935,"style":1414},[1167],[1129,15937,15232],{"className":15938},[1172,1173],[1129,15940,1250],{"className":15941},[1344],[1129,15943,6833],{"className":15944,"style":1174},[1172,1173],[1129,15946],{"className":15947,"style":1278},[1277],[1129,15949,4576],{"className":15950},[1282],[1129,15952],{"className":15953,"style":1278},[1277],[1129,15955,15957,15960,16000,16003,16006,16057],{"className":15956},[1163],[1129,15958],{"className":15959,"style":2662},[1167],[1129,15961,15963,15966],{"className":15962},[1172],[1129,15964,2567],{"className":15965},[1172,1173],[1129,15967,15969],{"className":15968},[1303],[1129,15970,15972,15992],{"className":15971},[1307,1523],[1129,15973,15975,15989],{"className":15974},[1311],[1129,15976,15978],{"className":15977,"style":2601},[1315],[1129,15979,15980,15983],{"style":2604},[1129,15981],{"className":15982,"style":1324},[1323],[1129,15984,15986],{"className":15985},[1328,1329,1330,1331],[1129,15987,2570],{"className":15988,"style":2614},[1172,1173,1331],[1129,15990,1577],{"className":15991},[1576],[1129,15993,15995],{"className":15994},[1311],[1129,15996,15998],{"className":15997,"style":2624},[1315],[1129,15999],{},[1129,16001,1353],{"className":16002},[1427],[1129,16004],{"className":16005,"style":1431},[1277],[1129,16007,16009,16012],{"className":16008},[1172],[1129,16010,2645],{"className":16011,"style":1174},[1172,1173],[1129,16013,16015],{"className":16014},[1303],[1129,16016,16018,16049],{"className":16017},[1307,1523],[1129,16019,16021,16046],{"className":16020},[1311],[1129,16022,16024,16035],{"className":16023,"style":1316},[1315],[1129,16025,16026,16029],{"style":2683},[1129,16027],{"className":16028,"style":1324},[1323],[1129,16030,16032],{"className":16031},[1328,1329,1330,1331],[1129,16033,2570],{"className":16034,"style":2614},[1172,1173,1331],[1129,16036,16037,16040],{"style":1319},[1129,16038],{"className":16039,"style":1324},[1323],[1129,16041,16043],{"className":16042},[1328,1329,1330,1331],[1129,16044,1991],{"className":16045},[1172,1331],[1129,16047,1577],{"className":16048},[1576],[1129,16050,16052],{"className":16051},[1311],[1129,16053,16055],{"className":16054,"style":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个高斯分模型的密度。要用 EM 算法估计参数 ",[1129,16090,16092,16137],{"className":16091},[1132],[1129,16093,16095],{"className":16094},[1136],[1138,16096,16097],{"xmlns":1140},[1142,16098,16099,16134],{},[1145,16100,16101,16103,16105,16107,16113,16115,16121,16123,16131],{},[1148,16102,1978],{},[1229,16104,1231],{},[1229,16106,4761],{"stretchy":1249},[2563,16108,16109,16111],{},[1148,16110,2732],{},[1148,16112,2570],{},[1229,16114,1353],{"separator":1159},[2563,16116,16117,16119],{},[1148,16118,2567],{},[1148,16120,2570],{},[1229,16122,1353],{"separator":1159},[2641,16124,16125,16127,16129],{},[1148,16126,2645],{},[1148,16128,2570],{},[1244,16130,1991],{},[1229,16132,16133],{"stretchy":1249},"}",[1152,16135,16136],{"encoding":1154},"\\theta = \\{\\alpha_k, \\mu_k, \\sigma_k^2\\}",[1129,16138,16140,16158],{"className":16139,"ariaHidden":1159},[1158],[1129,16141,16143,16146,16149,16152,16155],{"className":16142},[1163],[1129,16144],{"className":16145,"style":2850},[1167],[1129,16147,1978],{"className":16148,"style":2141},[1172,1173],[1129,16150],{"className":16151,"style":1278},[1277],[1129,16153,1231],{"className":16154},[1282],[1129,16156],{"className":16157,"style":1278},[1277],[1129,16159,16161,16164,16167,16207,16210,16213,16253,16256,16259,16310],{"className":16160},[1163],[1129,16162],{"className":16163,"style":2662},[1167],[1129,16165,4761],{"className":16166},[1344],[1129,16168,16170,16173],{"className":16169},[1172],[1129,16171,2732],{"className":16172,"style":2754},[1172,1173],[1129,16174,16176],{"className":16175},[1303],[1129,16177,16179,16199],{"className":16178},[1307,1523],[1129,16180,16182,16196],{"className":16181},[1311],[1129,16183,16185],{"className":16184,"style":2601},[1315],[1129,16186,16187,16190],{"style":2769},[1129,16188],{"className":16189,"style":1324},[1323],[1129,16191,16193],{"className":16192},[1328,1329,1330,1331],[1129,16194,2570],{"className":16195,"style":2614},[1172,1173,1331],[1129,16197,1577],{"className":16198},[1576],[1129,16200,16202],{"className":16201},[1311],[1129,16203,16205],{"className":16204,"style":2624},[1315],[1129,16206],{},[1129,16208,1353],{"className":16209},[1427],[1129,16211],{"className":16212,"style":1431},[1277],[1129,16214,16216,16219],{"className":16215},[1172],[1129,16217,2567],{"className":16218},[1172,1173],[1129,16220,16222],{"className":16221},[1303],[1129,16223,16225,16245],{"className":16224},[1307