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\\text{Poisson}(b)",[1100,1146,1150,1177],{"className":1147,"ariaHidden":1149},[1148],"katex-html","true",[1100,1151,1154,1159,1165,1170,1174],{"className":1152},[1153],"base",[1100,1155],{"className":1156,"style":1158},[1157],"strut","height:0.6833em;",[1100,1160,1121],{"className":1161,"style":1164},[1162,1163],"mord","mathnormal","margin-right:0.0502em;",[1100,1166],{"className":1167,"style":1169},[1168],"mspace","margin-right:0.2778em;",[1100,1171,1125],{"className":1172},[1173],"mrel",[1100,1175],{"className":1176,"style":1169},[1168],[1100,1178,1180,1184,1191,1195,1198],{"className":1179},[1153],[1100,1181],{"className":1182,"style":1183},[1157],"height:1em;vertical-align:-0.25em;",[1100,1185,1188],{"className":1186},[1162,1187],"text",[1100,1189,1129],{"className":1190},[1162],[1100,1192,1133],{"className":1193},[1194],"mopen",[1100,1196,1136],{"className":1197},[1162,1163],[1100,1199,1139],{"className":1200},[1201],"mclose"," 和 ",[1100,1204,1206,1232],{"className":1205},[1103],[1100,1207,1209],{"className":1208},[1107],[1109,1210,1211],{"xmlns":1111},[1113,1212,1213,1229],{},[1116,1214,1215,1218,1220,1222,1224,1227],{},[1119,1216,1217],{},"S",[1123,1219,1125],{},[1127,1221,1129],{},[1123,1223,1133],{"stretchy":1132},[1119,1225,1226],{},"q",[1123,1228,1139],{"stretchy":1132},[1141,1230,1231],{"encoding":1143},"S \\sim \\text{Poisson}(q)",[1100,1233,1235,1254],{"className":1234,"ariaHidden":1149},[1148],[1100,1236,1238,1241,1245,1248,1251],{"className":1237},[1153],[1100,1239],{"className":1240,"style":1158},[1157],[1100,1242,1217],{"className":1243,"style":1244},[1162,1163],"margin-right:0.0576em;",[1100,1246],{"className":1247,"style":1169},[1168],[1100,1249,1125],{"className":1250},[1173],[1100,1252],{"className":1253,"style":1169},[1168],[1100,1255,1257,1260,1266,1269,1273],{"className":1256},[1153],[1100,1258],{"className":1259,"style":1183},[1157],[1100,1261,1263],{"className":1262},[1162,1187],[1100,1264,1129],{"className":1265},[1162],[1100,1267,1133],{"className":1268},[1194],[1100,1270,1226],{"className":1271,"style":1272},[1162,1163],"margin-right:0.0359em;",[1100,1274,1139],{"className":1275},[1201],"，观测值 ",[1100,1278,1280,1319],{"className":1279},[1103],[1100,1281,1283],{"className":1282},[1107],[1109,1284,1285],{"xmlns":1111},[1113,1286,1287,1316],{},[1116,1288,1289,1292,1295,1297,1300,1302,1304,1306,1308,1310,1312,1314],{},[1119,1290,1291],{},"Y",[1123,1293,1294],{},"=",[1119,1296,1121],{},[1123,1298,1299],{},"+",[1119,1301,1217],{},[1123,1303,1125],{},[1127,1305,1129],{},[1123,1307,1133],{"stretchy":1132},[1119,1309,1136],{},[1123,1311,1299],{},[1119,1313,1226],{},[1123,1315,1139],{"stretchy":1132},[1141,1317,1318],{"encoding":1143},"Y = B + S \\sim \\text{Poisson}(b + q)",[1100,1320,1322,1341,1361,1379,1406],{"className":1321,"ariaHidden":1149},[1148],[1100,1323,1325,1328,1332,1335,1338],{"className":1324},[1153],[1100,1326],{"className":1327,"style":1158},[1157],[1100,1329,1291],{"className":1330,"style":1331},[1162,1163],"margin-right:0.2222em;",[1100,1333],{"className":1334,"style":1169},[1168],[1100,1336,1294],{"className":1337},[1173],[1100,1339],{"className":1340,"style":1169},[1168],[1100,1342,1344,1348,1351,1354,1358],{"className":1343},[1153],[1100,1345],{"className":1346,"style":1347},[1157],"height:0.7667em;vertical-align:-0.0833em;",[1100,1349,1121],{"className":1350,"style":1164},[1162,1163],[1100,1352],{"className":1353,"style":1331},[1168],[1100,1355,1299],{"className":1356},[1357],"mbin",[1100,1359],{"className":1360,"style":1331},[1168],[1100,1362,1364,1367,1370,1373,1376],{"className":1363},[1153],[1100,1365],{"className":1366,"style":1158},[1157],[1100,1368,1217],{"className":1369,"style":1244},[1162,1163],[1100,1371],{"className":1372,"style":1169},[1168],[1100,1374,1125],{"className":1375},[1173],[1100,1377],{"className":1378,"style":1169},[1168],[1100,1380,1382,1385,1391,1394,1397,1400,1403],{"className":1381},[1153],[1100,1383],{"className":1384,"style":1183},[1157],[1100,1386,1388],{"className":1387},[1162,1187],[1100,1389,1129],{"className":1390},[1162],[1100,1392,1133],{"className":1393},[1194],[1100,1395,1136],{"className":1396},[1162,1163],[1100,1398],{"className":1399,"style":1331},[1168],[1100,1401,1299],{"className":1402},[1357],[1100,1404],{"className":1405,"style":1331},[1168],[1100,1407,1409,1412,1415],{"className":1408},[1153],[1100,1410],{"className":1411,"style":1183},[1157],[1100,1413,1226],{"className":1414,"style":1272},[1162,1163],[1100,1416,1139],{"className":1417},[1201]," 和辅助变量 ",[1100,1420,1422,1453],{"className":1421},[1103],[1100,1423,1425],{"className":1424},[1107],[1109,1426,1427],{"xmlns":1111},[1113,1428,1429,1450],{},[1116,1430,1431,1434,1436,1438,1440,1443,1446,1448],{},[1119,1432,1433],{},"W",[1123,1435,1125],{},[1127,1437,1129],{},[1123,1439,1133],{"stretchy":1132},[1119,1441,1442],{},"m",[1123,1444,1445],{},"⋅",[1119,1447,1136],{},[1123,1449,1139],{"stretchy":1132},[1141,1451,1452],{"encoding":1143},"W \\sim \\text{Poisson}(m \\cdot b)",[1100,1454,1456,1475,1502],{"className":1455,"ariaHidden":1149},[1148],[1100,1457,1459,1462,1466,1469,1472],{"className":1458},[1153],[1100,1460],{"className":1461,"style":1158},[1157],[1100,1463,1433],{"className":1464,"style":1465},[1162,1163],"margin-right:0.1389em;",[1100,1467],{"className":1468,"style":1169},[1168],[1100,1470,1125],{"className":1471},[1173],[1100,1473],{"className":1474,"style":1169},[1168],[1100,1476,1478,1481,1487,1490,1493,1496,1499],{"className":1477},[1153],[1100,1479],{"className":1480,"style":1183},[1157],[1100,1482,1484],{"className":1483},[1162,1187],[1100,1485,1129],{"className":1486},[1162],[1100,1488,1133],{"className":1489},[1194],[1100,1491,1442],{"className":1492},[1162,1163],[1100,1494],{"className":1495,"style":1331},[1168],[1100,1497,1445],{"className":1498},[1357],[1100,1500],{"className":1501,"style":1331},[1168],[1100,1503,1505,1508,1511],{"className":1504},[1153],[1100,1506],{"className":1507,"style":1183},[1157],[1100,1509,1136],{"className":1510},[1162,1163],[1100,1512,1139],{"className":1513},[1201],"，目标是估计参数 ",[1100,1516,1518,1531],{"className":1517},[1103],[1100,1519,1521],{"className":1520},[1107],[1109,1522,1523],{"xmlns":1111},[1113,1524,1525,1529],{},[1116,1526,1527],{},[1119,1528,1136],{},[1141,1530,1136],{"encoding":1143},[1100,1532,1534],{"className":1533,"ariaHidden":1149},[1148],[1100,1535,1537,1541],{"className":1536},[1153],[1100,1538],{"className":1539,"style":1540},[1157],"height:0.6944em;",[1100,1542,1136],{"className":1543},[1162,1163],"、",[1100,1546,1548,1561],{"className":1547},[1103],[1100,1549,1551],{"className":1550},[1107],[1109,1552,1553],{"xmlns":1111},[1113,1554,1555,1559],{},[1116,1556,1557],{},[1119,1558,1226],{},[1141,1560,1226],{"encoding":1143},[1100,1562,1564],{"className":1563,"ariaHidden":1149},[1148],[1100,1565,1567,1571],{"className":1566},[1153],[1100,1568],{"className":1569,"style":1570},[1157],"height:0.625em;vertical-align:-0.1944em;",[1100,1572,1226],{"className":1573,"style":1272},[1162,1163],"\nm?",[1096,1576,1577],{},"现提出基于随机加权推断模型（Inferential Model, IM）的算法通过引入随机权重处理离散分布，来构造置信区间",[1579,1580,1581],"h3",{"id":1581},"方法概述",[1096,1583,1584,1585,1614],{},"随机加权 IM 方法的核心是通过引入均匀随机变量和权重，将离散泊松分布连续化，从而逆解参数\n该方法假设 ",[1100,1586,1588,1601],{"className":1587},[1103],[1100,1589,1591],{"className":1590},[1107],[1109,1592,1593],{"xmlns":1111},[1113,1594,1595,1599],{},[1116,1596,1597],{},[1119,1598,1442],{},[1141,1600,1442],{"encoding":1143},[1100,1602,1604],{"className":1603,"ariaHidden":1149},[1148],[1100,1605,1607,1611],{"className":1606},[1153],[1100,1608],{"className":1609,"style":1610},[1157],"height:0.4306em;",[1100,1612,1442],{"className":1613},[1162,1163]," 已知算法分为四个步骤：建立关联模型、引入随机权重连续化、逆解参数、模拟验证覆盖率",[1579,1616,1617],{"id":1617},"算法步骤",[1619,1620,1622],"h4",{"id":1621},"_1-建立关联模型","1: 建立关联模型",[1096,1624,1625,1626,1654,1655,1764,1765,1839,1840,1930],{},"对观测值 ",[1100,1627,1629,1642],{"className":1628},[1103],[1100,1630,1632],{"className":1631},[1107],[1109,1633,1634],{"xmlns":1111},[1113,1635,1636,1640],{},[1116,1637,1638],{},[1119,1639,1291],{},[1141,1641,1291],{"encoding":1143},[1100,1643,1645],{"className":1644,"ariaHidden":1149},[1148],[1100,1646,1648,1651],{"className":1647},[1153],[1100,1649],{"className":1650,"style":1158},[1157],[1100,1652,1291],{"className":1653,"style":1331},[1162,1163],"，其分布函数为 ",[1100,1656,1658,1686],{"className":1657},[1103],[1100,1659,1661],{"className":1660},[1107],[1109,1662,1663],{"xmlns":1111},[1113,1664,1665,1683],{},[1116,1666,1667,1676,1678,1681],{},[1668,1669,1670,1673],"msub",{},[1119,1671,1672],{},"F",[1119,1674,1675],{},"θ",[1123,1677,1133],{"stretchy":1132},[1119,1679,1680],{},"y",[1123,1682,1139],{"stretchy":1132},[1141,1684,1685],{"encoding":1143},"F_{θ}(y)",[1100,1687,1689],{"className":1688,"ariaHidden":1149},[1148],[1100,1690,1692,1695,1755,1758,1761],{"className":1691},[1153],[1100,1693],{"className":1694,"style":1183},[1157],[1100,1696,1698,1701],{"className":1697},[1162],[1100,1699,1672],{"className":1700,"style":1465},[1162,1163],[1100,1702,1705],{"className":1703},[1704],"msupsub",[1100,1706,1710,1746],{"className":1707},[1708,1709],"vlist-t","vlist-t2",[1100,1711,1714,1741],{"className":1712},[1713],"vlist-r",[1100,1715,1719],{"className":1716,"style":1718},[1717],"vlist","height:0.3361em;",[1100,1720,1722,1727],{"style":1721},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[1100,1723],{"className":1724,"style":1726},[1725],"pstrut","height:2.7em;",[1100,1728,1734],{"className":1729},[1730,1731,1732,1733],"sizing","reset-size6","size3","mtight",[1100,1735,1737],{"className":1736},[1162,1733],[1100,1738,1675],{"className":1739,"style":1740},[1162,1163,1733],"margin-right:0.0278em;",[1100,1742,1745],{"className":1743},[1744],"vlist-s","​",[1100,1747,1749],{"className":1748},[1713],[1100,1750,1753],{"className":1751,"style":1752},[1717],"height:0.15em;",[1100,1754],{},[1100,1756,1133],{"className":1757},[1194],[1100,1759,1680],{"className":1760,"style":1272},[1162,1163],[1100,1762,1139],{"className":1763},[1201],"，其中 ",[1100,1766,1768,1790],{"className":1767},[1103],[1100,1769,1771],{"className":1770},[1107],[1109,1772,1773],{"xmlns":1111},[1113,1774,1775,1787],{},[1116,1776,1777,1779,1781,1783,1785],{},[1119,1778,1675],{},[1123,1780,1294],{},[1119,1782,1136],{},[1123,1784,1299],{},[1119,1786,1226],{},[1141,1788,1789],{"encoding":1143},"θ = b + q",[1100,1791,1793,1811,1830],{"className":1792,"ariaHidden":1149},[1148],[1100,1794,1796,1799,1802,1805,1808],{"className":1795},[1153],[1100,1797],{"className":1798,"style":1540},[1157],[1100,1800,1675],{"className":1801,"style":1740},[1162,1163],[1100,1803],{"className":1804,"style":1169},[1168],[1100,1806,1294],{"className":1807},[1173],[1100,1809],{"className":1810,"style":1169},[1168],[1100,1812,1814,1818,1821,1824,1827],{"className":1813},[1153],[1100,1815],{"className":1816,"style":1817},[1157],"height:0.7778em;vertical-align:-0.0833em;",[1100,1819,1136],{"className":1820},[1162,1163],[1100,1822],{"className":1823,"style":1331},[1168],[1100,1825,1299],{"className":1826},[1357],[1100,1828],{"className":1829,"style":1331},[1168],[1100,1831,1833,1836],{"className":1832},[1153],[1100,1834],{"className":1835,"style":1570},[1157],[1100,1837,1226],{"className":1838,"style":1272},[1162,1163],"\n引入辅助变量 ",[1100,1841,1843,1877],{"className":1842},[1103],[1100,1844,1846],{"className":1845},[1107],[1109,1847,1848],{"xmlns":1111},[1113,1849,1850,1874],{},[1116,1851,1852,1855,1857,1860,1862,1866,1869,1872],{},[1119,1853,1854],{},"u",[1123,1856,1125],{},[1127,1858,1859],{},"Uniform",[1123,1861,1133],{"stretchy":1132},[1863,1864,1865],"mn",{},"0",[1123,1867,1868],{"separator":1149},",",[1863,1870,1871],{},"1",[1123,1873,1139],{"stretchy":1132},[1141,1875,1876],{"encoding":1143},"u \\sim \\text{Uniform}(0,1)",[1100,1878,1880,1898],{"className":1879,"ariaHidden":1149},[1148],[1100,1881,1883,1886,1889,1892,1895],{"className":1882},[1153],[1100,1884],{"className":1885,"style":1610},[1157],[1100,1887,1854],{"className":1888},[1162,1163],[1100,1890],{"className":1891,"style":1169},[1168],[1100,1893,1125],{"className":1894},[1173],[1100,1896],{"className":1897,"style":1169},[1168],[1100,1899,1901,1904,1910,1913,1916,1920,1924,1927],{"className":1900},[1153],[1100,1902],{"className":1903,"style":1183},[1157],[1100,1905,1907],{"className":1906},[1162,1187],[1100,1908,1859],{"className":1909},[1162],[1100,1911,1133],{"className":1912},[1194],[1100,1914,1865],{"className":1915},[1162],[1100,1917,1868],{"className":1918},[1919],"mpunct",[1100,1921],{"className":1922,"style":1923},[1168],"margin-right:0.1667em;",[1100,1925,1871],{"className":1926},[1162],[1100,1928,1139],{"className":1929},[1201],"，建立关联：",[1096,1932,1933],{},[1100,1934,1936,1985],{"className":1935},[1103],[1100,1937,1939],{"className":1938},[1107],[1109,1940,1941],{"xmlns":1111},[1113,1942,1943,1982],{},[1116,1944,1945,1951,1953,1955,1958,1960,1962,1965,1967,1970,1976,1978,1980],{},[1668,1946,1947,1949],{},[1119,1948,1672],{},[1119,1950,1675],{},[1123,1952,1133],{"stretchy":1132},[1119,1954,1291],{},[1123,1956,1957],{},"−",[1863,1959,1871],{},[1123,1961,1139],{"stretchy":1132},[1123,1963,1964],{},"≤",[1119,1966,1854],{},[1123,1968,1969],{},"\u003C",[1668,1971,1972,1974],{},[1119,1973,1672],{},[1119,1975,1675],{},[1123,1977,1133],{"stretchy":1132},[1119,1979,1291],{},[1123,1981,1139],{"stretchy":1132},[1141,1983,1984],{"encoding":1143},"F_{θ}(Y-1) \\leq u \u003C F_{θ}(Y)",[1100,1986,1988,2052,2073,2092],{"className":1987,"ariaHidden":1149},[1148],[1100,1989,1991,1994,2037,2040,2043,2046,2049],{"className":1990},[1153],[1100,1992],{"className":1993,"style":1183},[1157],[1100,1995,1997,2000],{"className":1996},[1162],[1100,1998,1672],{"className":1999,"style":1465},[1162,1163],[1100,2001,2003],{"className":2002},[1704],[1100,2004,2006,2029],{"className":2005},[1708,1709],[1100,2007,2009,2026],{"className":2008},[1713],[1100,2010,2012],{"className":2011,"style":1718},[1717],[1100,2013,2014,2017],{"style":1721},[1100,2015],{"className":2016,"style":1726},[1725],[1100,2018,2020],{"className":2019},[1730,1731,1732,1733],[1100,2021,2023],{"className":2022},[1162,1733],[1100,2024,1675],{"className":2025,"style":1740},[1162,1163,1733],[1100,2027,1745],{"className":2028},[1744],[1100,2030,2032],{"className":2031},[1713],[1100,2033,2035],{"className":2034,"style":1752},[1717],[1100,2036],{},[1100,2038,1133],{"className":2039},[1194],[1100,2041,1291],{"className":2042,"style":1331},[1162,1163],[1100,2044],{"className":2045,"style":1331},[1168],[1100,2047,1957],{"className":2048},[1357],[1100,2050],{"className":2051,"style":1331},[1168],[1100,2053,2055,2058,2061,2064,2067,2070],{"className":2054},[1153],[1100,2056],{"className":2057,"style":1183},[1157],[1100,2059,1871],{"className":2060},[1162],[1100,2062,1139],{"className":2063},[1201],[1100,2065],{"className":2066,"style":1169},[1168],[1100,2068,1964],{"className":2069},[1173],[1100,2071],{"className":2072,"style":1169},[1168],[1100,2074,2076,2080,2083,2086,2089],{"className":2075},[1153],[1100,2077],{"className":2078,"style":2079},[1157],"height:0.5782em;vertical-align:-0.0391em;",[1100,2081,1854],{"className":2082},[1162,1163],[1100,2084],{"className":2085,"style":1169},[1168],[1100,2087,1969],{"className":2088},[1173],[1100,2090],{"className":2091,"style":1169},[1168],[1100,2093,2095,2098,2141,2144,2147],{"className":2094},[1153],[1100,2096],{"className":2097,"style":1183},[1157],[1100,2099,2101,2104],{"className":2100},[1162],[1100,2102,1672],{"className":2103,"style":1465},[1162,1163],[1100,2105,2107],{"className":2106},[1704],[1100,2108,2110,2133],{"className":2109},[1708,1709],[1100,2111,2113,2130],{"className":2112},[1713],[1100,2114,2116],{"className":2115,"style":1718},[1717],[1100,2117,2118,2121],{"style":1721},[1100,2119],{"className":2120,"style":1726},[1725],[1100,2122,2124],{"className":2123},[1730,1731,1732,1733],[1100,2125,2127],{"className":2126},[1162,1733],[1100,2128,1675],{"className":2129,"style":1740},[1162,1163,1733],[1100,2131,1745],{"className":2132},[1744],[1100,2134,2136],{"className":2135},[1713],[1100,2137,2139],{"className":2138,"style":1752},[1717],[1100,2140],{},[1100,2142,1133],{"className":2143},[1194],[1100,2145,1291],{"className":2146,"style":1331},[1162,1163],[1100,2148,1139],{"className":2149},[1201],[1096,2151,1625,2152,1654,2180,2275,2276,1930],{},[1100,2153,2155,2168],{"className":2154},[1103],[1100,2156,2158],{"className":2157},[1107],[1109,2159,2160],{"xmlns":1111},[1113,2161,2162,2166],{},[1116,2163,2164],{},[1119,2165,1433],{},[1141,2167,1433],{"encoding":1143},[1100,2169,2171],{"className":2170,"ariaHidden":1149},[1148],[1100,2172,2174,2177],{"className":2173},[1153],[1100,2175],{"className":2176,"style":1158},[1157],[1100,2178,1433],{"className":2179,"style":1465},[1162,1163],[1100,2181,2183,2212],{"className":2182},[1103],[1100,2184,2186],{"className":2185},[1107],[1109,2187,2188],{"xmlns":1111},[1113,2189,2190,2209],{},[1116,2191,2192,2202,2204,2207],{},[1668,2193,2194,2196],{},[1119,2195,1672],{},[1116,2197,2198,2200],{},[1119,2199,1442],{},[1119,2201,1136],{},[1123,2203,1133],{"stretchy":1132},[1119,2205,2206],{},"w",[1123,2208,1139],{"stretchy":1132},[1141,2210,2211],{"encoding":1143},"F_{mb}(w)",[1100,2213,2215],{"className":2214,"ariaHidden":1149},[1148],[1100,2216,2218,2221,2265,2268,2272],{"className":2217},[1153],[1100,2219],{"className":2220,"style":1183},[1157],[1100,2222,2224,2227],{"className":2223},[1162],[1100,2225,1672],{"className":2226,"style":1465},[1162,1163],[1100,2228,2230],{"className":2229},[1704],[1100,2231,2233,2257],{"className":2232},[1708,1709],[1100,2234,2236,2254],{"className":2235},[1713],[1100,2237,2239],{"className":2238,"style":1718},[1717],[1100,2240,2241,2244],{"style":1721},[1100,2242],{"className":2243,"style":1726},[1725],[1100,2245,2247],{"className":2246},[1730,1731,1732,1733],[1100,2248,2250],{"className":2249},[1162,1733],[1100,2251,2253],{"className":2252},[1162,1163,1733],"mb",[1100,2255,1745],{"className":2256},[1744],[1100,2258,2260],{"className":2259},[1713],[1100,2261,2263],{"className":2262,"style":1752},[1717],[1100,2264],{},[1100,2266,1133],{"className":2267},[1194],[1100,2269,2206],{"className":2270,"style":2271},[1162,1163],"margin-right:0.0269em;",[1100,2273,1139],{"className":2274},[1201],"，引入辅助变量 ",[1100,2277,2279,2308],{"className":2278},[1103],[1100,2280,2282],{"className":2281},[1107],[1109,2283,2284],{"xmlns":1111},[1113,2285,2286,2305],{},[1116,2287,2288,2291,2293,2295,2297,2299,2301,2303],{},[1119,2289,2290],{},"v",[1123,2292,1125],{},[1127,2294,1859],{},[1123,2296,1133],{"stretchy":1132},[1863,2298,1865],{},[1123,2300,1868],{"separator":1149},[1863,2302,1871],{},[1123,2304,1139],{"stretchy":1132},[1141,2306,2307],{"encoding":1143},"v \\sim \\text{Uniform}(0,1)",[1100,2309,2311,2329],{"className":2310,"ariaHidden":1149},[1148],[1100,2312,2314,2317,2320,2323,2326],{"className":2313},[1153],[1100,2315],{"className":2316,"style":1610},[1157],[1100,2318,2290],{"className":2319,"style":1272},[1162,1163],[1100,2321],{"className":2322,"style":1169},[1168],[1100,2324,1125],{"className":2325},[1173],[1100,2327],{"className":2328,"style":1169},[1168],[1100,2330,2332,2335,2341,2344,2347,2350,2353,2356],{"className":2331},[1153],[1100,2333],{"className":2334,"style":1183},[1157],[1100,2336,2338],{"className":2337},[1162,1187],[1100,2339,1859],{"className":2340},[1162],[1100,2342,1133],{"className":2343},[1194],[1100,2345,1865],{"className":2346},[1162],[1100,2348,1868],{"className":2349},[1919],[1100,2351],{"className":2352,"style":1923},[1168],[1100,2354,1871],{"className":2355},[1162],[1100,2357,1139],{"className":2358},[1201],[1096,2360,2361],{},[1100,2362,2364,2418],{"className":2363},[1103],[1100,2365,2367],{"className":2366},[1107],[1109,2368,2369],{"xmlns":1111},[1113,2370,2371,2415],{},[1116,2372,2373,2383,2385,2387,2389,2391,2393,2395,2397,2399,2409,2411,2413],{},[1668,2374,2375,2377],{},[1119,2376,1672],{},[1116,2378,2379,2381],{},[1119,2380,1442],{},[1119,2382,1136],{},[1123,2384,1133],{"stretchy":1132},[1119,2386,1433],{},[1123,2388,1957],{},[1863,2390,1871],{},[1123,2392,1139],{"stretchy":1132},[1123,2394,1964],{},[1119,2396,2290],{},[1123,2398,1964],{},[1668,2400,2401,2403],{},[1119,2402,1672],{},[1116,2404,2405,2407],{},[1119,2406,1442],{},[1119,2408,1136],{},[1123,2410,1133],{"stretchy":1132},[1119,2412,1433],{},[1123,2414,1139],{"stretchy":1132},[1141,2416,2417],{"encoding":1143},"F_{mb}(W-1) \\leq v \\leq F_{mb}(W)",[1100,2419,2421,2485,2506,2525],{"className":2420,"ariaHidden":1149},[1148],[1100,2422,2424,2427,2470,2473,2476,2479,2482],{"className":2423},[1153],[1100,2425],{"className":2426,"style":1183},[1157],[1100,2428,2430,2433],{"className":2429},[1162],[1100,2431,1672],{"className":2432,"style":1465},[1162,1163],[1100,2434,2436],{"className":2435},[1704],[1100,2437,2439,2462],{"className":2438},[1708,1709],[1100,2440,2442,2459],{"className":2441},[1713],[1100,2443,2445],{"className":2444,"style":1718},[1717],[1100,2446,2447,2450],{"style":1721},[1100,2448],{"className":2449,"style":1726},[1725],[1100,2451,2453],{"className":2452},[1730,1731,1732,1733],[1100,2454,2456],{"className":2455},[1162,1733],[1100,2457,2253],{"className":2458},[1162,1163,1733],[1100,2460,1745],{"className":2461},[1744],[1100,2463,2465],{"className":2464},[1713],[1100,2466,2468],{"className":2467,"style":1752},[1717],[1100,2469],{},[1100,2471,1133],{"className":2472},[1194],[1100,2474,1433],{"className":2475,"style":1465},[1162,1163],[1100,2477],{"className":2478,"style":1331},[1168],[1100,2480,1957],{"className":2481},[1357],[1100,2483],{"className":2484,"style":1331},[1168],[1100,2486,2488,2491,2494,2497,2500,2503],{"className":2487},[1153],[1100,2489],{"className":2490,"style":1183},[1157],[1100,2492,1871],{"className":2493},[1162],[1100,2495,1139],{"className":2496},[1201],[1100,2498],{"className":2499,"style":1169},[1168],[1100,2501,1964],{"className":2502},[1173],[1100,2504],{"className":2505,"style":1169},[1168],[1100,2507,2509,2513,2516,2519,2522],{"className":2508},[1153],[1100,2510],{"className":2511,"style":2512},[1157],"height:0.7719em;vertical-align:-0.136em;",[1100,2514,2290],{"className":2515,"style":1272},[1162,1163],[1100,2517],{"className":2518,"style":1169},[1168],[1100,2520,1964],{"className":2521},[1173],[1100,2523],{"className":2524,"style":1169},[1168],[1100,2526,2528,2531,2574,2577,2580],{"className":2527},[1153],[1100,2529],{"className":2530,"style":1183},[1157],[1100,2532,2534,2537],{"className":2533},[1162],[1100,2535,1672],{"className":2536,"style":1465},[1162,1163],[1100,2538,2540],{"className":2539},[1704],[1100,2541,2543,2566],{"className":2542},[1708,1709],[1100,2544,2546,2563],{"className":2545},[1713],[1100,2547,2549],{"className":2548,"style":1718},[1717],[1100,2550,2551,2554],{"style":1721},[1100,2552],{"className":2553,"style":1726},[1725],[1100,2555,2557],{"className":2556},[1730,1731,1732,1733],[1100,2558,2560],{"className":2559},[1162,1733],[1100,2561,2253],{"className":2562},[1162,1163,1733],[1100,2564,1745],{"className":2565},[1744],[1100,2567,2569],{"className":2568},[1713],[1100,2570,2572],{"className":2571,"style":1752},[1717],[1100,2573],{},[1100,2575,1133],{"className":2576},[1194],[1100,2578,1433],{"className":2579,"style":1465},[1162,1163],[1100,2581,1139],{"className":2582},[1201],[1619,2584,2586],{"id":2585},"_2-引入随机权重进行连续化","2: 引入随机权重进行连续化",[1096,2588,2589,2590,2770,2771,2866],{},"引入随机权重 ",[1100,2591,2593,2634],{"className":2592},[1103],[1100,2594,2596],{"className":2595},[1107],[1109,2597,2598],{"xmlns":1111},[1113,2599,2600,2631],{},[1116,2601,2602,2608,2610,2617,2619,2621,2623,2625,2627,2629],{},[1668,2603,2604,2606],{},[1119,2605,2206],{},[1863,2607,1871],{},[1123,2609,1868],{"separator":1149},[1668,2611,2612,2614],{},[1119,2613,2206],{},[1863,2615,2616],{},"2",[1123,2618,1125],{},[1127,2620,1859],{},[1123,2622,1133],{"stretchy":1132},[1863,2624,1865],{},[1123,2626,1868],{"separator":1149},[1863,2628,1871],{},[1123,2630,1139],{"stretchy":1132},[1141,2632,2633],{"encoding":1143},"w_1, w_2 \\sim \\text{Uniform}(0,1)",[1100,2635,2637,2740],{"className":2636,"ariaHidden":1149},[1148],[1100,2638,2640,2643,2685,2688,2691,2731,2734,2737],{"className":2639},[1153],[1100,2641],{"className":2642,"style":1570},[1157],[1100,2644,2646,2649],{"className":2645},[1162],[1100,2647,2206],{"className":2648,"style":2271},[1162,1163],[1100,2650,2652],{"className":2651},[1704],[1100,2653,2655,2677],{"className":2654},[1708,1709],[1100,2656,2658,2674],{"className":2657},[1713],[1100,2659,2662],{"className":2660,"style":2661},[1717],"height:0.3011em;",[1100,2663,2665,2668],{"style":2664},"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;",[1100,2666],{"className":2667,"style":1726},[1725],[1100,2669,2671],{"className":2670},[1730,1731,1732,1733],[1100,2672,1871],{"className":2673},[1162,1733],[1100,2675,1745],{"className":2676},[1744],[1100,2678,2680],{"className":2679},[1713],[1100,2681,2683],{"className":2682,"style":1752},[1717],[1100,2684],{},[1100,2686,1868],{"className":2687},[1919],[1100,2689],{"className":2690,"style":1923},[1168],[1100,2692,2694,2697],{"className":2693},[1162],[1100,2695,2206],{"className":2696,"style":2271},[1162,1163],[1100,2698,2700],{"className":2699},[1704],[1100,2701,2703,2723],{"className":2702},[1708,1709],[1100,2704,2706,2720],{"className":2705},[1713],[1100,2707,2709],{"className":2708,"style":2661},[1717],[1100,2710,2711,2714],{"style":2664},[1100,2712],{"className":2713,"style":1726},[1725],[1100,2715,2717],{"className":2716},[1730,1731,1732,1733],[1100,2718,2616],{"className":2719},[1162,1733],[1100,2721,1745],{"className":2722},[1744],[1100,2724,2726],{"className":2725},[1713],[1100,2727,2729],{"className":2728,"style":1752},[1717],[1100,2730],{},[1100,2732],{"className":2733,"style":1169},[1168],[1100,2735,1125],{"className":2736},[1173],[1100,2738],{"className":2739,"style":1169},[1168],[1100,2741,2743,2746,2752,2755,2758,2761,2764,2767],{"className":2742},[1153],[1100,2744],{"className":2745,"style":1183},[1157],[1100,2747,2749],{"className":2748},[1162,1187],[1100,2750,1859],{"className":2751},[1162],[1100,2753,1133],{"className":2754},[1194],[1100,2756,1865],{"className":2757},[1162],[1100,2759,1868],{"className":2760},[1919],[1100,2762],{"className":2763,"style":1923},[1168],[1100,2765,1871],{"className":2766},[1162],[1100,2768,1139],{"className":2769},[1201],"，",[1100,2772,2774,2806],{"className":2773},[1103],[1100,2775,2777],{"className":2776},[1107],[1109,2778,2779],{"xmlns":1111},[1113,2780,2781,2803],{},[1116,2782,2783,2785,2787,2789,2791,2793,2795,2797,2799,2801],{},[1119,2784,1854],{},[1123,2786,1868],{"separator":1149},[1119,2788,2290],{},[1123,2790,1125],{},[1127,2792,1859],{},[1123,2794,1133],{"stretchy":1132},[1863,2796,1865],{},[1123,2798,1868],{"separator":1149},[1863,2800,1871],{},[1123,2802,1139],{"stretchy":1132},[1141,2804,2805],{"encoding":1143},"u, v \\sim \\text{Uniform}(0,1)",[1100,2807,2809,2836],{"className":2808,"ariaHidden":1149},[1148],[1100,2810,2812,2815,2818,2821,2824,2827,2830,2833],{"className":2811},[1153],[1100,2813],{"className":2814,"style":1570},[1157],[1100,2816,1854],{"className":2817},[1162,1163],[1100,2819,1868],{"className":2820},[1919],[1100,2822],{"className":2823,"style":1923},[1168],[1100,2825,2290],{"className":2826,"style":1272},[1162,1163],[1100,2828],{"className":2829,"style":1169},[1168],[1100,2831,1125],{"className":2832},[1173],[1100,2834],{"className":2835,"style":1169},[1168],[1100,2837,2839,2842,2848,2851,2854,2857,2860,2863],{"className":2838},[1153],[1100,2840],{"className":2841,"style":1183},[1157],[1100,2843,2845],{"className":2844},[1162,1187],[1100,2846,1859],{"className":2847},[1162],[1100,2849,1133],{"className":2850},[1194],[1100,2852,1865],{"className":2853},[1162],[1100,2855,1868],{"className":2856},[1919],[1100,2858],{"className":2859,"style":1923},[1168],[1100,2861,1871],{"className":2862},[1162],[1100,2864,1139],{"className":2865},[1201],"构造方程：",[1096,2868,2869],{},[1100,2870,2872,2950],{"className":2871},[1103],[1100,2873,2875],{"className":2874},[1107],[1109,2876,2877],{"xmlns":1111},[1113,2878,2879,2947],{},[1116,2880,2881,2884,2886,2888,2890,2893,2899,2905,2907,2909,2911,2913,2915,2917,2919,2921,2923,2929,2931,2937,2939,2941,2943,2945],{},[1119,2882,2883],{},"G",[1123,2885,1133],{"stretchy":1132},[1119,2887,1675],{},[1123,2889,1139],{"stretchy":1132},[1123,2891,2892],{},":",[1668,2894,2895,2897],{},[1119,2896,2206],{},[1863,2898,1871],{},[1668,2900,2901,2903],{},[1119,2902,1672],{},[1119,2904,1675],{},[1123,2906,1133],{"stretchy":1132},[1119,2908,1291],{},[1123,2910,1957],{},[1863,2912,1871],{},[1123,2914,1139],{"stretchy":1132},[1123,2916,1299],{},[1123,2918,1133],{"stretchy":1132},[1863,2920,1871],{},[1123,2922,1957],{},[1668,2924,2925,2927],{},[1119,2926,2206],{},[1863,2928,1871],{},[1123,2930,1139],{"stretchy":1132},[1668,2932,2933,2935],{},[1119,2934,1672],{},[1119,2936,1675],{},[1123,2938,1133],{"stretchy":1132},[1119,2940,1291],{},[1123,2942,1139],{"stretchy":1132},[1123,2944,1294],{},[1119,2946,1854],{},[1141,2948,2949],{"encoding":1143},"G(θ): w_1 F_{θ}(Y-1) + (1-w_1) F_{θ}(Y) = u",[1100,2951,2953,2980,3084,3105,3126,3236],{"className":2952,"ariaHidden":1149},[1148],[1100,2954,2956,2959,2962,2965,2968,2971,2974,2977],{"className":2955},[1153],[1100,2957],{"className":2958,"style":1183},[1157],[1100,2960,2883],{"className":2961},[1162,1163],[1100,2963,1133],{"className":2964},[1194],[1100,2966,1675],{"className":2967,"style":1740},[1162,1163],[1100,2969,1139],{"className":2970},[1201],[1100,2972],{"className":2973,"style":1169},[1168],[1100,2975,2892],{"className":2976},[1173],[1100,2978],{"className":2979,"style":1169},[1168],[1100,2981,2983,2986,3026,3069,3072,3075,3078,3081],{"className":2982},[1153],[1100,2984],{"className":2985,"style":1183},[1157],[1100,2987,2989,2992],{"className":2988},[1162],[1100,2990,2206],{"className":2991,"style":2271},[1162,1163],[1100,2993,2995],{"className":2994},[1704],[1100,2996,2998,3018],{"className":2997},[1708,1709],[1100,2999,3001,3015],{"className":3000},[1713],[1100,3002,3004],{"className":3003,"style":2661},[1717],[1100,3005,3006,3009],{"style":2664},[1100,3007],{"className":3008,"style":1726},[1725],[1100,3010,3012],{"className":3011},[1730,1731,1732,1733],[1100,3013,1871],{"className":3014},[1162,1733],[1100,3016,1745],{"className":3017},[1744],[1100,3019,3021],{"className":3020},[1713],[1100,3022,3024],{"className":3023,"style":1752},[1717],[1100,3025],{},[1100,3027,3029,3032],{"className":3028},[1162],[1100,3030,1672],{"className":3031,"style":1465},[1162,1163],[1100,3033,3035],{"className":3034},[1704],[1100,3036,3038,3061],{"className":3037},[1708,1709],[1100,3039,3041,3058],{"className":3040},[1713],[1100,3042,3044],{"className":3043,"style":1718},[1717],[1100,3045,3046,3049],{"style":1721},[1100,3047],{"className":3048,"style":1726},[1725],[1100,3050,3052],{"className":3051},[1730,1731,1732,1733],[1100,3053,3055],{"className":3054},[1162,1733],[1100,3056,1