,1523],[1129,16226,16228,16242],{"className":16227},[1311],[1129,16229,16231],{"className":16230,"style":2601},[1315],[1129,16232,16233,16236],{"style":2604},[1129,16234],{"className":16235,"style":1324},[1323],[1129,16237,16239],{"className":16238},[1328,1329,1330,1331],[1129,16240,2570],{"className":16241,"style":2614},[1172,1173,1331],[1129,16243,1577],{"className":16244},[1576],[1129,16246,16248],{"className":16247},[1311],[1129,16249,16251],{"className":16250,"style":2624},[1315],[1129,16252],{},[1129,16254,1353],{"className":16255},[1427],[1129,16257],{"className":16258,"style":1431},[1277],[1129,16260,16262,16265],{"className":16261},[1172],[1129,16263,2645],{"className":16264,"style":1174},[1172,1173],[1129,16266,16268],{"className":16267},[1303],[1129,16269,16271,16302],{"className":16270},[1307,1523],[1129,16272,16274,16299],{"className":16273},[1311],[1129,16275,16277,16288],{"className":16276,"style":1316},[1315],[1129,16278,16279,16282],{"style":2683},[1129,16280],{"className":16281,"style":1324},[1323],[1129,16283,16285],{"className":16284},[1328,1329,1330,1331],[1129,16286,2570],{"className":16287,"style":2614},[1172,1173,1331],[1129,16289,16290,16293],{"style":1319},[1129,16291],{"className":16292,"style":1324},[1323],[1129,16294,16296],{"className":16295},[1328,1329,1330,1331],[1129,16297,1991],{"className":16298},[1172,1331],[1129,16300,1577],{"className":16301},[1576],[1129,16303,16305],{"className":16304},[1311],[1129,16306,16308],{"className":16307,"style":2713},[1315],[1129,16309],{},[1129,16311,16133],{"className":16312},[1352],[1091,16314,16315,7341,16318,2955],{},[1101,16316,16317],{},"定义隐变量",[1129,16319,16321,16343],{"className":16320},[1132],[1129,16322,16324],{"className":16323},[1136],[1138,16325,16326],{"xmlns":1140},[1142,16327,16328,16340],{},[1145,16329,16330],{},[2563,16331,16332,16334],{},[1148,16333,2810],{},[1145,16335,16336,16338],{},[1148,16337,2818],{},[1148,16339,2570],{},[1152,16341,16342],{"encoding":1154},"\\gamma_{jk}",[1129,16344,16346],{"className":16345,"ariaHidden":1159},[1158],[1129,16347,16349,16353],{"className":16348},[1163],[1129,16350],{"className":16351,"style":16352},[1167],"height:0.7167em;vertical-align:-0.2861em;",[1129,16354,16356,16359],{"className":16355},[1172],[1129,16357,2810],{"className":16358,"style":2860},[1172,1173],[1129,16360,16362],{"className":16361},[1303],[1129,16363,16365,16391],{"className":16364},[1307,1523],[1129,16366,16368,16388],{"className":16367},[1311],[1129,16369,16371],{"className":16370,"style":2601},[1315],[1129,16372,16373,16376],{"style":2900},[1129,16374],{"className":16375,"style":1324},[1323],[1129,16377,16379],{"className":16378},[1328,1329,1330,1331],[1129,16380,16382,16385],{"className":16381},[1172,1331],[1129,16383,2818],{"className":16384,"style":2913},[1172,1173,1331],[1129,16386,2570],{"className":16387,"style":2614},[1172,1173,1331],[1129,16389,1577],{"className":16390},[1576],[1129,16392,16394],{"className":16393},[1311],[1129,16395,16397],{"className":16396,"style":2926},[1315],[1129,16398],{},[1091,16400,16401],{},[1129,16402,16404,16484],{"className":16403},[1132],[1129,16405,16407],{"className":16406},[1136],[1138,16408,16409],{"xmlns":1140},[1142,16410,16411,16481],{},[1145,16412,16413,16423,16425],{},[2563,16414,16415,16417],{},[1148,16416,2810],{},[1145,16418,16419,16421],{},[1148,16420,2818],{},[1148,16422,2570],{},[1229,16424,1231],{},[1145,16426,16427,16429],{},[1229,16428,4761],{"fence":1159},[4763,16430,16431,16462],{"rowspacing":4765,"columnalign":4766,"columnspacing":3642},[4768,16432,16433,16443],{},[4771,16434,16435],{},[1458,16436,16437],{"scriptlevel":1377,"displaystyle":1249},[1145,16438,16439,16441],{},[1244,16440,1246],{},[1229,16442,1353],{"separator":1159},[4771,16444,16445],{},[1458,16446,16447],{"scriptlevel":1377,"displaystyle":1249},[1145,16448,16449,16452,16454,16457,16459],{},[1648,16450,16451],{},"第 ",[1148,16453,2818],{},[1648,16455,16456],{}," 个观测来自第 ",[1148,16458,2570],{},[1648,16460,16461],{}," 个分模型",[4768,16463,16464,16474],{},[4771,16465,16466],{},[1458,16467,16468],{"scriptlevel":1377,"displaystyle":1249},[1145,16469,16470,16472],{},[1244,16471,1377],{},[1229,16473,1353],{"separator":1159},[4771,16475,16476],{},[1458,16477,16478],{"scriptlevel":1377,"displaystyle":1249},[1648,16479,16480],{},"否则",[1152,16482,16483],{"encoding":1154},"\\gamma_{jk} = \\begin{cases} 1, & \\text{第 } j \\text{ 个观测来自第 } k \\text{ 个分模型} \\\\ 0, & \\text{否则} \\end{cases}",[1129,16485,16487,16548],{"className":16486,"ariaHidden":1159},[1158],[1129,16488,16490,16493,16539,16542,16545],{"className":16489},[1163],[1129,16491],{"className":16492,"style":16352},[1167],[1129,16494,16496,16499],{"className":16495},[1172],[1129,16497,2810],{"className":16498,"style":2860},[1172,1173],[1129,16500,16502],{"className":16501},[1303],[1129,16503,16505,16531],{"className":16504},[1307,1523],[1129,16506,16508,16528],{"className":16507},[1311],[1129,16509,16511],{"className":16510,"style":2601},[1315],[1129,16512,16513,16516],{"style":2900},[1129,16514],{"className":16515,"style":1324},[1323],[1129,16517,16519],{"className":16518},[1328,1329,1330,1331],[1129,16520,16522,16525],{"className":16521},[1172,1331],[1129,16523,2818],{"className":16524,"style":2913},[1172,1173,1331],[1129,16526,2570],{"className":16527,"style":2614},[1172,1173,1331],[1129,16529,1577],{"className":16530},[1576],[1129,16532,16534],{"className":16533},[1311],[1129,16535,16537],{"className":16536,"style":2926},[1315],[1129,16538],{},[1129,16540],{"className":16541,"style":1278},[1277],[1129,16543,1231],{"className":16544},[1282],[1129,16546],{"className":16547,"style":1278},[1277],[1129,16549,16551,16555],{"className":16550},[1163],[1129,16552],{"className":16553,"style":16554},[1167],"height:3em;vertical-align:-1.25em;",[1129,16556,16558,16565,16714],{"className":16557},[4893],[1129,16559,16561],{"className":16560,"style":11875},[1344,11874],[1129,16562,4761],{"className":16563},[4900,16564],"size4",[1129,16566,16568],{"className":16567},[1172],[1129,16569,16571,16626,16629],{"className":16570},[4763],[1129,16572,16574],{"className":16573},[5006],[1129,16575,16577,16617],{"className":16576},[1307,1523],[1129,16578,16580,16614],{"className":16579},[1311],[1129,16581,16584,16599],{"className":16582,"style":16583},[1315],"height:1.69em;",[1129,16585,16587,16590],{"style":16586},"top:-3.69em;",[1129,16588],{"className":16589,"style":5674},[1323],[1129,16591,16593,16596],{"className":16592},[1172],[1129,16594,1246],{"className":16595},[1172],[1129,16597,1353],{"className":16598},[1427],[1129,16600,16602,16605],{"style":16601},"top:-2.25em;",[1129,16603],{"className":16604,"style":5674},[1323],[1129,16606,16608,16611],{"className":16607},[1172],[1129,16609,1377],{"className":16610},[1172],[1129,16612,1353],{"className":16613},[1427],[1129,16615,1577],{"className":16616},[1576],[1129,16618,16620],{"className":16619},[1311],[1129,16621,16624],{"className":16622,"style":16623},[1315],"height:1.19em;",[1129,16625],{},[1129,16627],{"className":16628,"style":5263},[5262],[1129,16630,16632],{"className":16631},[5006],[1129,16633,16635,16706],{"className":16634},[1307,1523],[1129,16636,16638,16703],{"className":16637},[1311],[1129,16639,16641,16689],{"className":16640,"style":16583},[1315],[1129,16642,16643,16646],{"style":16586},[1129,16644],{"className":16645,"style":5674},[1323],[1129,16647,16649,16660,16663,16676,16679],{"className":16648},[1172],[1129,16650,16652,16656],{"className":16651},[1172,3585],[1129,16653,16655],{"className":16654},[1172,6909],"第",[1129,16657,16659],{"className":16658},[1172]," ",[1129,16661,2818],{"className":16662,"style":2913},[1172,1173],[1129,16664,16666,16669,16673],{"className":16665},[1172,3585],[1129,16667,16659],{"className":16668},[1172],[1129,16670,16672],{"className":16671},[1172,6909],"个观测来自第",[1129,16674,16659],{"className":16675},[1172],[1129,16677,2570],{"className":16678,"style":2614},[1172,1173],[1129,16680,16682,16685],{"className":16681},[1172,3585],[1129,16683,16659],{"className":16684},[1172],[1129,16686,16688],{"className":16687},[1172,6909],"个分模型",[1129,16690,16691,16694],{"style":16601},[1129,16692],{"className":16693,"style":5674},[1323],[1129,16695,16697],{"className":16696},[1172],[1129,16698,16700],{"className":16699},[1172,3585],[1129,16701,16480],{"className":16702},[1172,6909],[1129,16704,1577],{"className":16705},[1576],[1129,16707,16709],{"className":16708},[1311],[1129,16710,16712],{"className":16711,"style":16623},[1315],[1129,16713],{},[1129,16715],{"className":16716},[1352,1516],[1091,16718,16719,16720,16791,16792,1353,16871,16874,16875,17100],{},"有了观测数据 ",[1129,16721,16723,16741],{"className":16722},[1132],[1129,16724,16726],{"className":16725},[1136],[1138,16727,16728],{"xmlns":1140},[1142,16729,16730,16738],{},[1145,16731,16732],{},[2563,16733,16734,16736],{},[1148,16735,6833],{},[1148,16737,2818],{},[1152,16739,16740],{"encoding":1154},"y_j",[1129,16742,16744],{"className":16743,"ariaHidden":1159},[1158],[1129,16745,16747,16750],{"className":16746},[1163],[1129,16748],{"className":16749,"style":16352},[1167],[1129,16751,16753,16756],{"className":16752},[1172],[1129,16754,6833],{"className":16755,"style":1174},[1172,1173],[1129,16757,16759],{"className":16758},[1303],[1129,16760,16762,16783],{"className":16761},[1307,1523],[1129,16763,16765,16780],{"className":16764},[1311],[1129,16766,16769],{"className":16767,"style":16768},[1315],"height:0.3117em;",[1129,16770,16771,16774],{"style":11351},[1129,16772],{"className":16773,"style":1324},[1323],[1129,16775,16777],{"className":16776},[1328,1329,1330,1331],[1129,16778,2818],{"className":16779,"style":2913},[1172,1173,1331],[1129,16781,1577],{"className":16782},[1576],[1129,16784,16786],{"className":16785},[1311],[1129,16787,16789],{"className":16788,"style":2926},[1315],[1129,16790],{}," 和未观测数据 ",[1129,16793,16795,16816],{"className":16794},[1132],[1129,16796,16798],{"className":16797},[1136],[1138,16799,16800],{"xmlns":1140},[1142,16801,16802,16814],{},[1145,16803,16804],{},[2563,16805,16806,16808],{},[1148,16807,2810],{},[1145,16809,16810,16812],{},[1148,16811,2818],{},[1148,16813,2570],{},[1152,16815,16342],{"encoding":1154},[1129,16817,16819],{"className":16818,"ariaHidden":1159},[1158],[1129,16820,16822,16825],{"className":16821},[1163],[1129,16823],{"className":16824,"style":16352},[1167],[1129,16826,16828,16831],{"className":16827},[1172],[1129,16829,2810],{"className":16830,"style":2860},[1172,1173],[1129,16832,16834],{"className":16833},[1303],[1129,16835,16837,16863],{"className":16836},[1307,1523],[1129,16838,16840,16860],{"className":16839},[1311],[1129,16841,16843],{"className":16842,"style":2601},[1315],[1129,16844,16845,16848],{"style":2900},[1129,16846],{"className":16847,"style":1324},[1323],[1129,16849,16851],{"className":16850},[1328,1329,1330,1331],[1129,16852,16854,16857],{"className":16853},[1172,1331],[1129,16855,2818],{"className":16856,"style":2913},[1172,1173,1331],[1129,16858,2570],{"className":16859,"style":2614},[1172,1173,1331],[1129,16861,1577],{"className":16862},[1576],[1129,16864,16866],{"className":16865},[1311],[1129,16867,16869],{"className":16868,"style":2926},[1315],[1129,16870],{},[1101,16872,16873],{},"完全数据","就是 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17221,2818],{},[1148,17223,2570],{},[1229,17225,1353],{"separator":1159},[1277,17227],{"width":6868},[2563,17229,17230,17232],{},[1148,17231,3533],{},[1148,17233,2570],{},[1229,17235,1231],{},[2641,17237,17238,17240,17248],{},[1229,17239,9107],{},[1145,17241,17242,17244,17246],{},[1148,17243,2818],{},[1229,17245,1231],{},[1244,17247,1246],{},[1148,17249,15020],{},[2563,17251,17252,17254],{},[1148,17253,2810],{},[1145,17255,17256,17258],{},[1148,17257,2818],{},[1148,17259,2570],{},[1152,17261,17262],{"encoding":1154},"P(y,\\gamma\\mid\\theta) = \\prod_{k=1}^{K} \\alpha_k^{\\,n_k} \\prod_{j=1}^{N} \\Big[\\phi(y_j\\mid\\mu_k,\\sigma_k^2)\\Big]^{\\gamma_{jk}}, \\qquad n_k = 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步:确定 Q 函数","。把 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换成它的条件期望 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个分模型生成的后验概率):",[1091,19294,19295],{},[1129,19296,19298,19423],{"className":19297},[1132],[1129,19299,19301],{"className":19300},[1136],[1138,19302,19303],{"xmlns":1140},[1142,19304,19305,19420],{},[1145,19306,19307,19321,19323],{},[2563,19308,19309,19315],{},[2806,19310,19311,19313],{"accent":1159},[1148,19312,2810],{},[1229,19314,2813],{},[1145,19316,19317,19319],{},[1148,19318,2818],{},[1148,19320,2570],{},[1229,19322,1231],{},[1461,19324,19325,19365],{},[1145,19326,19327,19333,19335,19337,19339,19345,19347,19353,19355,19363],{},[2563,19328,19329,19331],{},[1148,19330,2732],{},[1148,19332,2570],{},[1648,19334,1650],{},[1148,19336,15232],{},[1229,19338,1250],{"stretchy":1249},[2563,19340,19341,19343],{},[1148,19342,6833],{},[1148,19344,2818],{},[1229,19346,4576],{},[2563,19348,19349,19351],{},[1148,19350,2567],{},[1148,19352,2570],{},[1229,19354,1353],{"separator":1159},[2641,19356,19357,19359,19361],{},[1148,19358,2645],{},[1148,19360,2570],{},[1244,19362,1991],{},[1229,19364,1256],{"stretchy":1249},[1145,19366,19367,19382,19388,19390,19392,19394,19400,19402,19408,19410,19418],{},[2641,19368,19369,19371,19380],{},[1229,19370,9107],{},[1145,19372,19373,19376,19378],{},[1148,19374,19375],{},"l",[1229,19377,1231],{},[1244,19379,1246],{},[1148,19381,15221],{},[2563,19383,19384,19386],{},[1148,19385,2732],{},[1148,19387,19375],{},[1648,19389,1650],{},[1148,19391,15232],{},[1229,19393,1250],{"stretchy":1249},[2563,19395,19396,19398],{},[1148,19397,6833],{},[1148,19399,2818],{},[1229,19401,4576],{},[2563,19403,19404,19406],{},[1148,19405,2567],{},[1148,19407,19375],{},[1229,19409,1353],{"separator":1159},[2641,19411,19412,19414,19416],{},[1148,19413,2645],{},[1148,19415,19375],{},[1244,19417,1991],{},[1229,19419,1256],{"stretchy":1249},[1152,19421,19422],{"encoding":1154},"\\hat\\gamma_{jk} 