675],{"className":3057,"style":1740},[1162,1163,1733],[1100,3059,1745],{"className":3060},[1744],[1100,3062,3064],{"className":3063},[1713],[1100,3065,3067],{"className":3066,"style":1752},[1717],[1100,3068],{},[1100,3070,1133],{"className":3071},[1194],[1100,3073,1291],{"className":3074,"style":1331},[1162,1163],[1100,3076],{"className":3077,"style":1331},[1168],[1100,3079,1957],{"className":3080},[1357],[1100,3082],{"className":3083,"style":1331},[1168],[1100,3085,3087,3090,3093,3096,3099,3102],{"className":3086},[1153],[1100,3088],{"className":3089,"style":1183},[1157],[1100,3091,1871],{"className":3092},[1162],[1100,3094,1139],{"className":3095},[1201],[1100,3097],{"className":3098,"style":1331},[1168],[1100,3100,1299],{"className":3101},[1357],[1100,3103],{"className":3104,"style":1331},[1168],[1100,3106,3108,3111,3114,3117,3120,3123],{"className":3107},[1153],[1100,3109],{"className":3110,"style":1183},[1157],[1100,3112,1133],{"className":3113},[1194],[1100,3115,1871],{"className":3116},[1162],[1100,3118],{"className":3119,"style":1331},[1168],[1100,3121,1957],{"className":3122},[1357],[1100,3124],{"className":3125,"style":1331},[1168],[1100,3127,3129,3132,3172,3175,3218,3221,3224,3227,3230,3233],{"className":3128},[1153],[1100,3130],{"className":3131,"style":1183},[1157],[1100,3133,3135,3138],{"className":3134},[1162],[1100,3136,2206],{"className":3137,"style":2271},[1162,1163],[1100,3139,3141],{"className":3140},[1704],[1100,3142,3144,3164],{"className":3143},[1708,1709],[1100,3145,3147,3161],{"className":3146},[1713],[1100,3148,3150],{"className":3149,"style":2661},[1717],[1100,3151,3152,3155],{"style":2664},[1100,3153],{"className":3154,"style":1726},[1725],[1100,3156,3158],{"className":3157},[1730,1731,1732,1733],[1100,3159,1871],{"className":3160},[1162,1733],[1100,3162,1745],{"className":3163},[1744],[1100,3165,3167],{"className":3166},[1713],[1100,3168,3170],{"className":3169,"style":1752},[1717],[1100,3171],{},[1100,3173,1139],{"className":3174},[1201],[1100,3176,3178,3181],{"className":3177},[1162],[1100,3179,1672],{"className":3180,"style":1465},[1162,1163],[1100,3182,3184],{"className":3183},[1704],[1100,3185,3187,3210],{"className":3186},[1708,1709],[1100,3188,3190,3207],{"className":3189},[1713],[1100,3191,3193],{"className":3192,"style":1718},[1717],[1100,3194,3195,3198],{"style":1721},[1100,3196],{"className":3197,"style":1726},[1725],[1100,3199,3201],{"className":3200},[1730,1731,1732,1733],[1100,3202,3204],{"className":3203},[1162,1733],[1100,3205,1675],{"className":3206,"style":1740},[1162,1163,1733],[1100,3208,1745],{"className":3209},[1744],[1100,3211,3213],{"className":3212},[1713],[1100,3214,3216],{"className":3215,"style":1752},[1717],[1100,3217],{},[1100,3219,1133],{"className":3220},[1194],[1100,3222,1291],{"className":3223,"style":1331},[1162,1163],[1100,3225,1139],{"className":3226},[1201],[1100,3228],{"className":3229,"style":1169},[1168],[1100,3231,1294],{"className":3232},[1173],[1100,3234],{"className":3235,"style":1169},[1168],[1100,3237,3239,3242],{"className":3238},[1153],[1100,3240],{"className":3241,"style":1610},[1157],[1100,3243,1854],{"className":3244},[1162,1163],[1096,3246,3247],{},[1100,3248,3250,3337],{"className":3249},[1103],[1100,3251,3253],{"className":3252},[1107],[1109,3254,3255],{"xmlns":1111},[1113,3256,3257,3334],{},[1116,3258,3259,3262,3264,3266,3268,3270,3272,3278,3288,3290,3292,3294,3296,3298,3300,3302,3304,3306,3312,3314,3324,3326,3328,3330,3332],{},[1119,3260,3261],{},"H",[1123,3263,1133],{"stretchy":1132},[1119,3265,1442],{},[1119,3267,1136],{},[1123,3269,1139],{"stretchy":1132},[1123,3271,2892],{},[1668,3273,3274,3276],{},[1119,3275,2206],{},[1863,3277,2616],{},[1668,3279,3280,3282],{},[1119,3281,1672],{},[1116,3283,3284,3286],{},[1119,3285,1442],{},[1119,3287,1136],{},[1123,3289,1133],{"stretchy":1132},[1119,3291,1433],{},[1123,3293,1957],{},[1863,3295,1871],{},[1123,3297,1139],{"stretchy":1132},[1123,3299,1299],{},[1123,3301,1133],{"stretchy":1132},[1863,3303,1871],{},[1123,3305,1957],{},[1668,3307,3308,3310],{},[1119,3309,2206],{},[1863,3311,2616],{},[1123,3313,1139],{"stretchy":1132},[1668,3315,3316,3318],{},[1119,3317,1672],{},[1116,3319,3320,3322],{},[1119,3321,1442],{},[1119,3323,1136],{},[1123,3325,1133],{"stretchy":1132},[1119,3327,1433],{},[1123,3329,1139],{"stretchy":1132},[1123,3331,1294],{},[1119,3333,2290],{},[1141,3335,3336],{"encoding":1143},"H(mb): w_2 F_{mb}(W-1) + (1-w_2) F_{mb}(W) = v",[1100,3338,3340,3368,3472,3493,3514,3624],{"className":3339,"ariaHidden":1149},[1148],[1100,3341,3343,3346,3350,3353,3356,3359,3362,3365],{"className":3342},[1153],[1100,3344],{"className":3345,"style":1183},[1157],[1100,3347,3261],{"className":3348,"style":3349},[1162,1163],"margin-right:0.0813em;",[1100,3351,1133],{"className":3352},[1194],[1100,3354,2253],{"className":3355},[1162,1163],[1100,3357,1139],{"className":3358},[1201],[1100,3360],{"className":3361,"style":1169},[1168],[1100,3363,2892],{"className":3364},[1173],[1100,3366],{"className":3367,"style":1169},[1168],[1100,3369,3371,3374,3414,3457,3460,3463,3466,3469],{"className":3370},[1153],[1100,3372],{"className":3373,"style":1183},[1157],[1100,3375,3377,3380],{"className":3376},[1162],[1100,3378,2206],{"className":3379,"style":2271},[1162,1163],[1100,3381,3383],{"className":3382},[1704],[1100,3384,3386,3406],{"className":3385},[1708,1709],[1100,3387,3389,3403],{"className":3388},[1713],[1100,3390,3392],{"className":3391,"style":2661},[1717],[1100,3393,3394,3397],{"style":2664},[1100,3395],{"className":3396,"style":1726},[1725],[1100,3398,3400],{"className":3399},[1730,1731,1732,1733],[1100,3401,2616],{"className":3402},[1162,1733],[1100,3404,1745],{"className":3405},[1744],[1100,3407,3409],{"className":3408},[1713],[1100,3410,3412],{"className":3411,"style":1752},[1717],[1100,3413],{},[1100,3415,3417,3420],{"className":3416},[1162],[1100,3418,1672],{"className":3419,"style":1465},[1162,1163],[1100,3421,3423],{"className":3422},[1704],[1100,3424,3426,3449],{"className":3425},[1708,1709],[1100,3427,3429,3446],{"className":3428},[1713],[1100,3430,3432],{"className":3431,"style":1718},[1717],[1100,3433,3434,3437],{"style":1721},[1100,3435],{"className":3436,"style":1726},[1725