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代入,就得到 Q 函数的具体表达式。",[1091,20420,20421,20423],{},[1101,20422,9861],{},":对各参数求偏导并令其为 0,得到更新公式:",[1091,20425,20426],{},[1129,20427,20429,20675],{"className":20428},[1132],[1129,20430,20432],{"className":20431},[1136],[1138,20433,20434],{"xmlns":1140},[1142,20435,20436,20672],{},[1145,20437,20438,20444,20446,20516,20518,20520,20528,20530,20614,20616,20618,20624,20626,20660,20662],{},[2563,20439,20440,20442],{},[1148,20441,2567],{},[1148,20443,2570],{},[1229,20445,1231],{},[1461,20447,20448,20486],{},[1145,20449,20450,20464,20478,20480],{},[2641,20451,20452,20454,20462],{},[1229,20453,9107],{},[1145,20455,20456,20458,20460],{},[1148,20457,2818],{},[1229,20459,1231],{},[1244,20461,1246],{},[1148,20463,15020],{},[2563,20465,20466,20472],{},[2806,20467,20468,20470],{"accent":1159},[1148,20469,2810],{},[1229,20471,2813],{},[1145,20473,20474,20476],{},[1148,20475,2818],{},[1148,20477,2570],{},[1648,20479,1650],{},[2563,20481,20482,20484],{},[1148,20483,6833],{},[1148,20485,2818],{},[1145,20487,20488,20502],{},[2641,20489,20490,20492,20500],{},[1229,20491,9107],{},[1145,20493,20494,20496,20498],{},[1148,20495,2818],{},[1229,20497,1231],{},[1244,20499,1246],{},[1148,20501,15020],{},[2563,20503,20504,20510],{},[2806,20505,20506,20508],{"accent":1159},[1148,20507,2810],{},[1229,20509,2813],{},[1145,20511,20512,20514],{},[1148,20513,2818],{},[1148,20515,2570],{},[1229,20517,1353],{"separator":1159},[1277,20519],{"width":6868},[2641,20521,20522,20524,20526],{},[1148,20523,2645],{},[1148,20525,2570],{},[1244,20527,1991],{},[1229,20529,1231],{},[1461,20531,20532,20584],{},[1145,20533,20534,20548,20562,20564,20570,20572,20578],{},[2641,20535,20536,20538,20546],{},[1229,20537,9107],{},[1145,20539,20540,20542,20544],{},[1148,20541,2818],{},[1229,20543,1231],{},[1244,20545,1246],{},[1148,20547,15020],{},[2563,20549,20550,20556],{},[2806,20551,20552,20554],{"accent":1159},[1148,20553,2810],{},[1229,20555,2813],{},[1145,20557,20558,20560],{},[1148,20559,2818],{},[1148,20561,2570],{},[1229,20563,1250],{"stretchy":1249},[2563,20565,20566,20568],{},[1148,20567,6833],{},[1148,20569,2818],{},[1229,20571,1242],{},[2563,20573,20574,20576],{},[1148,20575,2567],{},[1148,20577,2570],{},[1233,20579,20580,20582],{},[1229,20581,1256],{"stretchy":1249},[1244,20583,1991],{},[1145,20585,20586,20600],{},[2641,20587,20588,20590,20598],{},[1229,20589,9107],{},[1145,20591,20592,20594,20596],{},[1148,20593,2818],{},[1229,20595,1231],{},[1244,20597,1246],{},[1148,20599,15020],{},[2563,20601,20602,20608],{},[2806,20603,20604,20606],{"accent":1159},[1148,20605,2810],{},[1229,20607,2813],{},[1145,20609,20610,20612],{},[1148,20611,2818],{},[1148,20613,2570],{},[1229,20615,1353],{"separator":1159},[1277,20617],{"width":6868},[2563,20619,20620,20622],{},[1148,20621,2732],{},[1148,20623,2570],{},[1229,20625,1231],{},[1461,20627,20628,20658],{},[1145,20629,20630,20644],{},[2641,20631,20632,20634,20642],{},[1229,20633,9107],{},[1145,20635,20636,20638,20640],{},[1148,20637,2818],{},[1229,20639,1231],{},[1244,20641,1246],{},[1148,20643,15020],{},[2563,20645,20646,20652],{},[2806,20647,20648,20650],{"accent":1159},[1148,20649,2810],{},[1229,20651,2813],{},[1145,20653,20654,20656],{},[1148,20655,2818],{},[1148,20657,2570],{},[1148,20659,15020],{},[1229,20661,1231],{},[1461,20663,20664,20670],{},[2563,20665,20666,20668],{},[1148,20667,3533],{},[1148,20669,2570],{},[1148,20671,15020],{},[1152,20673,20674],{"encoding":1154},"\\mu_k = \\frac{\\sum_{j=1}^{N}\\hat\\gamma_{jk}\\,y_j}{\\sum_{j=1}^{N}\\hat\\gamma_{jk}}, \\qquad \\sigma_k^2 = \\frac{\\sum_{j=1}^{N}\\hat\\gamma_{jk}(y_j-\\mu_k)^2}{\\sum_{j=1}^{N}\\hat\\gamma_{jk}}, \\qquad \\alpha_k = \\frac{\\sum_{j=1}^{N}\\hat\\gamma_{jk}}{N} = 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步、M 步交替迭代到收敛,就得到 GMM 的参数估计。",[3512,22115,22117],{"id":22116},"分布式-em-算法","分布式 EM 算法",[1091,22119,22120,22121,22261],{},"在高斯混合模型下,当数据量 ",[1129,22122,22124,22154],{"className":22123},[1132],[1129,22125,22127],{"className":22126},[1136],[1138,22128,22129],{"xmlns":1140},[1142,22130,22131,22151],{},[1145,22132,22133,22139,22141,22143,22145],{},[2563,22134,22135,22137],{},[1148,22136,6833],{},[1244,22138,1246],{},[1229,22140,1353],{"separator":1159},[1229,22142,15011],{},[1229,22144,1353],{"separator":1159},[2563,22146,22147,22149],{},[1148,22148,6833],{},[1148,22150,15020],{},[1152,22152,22153],{"encoding":1154},"y_1,\\dots,y_N",[1129,22155,22157],{"className":22156,"ariaHidden":1159},[1158],[1129,22158,22160,22163,22203,22206,22209,22212,22215,22218,22221],{"className":22159},[1163],[1129,22161],{"className":22162,"style":1168},[1167],[1129,22164,22166,22169],{"className":22165},[1172],[1129,22167,6833],{"className":22168,"style":1174},[1172,1173],[1129,22170,22172],{"className":22171},[1303],[1129,22173,22175,22195],{"className":22174},[1307,1523],[1129,22176,22178,22192],{"className":22177},[1311],[1129,22179,22181],{"className":22180,"style":7638},[1315],[1129,22182,22183,22186],{"style":11351},[1129,22184],{"className":22185,"style":1324},[1323],[1129,22187,22189],{"className":22188},[1328,1329,1330,1331],[1129,22190,1246],{"className":22191},[1172,1331],[1129,22193,1577],{"className":22194},[1576],[1129,22196,22198],{"className":22197},[1311],[1129,22199,22201],{"className":22200,"style":2624},[1315],[1129,22202],{},[1129,22204,1353],{"className":22205},[1427],[1129,22207],{"className":22208,"style":1431},[1277],[1129,22210,15011],{"className":22211},[4893],[1129,22213],{"className":22214,"style":1431},[1277],[1129,22216,1353],{"className":22217},[1427],[1129,22219],{"className":22220,"style":1431},[1277],[1129,22222,22224,22227],{"className":22223},[1172],[1129,22225,6833],{"className":22226,"style":1174},[1172,1173],[1129,22228,22230],{"className":22229},[1303],[1129,22231,22233,22253],{"className":22232},[1307,1523],[1129,22234,22236,22250],{"className":22235},[1311],[1129,22237,22239],{"className":22238,"style":15155},[1315],[1129,22240,22241,22244],{"style":11351},[1129,22242],{"className":22243,"style":1324},[1323],[1129,22245,22247],{"className":22246},[1328,1329,1330,1331],[1129,22248,15020],{"className":22249,"style":1348},[1172,1173,1331],[1129,22251,1577],{"className":22252},[1576],[1129,22254,22256],{"className":22255},[1311],[1129,22257,22259],{"className":22258,"style":2624},[1315],[1129,22260],{}," 很大时,可以把 EM 做成分布式的。",[1091,22263,22264,22265,22267,22268,7341,22271,22393,22394,22397,22398,2627,22529,2627,22706,22899],{},"在 ",[1101,22266,8845],{},"把数据分散到各个节点,每个节点在本地算出各自数据的",[1101,22269,22270],{},"条件概率(响应度)",[1129,22272,22274,22299],{"className":22273},[1132],[1129,22275,22277],{"className":22276},[1136],[1138,22278,22279],{"xmlns":1140},[1142,22280,22281,22297],{},[1145,22282,22283],{},[2563,22284,22285,22291],{},[2806,22286,22287,22289],{"accent":1159},[1148,22288,2810],{},[1229,22290,2813],{},[1145,22292,22293,22295],{},[1148,22294,2818],{},[1148,22296,2570],{},[1152,22298,2823],{"encoding":1154},[1129,22300,22302],{"className":22301,"ariaHidden":1159},[1158],[1129,22303,22305,22308],{"className":22304},[1163],[1129,22306],{"className":22307,"style":2833},[1167],[1129,22309,22311,22353],{"className":22310},[1172],[1129,22312,22314],{"className":22313},[1172,2840],[1129,22315,22317,22345],{"className":22316},[1307,1523],[1129,22318,22320,22342],{"className":22319},[1311],[1129,22321,22323,22331],{"className":22322,"style":2850},[1315],[1129,22324,22325,22328],{"style":2853},[1129,22326],{"className":22327,"style":1537},[1323],[1129,22329,2810],{"className":22330,"style":2860},[1172,1173],[1129,22332,22333,22336],{"style":2853},[1129,22334],{"className":22335,"style":1537},[1323],[1129,22337,22339],{"className":22338,"style":2870},[2869],[1129,22340,2813],{"className":22341},[1172],[1129,22343,1577],{"className":22344},[1576],[1129,22346,22348],{"className":22347},[1311],[1129,22349,22351],{"className":22350,"style":2883},[1315],[1129,22352],{},[1129,22354,22356],{"className":22355},[1303],[1129,22357,22359,22385],{"className":22358},[1307,1523],[1129,22360,22362,22382],{"className":22361},[1311],[1129,22363,22365],{"className":22364,"style":2601},[1315],[1129,22366,22367,22370],{"style":2900},[1129,22368],{"className":22369,"style":1324},[1323],[1129,22371,22373],{"className":22372},[1328,1329,1330,1331],[1129,22374,22376,22379],{"className":22375},[1172,1331],[1129,22377,2818],{"className":22378,"style":2913},[1172,1173,1331],[1129,22380,2570],{"className":22381,"style":2614},[1172,1173,1331],[1129,22383,1577],{"className":22384},[1576],[1129,22386,22388],{"className":22387},[1311],[1129,22389,22391],{"className":22390,"style":2926},[1315],[1129,22392],{}," 以及对应的",[1101,22395,22396],{},"期望充分统计量","(如 ",[1129,22399,22401,22429],{"className":22400},[1132],[1129,22402,22404],{"className":22403},[1136],[1138,22405,22406],{"xmlns":1140},[1142,22407,22408,22426],{},[1145,22409,22410,22412],{},[1229,22411,9107],{},[2563,22413,22414,22420],{},[2806,22415,22416,22418],{"accent":1159},[1148,22417,2810],{},[1229,22419,2813],{},[1145,22421,22422,22424],{},[1148,22423,2818],{},[1148,22425,2570],{},[1152,22427,22428],{"encoding":1154},"\\sum \\hat\\gamma_{jk}",[1129,22430,22432],{"className":22431,"ariaHidden":1159},[1158],[1129,22433,22435,22438,22441,22444],{"className":22434},[1163],[1129,22436],{"className":22437,"style":16937},[1167],[1129,22439,9107],{"className":22440,"style":9429},[1596,6765,6766],[1129,22442],{"className":22443,"style":1431},[1277],[1129,22445,22447,22489],{"className":22446},[1172],[1129,22448,22450],{"className":22449},[1172,2840],[1129,22451,22453,22481],{"className":22452},[1307,1523],[1129,22454,22456,22478],{"className":22455},[1311],[1129,22457,22459,22467],{"className":22458,"style":2850},[1315],[1129,22460,22461,22464],{"style":2853},[1129,22462],{"className":22463,"style":1537},[1323],[1129,22465,2810],{"className":22466,"style":2860},[1172,1173],[1129,22468,22469,22472],{"style":2853},[1129,22470],{"className":22471,"style":1537},[1323],[1129,22473,22475],{"className":22474,"style":2870},[2869],[1129,22476,2813],{"className":22477},[1172],[1129,22479,1577],{"className":22480},[1576],[1129,22482,22484],{"className":22483},[1311],[1129,22485,22487],{"className":22486,"style":2883},[1315],[1129,22488],{},[1129,22490,22492],{"className":22491},[1303],[1129,22493,22495,22521],{"className":22494},[1307,1523],[1129,22496,22498,22518],{"className":22497},[1311],[1129,22499,22501],{"className":22500,"style":2601},[1315],[1129,22502,22503,22506],{"style":2900},[1129,22504],{"className":22505,"style":1324},[1323],[1129,22507,22509],{"className":22508},[1328,1329,1330,1331],[1129,22510,22512,22515],{"className":22511},[1172,1331],[1129,22513,2818],{"className":22514,"style":2913},[1172,1173,1331],[1129,22516,2570],{"className":22517,"style":2614},[1172,1173,1331],[1129,22519,1577],{"className":22520},[1576],[1129,22522,22524],{"className":22523},[1311],[1129,22525,22527],{"className":22526,"style":2926},[1315],[1129,22528],{},[1129,22530,22532,22566],{"className":22531},[1132],[1129,22533,22535],{"className":22534},[1136],[1138,22536,22537],{"xmlns":1140},[1142,22538,22539,22563],{},[1145,22540,22541,22543,22557],{},[1229,22542,9107],{},[2563,22544,22545,22551],{},[2806,22546,22547,22549],{"accent":1159},[1148,22548,2810],{},[1229,22550,2813],{},[1145,22552,22553,22555],{},[1148,22554,2818],{},[1148,22556,2570],{},[2563,22558,22559,22561],{},[1148,22560,6833],{},[1148,22562,2818],{},[1152,22564,22565],{"encoding":1154},"\\sum \\hat\\gamma_{jk}y_j",[1129,22567,22569],{"className":22568,"ariaHidden":1159},[1158],[1129,22570,22572,22575,22578,22581,22666],{"className":22571},[1163],[1129,22573],{"className":22574,"style":16937},[1167],[1129,22576,9107],{"className":22577,"style":9429},[1596,6765,6766],[1129,22579],{"className":22580,"style":1431},[1277],[1129,22582,22584,22626],{"className":22583},[1172],[1129,22585,22587],{"className":22586},[1172,2840],[1129,22588,22590,22618],{"className":22589},[1307,1523],[1129,22591,22593,22615],{"className":22592},[1311],[1129,22594,22596,22604],{"className":22595,"style":2850},[1315],[1129,22597,22598,22601],{"style":2853},[1129,22599],{"className":22600,"style":1537},[1323],[1129,22602,2810],{"className":22603,"style":2860},[1172,1173],[1129,22605,22606,22609],{"style":2853},[1129,22607],{"className":22608,"style":1537},[1323],[1129,22610,22612],{"className":22611,"style":2870},[2869],[1129,22613,2813],{"className":22614},[1172],[1129,22616,1577],{"className":22617},[1576],[1129,22619,22621],{"className":22620},[1311],[1129,22622,22624],{"className":22623,"style":2883},[1315],[1129,22625],{},[1129,22627,22629],{"className":22628},[1303],[1129,22630,22632,22658],{"className":22631},[1307,1523],[1129,22633,22635,22655],{"className":22634},[1311],[1129,22636,22638],{"className":22637,"style":2601},[1315],[1129,22639,22640,22643],{"style":2900},[1129,22641],{"className":22642,"style":1324},[1323],[1129,22644,22646],{"className":22645},[1328,1329,1330,1331],[1129,22647,22649,22652],{"className":22648},[1172,1331],[1129,22650,2818],{"className":22651,"style":2913},[1172,1173,1331],[1129,22653,2570],{"className":22654,"style":2614},[1172,1173,1331],[1129,22656,1577],{"className":22657},[1576],[1129,22659,22661],{"className":22660},[1311],[1129,22662,22664],{"className":22663,"style":2926},[1315],[1129,22665],{},[1129,22667,22669,22672],{"className":22668},[1172],[1129,22670,6833],{"className":22671,"style":1174},[1172,1173],[1129,22673,22675],{"className":22674},[1303],[1129,22676,22678,22698],{"className":22677},[1307,1523],[1129,22679,22681,22695],{"className":22680},[1311],[1129,22682,22684],{"className":22683,"style":16768},[1315],[1129,22685,22686,22689],{"style":11351},[1129,22687],{"className":22688,"style":1324},[1323],[1129,22690,22692],{"className":22691},[1328,1329,1330,1331],[1129,22693,2818],{"className":22694,"style":2913},[1172,1173,1331],[1129,22696,1577],{"className":22697},[1576],[1129,22699,22701],{"className":22700},[1311],[1129,22702,22704],{"className":22703,"style":2926},[1315],[1129,22705],{},[1129,22707,22709,22745],{"className":22708},[1132],[1129,22710,22712],{"className":22711},[1136],[1138,22713,22714],{"xmlns":1140},[1142,22715,22716,22742],{},[1145,22717,22718,22720,22734],{},[1229,22719,9107],{},[2563,22721,22722,22728],{},[2806,22723,22724,22726],{"accent":1159},[1148,22725,2810],{},[1229,22727,2813],{},[1145,22729,22730,22732],{},[1148,22731,2818],{},[1148,22733,2570],{},[2641,22735,22736,22738,22740],{},[1148,22737,6833],{},[1148,22739,2818],{},[1244,22741,1991],{},[1152,22743,22744],{"encoding":1154},"\\sum \\hat\\gamma_{jk}y_j^2",[1129,22746,22748],{"className":22747,"ariaHidden":1159},[1158],[1129,22749,22751,22755,22758,22761,22846],{"className":22750},[1163],[1129,22752],{"className":22753,"style":22754},[1167],"height:1.2089em;vertical-align:-0.3948em;",[1129,22756,9107],{"className":22757,"style":9429},[1596,6765,6766],[1129,22759],{"className":22760,"style":1431},[1277],[1129,22762,22764,22806],{"className":22763},[1172],[1129,22765,22767],{"className":22766},[1172,2840],[1129,22768,22770,22798],{"className":22769},[1307,1523],[1129,22771,22773,22795],{"className":22772},[1311],[1129,22774,22776,22784],{"className":22775,"style":2850},[1315],[1129,22777,22778,22781],{"style":2853},[1129,22779],{"className":22780,"style":1537},[1323],[1129,22782,2810],{"className":22783,"style":2860},[1172,1173],[1129,22785,22786,22789],{"style":2853},[1129,22787],{"className":22788,"style":1537},[1323],[1129,22790,22792],{"className":22791,"style":2870},[2869],[1129,22793,2813],{"className":22794},[1172],[1129,22796,1577],{"className":22797},[1576],[1129,22799,22801],{"className":22800},[1311],[1129,22802,22804],{"className":22803,"style":2883},[1315],[1129,22805],{},[1129,22807,22809],{"className":22808},[1303],[1129,22810,22812,22838],{"className":22811},[1307,1523],[1129,22813,22815,22835],{"className":22814},[1311],[1129,22816,22818],{"className":22817,"style":2601},[1315],[1129,22819,22820,22823],{"style":2900},[1129,22821],{"className":22822,"style":1324},[1323],[1129,22824,22826],{"className":22825},[1328,1329,1330,1331],[1129,22827,22829,22832],{"className":22828},[1172,1331],[1129,22830,2818],{"className":22831,"style":2913},[1172,1173,1331],[1129,22833,2570],{"className":22834,"style":2614},[1172,1173,1331],[1129,22836,1577],{"className":22837},[1576],[1129,22839,22841],{"className":22840},[1311],[1129,22842,22844],{"className":22843,"style":2926},[1315],[1129,22845],{},[1129,22847,22849,22852],{"className":22848},[1172],[1129,22850,6833],{"className":22851,"style":1174},[1172,1173],[1129,22853,22855],{"className":22854},[1303],[1129,22856,22858,22890],{"className":22857},[1307,1523],[1129,22859,22861,22887],{"className":22860},[1311],[1129,22862,22864,22876],{"className":22863,"style":1316},[1315],[1129,22865,22867,22870],{"style":22866},"top:-2.4413em;margin-left:-0.0359em;margin-right:0.05em;",[1129,22868],{"className":22869,"style":1324},[1323],[1129,22871,22873],{"className":22872},[1328,1329,1330,1331],[1129,22874,2818],{"className":22875,"style":2913},[1172,1173,1331],[1129,22877,22878,22881],{"style":1319},[1129,22879],{"className":22880,"style":1324},[1323],[1129,22882,22884],{"className":22883},[1328,1329,1330,1331],[1129,22885,1991],{"className":22886},[1172,1331],[1129,22888,1577],{"className":22889},[1576],[1129,22891,22893],{"className":22892},[1311],[1129,22894,22897],{"className":22895,"style":22896},[1315],"height:0.3948em;",[1129,22898],{},");",[1091,22901,22902,22903,22905,22906,1603],{},"到 ",[1101,22904,9861],{},"再把各节点的这些充分统计量汇总相加,统一更新全局参数 ",[1129,22907,22909,22945],{"className":22908},[1132],[1129,22910,22912],{"className":22911},[1136],[1138,22913,22914],{"xmlns":1140},[1142,22915,22916,22942],{},[1145,22917,22918,22924,22926,22932,22934],{},[2563,22919,22920,22922],{},[1148,22921,2732],{},[1148,22923,2570],{},[1229,22925,1353],{"separator":1159},[2563,22927,22928,22930],{},[1148,22929,2567],{},[1148,22931,2570],{},[1229,22933,1353],{"separator":1159},[2641,22935,22936,22938,22940],{},[1148,22937,2645],{},[1148,22939,2570],{},[1244,22941,1991],{},[1152,22943,22944],{"encoding":1154},"\\alpha_k, \\mu_k, 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