],[1100,3438,3440],{"className":3439},[1730,1731,1732,1733],[1100,3441,3443],{"className":3442},[1162,1733],[1100,3444,2253],{"className":3445},[1162,1163,1733],[1100,3447,1745],{"className":3448},[1744],[1100,3450,3452],{"className":3451},[1713],[1100,3453,3455],{"className":3454,"style":1752},[1717],[1100,3456],{},[1100,3458,1133],{"className":3459},[1194],[1100,3461,1433],{"className":3462,"style":1465},[1162,1163],[1100,3464],{"className":3465,"style":1331},[1168],[1100,3467,1957],{"className":3468},[1357],[1100,3470],{"className":3471,"style":1331},[1168],[1100,3473,3475,3478,3481,3484,3487,3490],{"className":3474},[1153],[1100,3476],{"className":3477,"style":1183},[1157],[1100,3479,1871],{"className":3480},[1162],[1100,3482,1139],{"className":3483},[1201],[1100,3485],{"className":3486,"style":1331},[1168],[1100,3488,1299],{"className":3489},[1357],[1100,3491],{"className":3492,"style":1331},[1168],[1100,3494,3496,3499,3502,3505,3508,3511],{"className":3495},[1153],[1100,3497],{"className":3498,"style":1183},[1157],[1100,3500,1133],{"className":3501},[1194],[1100,3503,1871],{"className":3504},[1162],[1100,3506],{"className":3507,"style":1331},[1168],[1100,3509,1957],{"className":3510},[1357],[1100,3512],{"className":3513,"style":1331},[1168],[1100,3515,3517,3520,3560,3563,3606,3609,3612,3615,3618,3621],{"className":3516},[1153],[1100,3518],{"className":3519,"style":1183},[1157],[1100,3521,3523,3526],{"className":3522},[1162],[1100,3524,2206],{"className":3525,"style":2271},[1162,1163],[1100,3527,3529],{"className":3528},[1704],[1100,3530,3532,3552],{"className":3531},[1708,1709],[1100,3533,3535,3549],{"className":3534},[1713],[1100,3536,3538],{"className":3537,"style":2661},[1717],[1100,3539,3540,3543],{"style":2664},[1100,3541],{"className":3542,"style":1726},[1725],[1100,3544,3546],{"className":3545},[1730,1731,1732,1733],[1100,3547,2616],{"className":3548},[1162,1733],[1100,3550,1745],{"className":3551},[1744],[1100,3553,3555],{"className":3554},[1713],[1100,3556,3558],{"className":3557,"style":1752},[1717],[1100,3559],{},[1100,3561,1139],{"className":3562},[1201],[1100,3564,3566,3569],{"className":3565},[1162],[1100,3567,1672],{"className":3568,"style":1465},[1162,1163],[1100,3570,3572],{"className":3571},[1704],[1100,3573,3575,3598],{"className":3574},[1708,1709],[1100,3576,3578,3595],{"className":3577},[1713],[1100,3579,3581],{"className":3580,"style":1718},[1717],[1100,3582,3583,3586],{"style":1721},[1100,3584],{"className":3585,"style":1726},[1725],[1100,3587,3589],{"className":3588},[1730,1731,1732,1733],[1100,3590,3592],{"className":3591},[1162,1733],[1100,3593,2253],{"className":3594},[1162,1163,1733],[1100,3596,1745],{"className":3597},[1744],[1100,3599,3601],{"className":3600},[1713],[1100,3602,3604],{"className":3603,"style":1752},[1717],[1100,3605],{},[1100,3607,1133],{"className":3608},[1194],[1100,3610,1433],{"className":3611,"style":1465},[1162,1163],[1100,3613,1139],{"className":3614},[1201],[1100,3616],{"className":3617,"style":1169},[1168],[1100,3619,1294],{"className":3620},[1173],[1100,3622],{"className":3623,"style":1169},[1168],[1100,3625,3627,3630],{"className":3626},[1153],[1100,3628],{"className":3629,"style":1610},[1157],[1100,3631,2290],{"className":3632,"style":1272},[1162,1163],[1096,3634,3635,1202,3663,3691,3692,1202,3764,3833],{},[1100,3636,3638,3651],{"className":3637},[1103],[1100,3639,3641],{"className":3640},[1107],[1109,3642,3643],{"xmlns":1111},[1113,3644,3645,3649],{},[1116,3646,3647],{},[1119,3648,2883],{},[1141,3650,2883],{"encoding":1143},[1100,3652,3654],{"className":3653,"ariaHidden":1149},[1148],[1100,3655,3657,3660],{"className":3656},[1153],[1100,3658],{"className":3659,"style":1158},[1157],[1100,3661,2883],{"className":3662},[1162,1163],[1100,3664,3666,3679],{"className":3665},[1103],[1100,3667,3669],{"className":3668},[1107],[1109,3670,3671],{"xmlns":1111},[1113,3672,3673,3677],{},[1116,3674,3675],{},[1119,3676,3261],{},[1141,3678,3261],{"encoding":1143},[1100,3680,3682],{"className":3681,"ariaHidden":1149},[1148],[1100,3683,3685,3688],{"className":3684},[1153],[1100,3686],{"className":3687,"style":1158},[1157],[1100,3689,3261],{"className":3690,"style":3349},[1162,1163]," 是关于参数的函数，且由于泊松分布函的单调性，逆函数 ",[1100,3693,3695,3718],{"className":3694},[1103],[1100,3696,3698],{"className":3697},[1107],[1109,3699,3700],{"xmlns":1111},[1113,3701,3702,3715],{},[1116,3703,3704],{},[3705,3706,3707,3709],"msup",{},[1119,3708,2883],{},[1116,3710,3711,3713],{},[1123,3712,1957],{},[1863,3714,1871],{},[1141,3716,3717],{"encoding":1143},"G^{-1}",[1100,3719,3721],{"className":3720,"ariaHidden":1149},[1148],[1100,3722,3724,3728],{"className":3723},[1153],[1100,3725],{"className":3726,"style":3727},[1157],"height:0.8141em;",[1100,3729,3731,3734],{"className":3730},[1162],[1100,3732,2883],{"className":3733},[1162,1163],[1100,3735,3737],{"className":3736},[1704],[1100,3738,3740],{"className":3739},[1708],[1100,3741,3743],{"className":3742},[1713],[1100,3744,3746],{"className":3745,"style":3727},[1717],[1100,3747,3749,3752],{"style":3748},"top:-3.063em;margin-right:0.05em;",[1100,3750],{"className":3751,"style":1726},[1725],[1100,3753,3755],{"className":3754},[1730,1731,1732,1733],[1100,3756,3758,3761],{"className":3757},[1162,1733],[1100,3759,1957],{"className":3760},[1162,1733],[1100,3762,1871],{"className":3763},[1162,1733],[1100,3765,3767,3789],{"className":3766},[1103],[1100,3768,3770],{"className":3769},[1107],[1109,3771,3772],{"xmlns":1111},[1113,3773,3774,3786],{},[1116,3775,3776],{},[3705,3777,3778,3780],{},[1119,3779,3261],{},[1116,3781,3782,3784],{},[1123,3783,1957],{},[1863,3785,1871],{},[1141,3787,3788],{"encoding":1143},"H^{-1}",[1100,3790,3792],{"className":3791,"ariaHidden":1149},[1148],[1100,3793,3795,3798],{"className":3794},[1153],[1100,3796],{"className":3797,"style":3727},[1157],[1100,3799,3801,3804],{"className":3800},[1162],[1100,3802,3261],{"className":3803,"style":3349},[1162,1163],[1100,3805,3807],{"className":3806},[1704],[1100,3808,3810],{"className":3809},[1708],[1100,3811,3813],{"className":3812},[1713],[1100,3814,3816],{"className":3815,"style":3727},[1717],[1100,3817,3818,3821],{"style":3748},[1100,3819],{"className":3820,"style":1726},[1725],[1100,3822,3824],{"className":3823},[1730,1731,1732,1733],[1100,3825,3827,3830],{"className":3826},[1162,1733],[1100,3828,1957],{"className":3829},[1162,1733],[1100,3831,1871],{"className":3832},[1162,1733]," 存在",[1619,3835,3837],{"id":3836},"_3-逆解参数使用-brentq-函数进行二分法求根","3: 逆解参数，使用 brentq 函数进行二分法求根",[1096,3839,3840,3841,1202,3869,3899],{},"从上述方程解出 ",[1100,3842,3844,3857],{"className":3843},[1103],[1100,3845,3847],{"className":3846},[1107],[1109,3848,3849],{"xmlns":1111},[1113,3850,3851,3855],{},[1116,3852,3853],{},[1119,3854,1675],{},[1141,3856,1675],{"encoding":1143},[1100,3858,3860],{"className":3859,"ariaHidden":1149},[1148],[1100,3861,3863,3866],{"className":3862},[1153],[1100,3864],{"className":3865,"style":1540},[1157],[1100,3867,1675],{"className":3868,"style":1740},[1162,1163],[1100,3870,3872,3887],{"className":3871},[1103],[1100,3873,3875],{"className":3874},[1107],[1109,3876,3877],{"xmlns":1111},[1113,3878,3879,3885],{},[1116,3880,3881,3883],{},[1119,3882,1442],{},[1119,3884,1136],{},[1141,3886,2253],{"encoding":1143},[1100,3888,3890],{"className":3889,"ariaHidden":1149},[1148],[1100,3891,3893,3896],{"className":3892},[1153],[1100,3894],{"className":3895,"style":1540},[1157],[1100,3897,2253],{"className":3898},[1162,1163],"：",[1096,3901,3902],{},[1100,3903,3905,3964],{"className":3904},[1103],[1100,3906,3908],{"className":3907},[1107],[1109,3909,3910],{"xmlns":1111},[1113,3911,3912,3961],{},[1116,3913,3914,3916,3918,3928,3930,3932,3934,3936,3939,3941,3943,3945,3955,3957,3959],{},[1119,3915,1675],{},[1123,3917,1294],{},[3705,3919,3920,3922],{},[1119,3921,2883],{},[1116,3923,3924,3926],{},[1123,3925,1957],{},[1863,3927,1871],{},[1123,3929,1133],{"stretchy":1132},[1119,3931,1854],{},[1123,3933,1139],{"stretchy":1132},[1123,3935,1868],{"separator":1149},[1168,3937],{"width":3938},"1em",[1119,3940,1442],{},[1119,3942,1136],{},[1123,3944,1294],{},[3705,3946,3947,3949],{},[1119,3948,3261],{},[1116,3950,3951,3953],{},[1123,3952,1957],{},[1863,3954,1871],{},[1123,3956,1133],{"stretchy":1132},[1119,3958,2290],{},[1123,3960,1139],{"stretchy":1132},[1141,3962,3963],{"encoding":1143},"θ = G^{-1}(u), \\quad mb = H^{-1}(v)",[1100,3965,3967,3985,4058],{"className":3966,"ariaHidden":1149},[1148],[1100,3968,3970,3973,3976,3979,3982],{"className":3969},[1153],[1100,3971],{"className":3972,"style":1540},[1157],[1100,3974,1675],{"className":3975,"style":1740},[1162,1163],[1100,3977],{"className":3978,"style":1169},[1168],[1100,3980,1294],{"className":3981},[1173],[1100,3983],{"className":3984,"style":1169},[1168],[1100,3986,3988,3992,4027,4030,4033,4036,4039,4043,4046,4049,4052,4055],{"className":3987},[1153],[1100,3989],{"className":3990,"style":3991},[1157],"height:1.0641em;vertical-align:-0.25em;",[1100,3993,3995,3998],{"className":3994},[1162],[1100,3996,2883],{"className":3997},[1162,1163],[1100,3999,4001],{"className":4000},[1704],[1100,4002,4004],{"className":4003},[1708],[1100,4005,4007],{"className":4006},[1713],[1100,4008,4010],{"className":4009,"style":3727},[1717],[1100,4011,4012,4015],{"style":3748},[1100,4013],{"className":4014,"style":1726},[1725],[1100,4016,4018],{"className":4017},[1730,1731,1732,1733],[1100,4019,4021,4024],{"className":4020},[1162,1733],[1100,4022,1957],{"className":4023},[1162,1733],[1100,4025,1871],{"className":4026},[1162,1733],[1100,4028,1133],{"className":4029},[1194],[1100,4031,1854],{"className":4032},[1162,1163],[1100,4034,1139],{"className":4035},[1201],[1100,4037,1868],{"className":4038},[1919],[1100,4040],{"className":4041,"style":4042},[1168],"margin-right:1em;",[1100,4044],{"className":4045,"style":1923},[1168],[1100,4047,2253],{"className":4048},[1162,1163],[1100,4050],{"className":4051,"style":1169},[1168],[1100,4053,1294],{"className":4054},[1173],[1100,4056],{"className":4057,"style":1169},[1168],[1100,4059,4061,4064,4099,4102,4105],{"className":4060},[1153],[1100,4062],{"className":4063,"style":3991},[1157],[1100,4065,4067,4070],{"className":4066},[1162],[1100,4068,3261],{"className":4069,"style":3349},[1162,1163],[1100,4071,4073],{"className":4072},[1704],[1100,4074,4076],{"className":4075},[1708],[1100,4077,4079],{"className":4078},[1713],[1100,4080,4082],{"className":4081,"style":3727},[1717],[1100,4083,4084,4087],{"style":3748},[1100,4085],{"className":4086,"style":1726},[1725],[1100,4088,4090],{"className":4089},[1730,1731,1732,1733],[1100,4091,4093,4096],{"className":4092},[1162,1733],[1100,4094,1957],{"className":4095},[1162,1733],[1100,4097,1871],{"className":4098},[1162,1733],[1100,4100,1133],{"className":4101},[1194],[1100,4103,2290],{"className":4104,"style":1272},[1162,1163],[1100,4106,1139],{"className":4107},[1201],[1096,4109,4110],{},"推导参数：",[1096,4112,4113],{},[1100,4114,4116,4211],{"className":4115},[1103],[1100,4117,4119],{"className":4118},[1107],[1109,4120,4121],{"xmlns":1111},[1113,4122,4123,4208],{},[1116,4124,4125,4127,4129,4152,4154,4156,4158,4160,4162,4164,4166,4168,4178,4180,4182,4184,4186],{},[1119,4126,1136],{},[1123,4128,1294],{},[4130,4131,4132,4150],"mfrac",{},[1116,4133,4134,4144,4146,4148],{},[3705,4135,4136,4138],{},[1119,4137,3261],{},[1116,4139,4140,4142],{},[1123,4141,1957],{},[1863,4143,1871],{},[1123,4145,1133],{"stretchy":1132},[1119,4147,2290],{},[1123,4149,1139],{"stretchy":1132},[1119,4151,1442],{},[1123,4153,1868],{"separator":1149},[1168,4155],{"width":3938},[1119,4157,1226],{},[1123,4159,1294],{},[1119,4161,1675],{},[1123,4163,1957],{},[1119,4165,1136],{},[1123,4167,1294],{},[3705,4169,4170,4172],{},[1119,4171,2883],{},[1116,4173,4174,4176],{},[1123,4175,1957],{},[1863,4177,1871],{},[1123,4179,1133],{"stretchy":1132},[1119,4181,1854],{},[1123,4183,1139],{"stretchy":1132},[1123,4185,1957],{},[4130,4187,4188,4206],{},[1116,4189,4190,4200,4202,4204],{},[3705,4191,4192,4194],{},[1119,4193,3261],{},[1116,4195,4196,4198],{},[1123,4197,1957],{},[1863,4199,1871],{},[1123,4201,1133],{"stretchy":1132},[1119,4203,2290],{},[1123,4205,1139],{"stretchy":1132},[1119,4207,1442],{},[1141,4209,4210],{"encoding":1143},"b = \\frac{H^{-1}(v)}{m}, \\quad q = θ - b = G^{-1}(u) - \\frac{H^{-1}(v)}{m}",[1100,4212,4214,4232,4383,4401,4419,4478],{"className":4213,"ariaHidden":1149},[1148],[1100,4215,4217,4220,4223,4226,4229],{"className":4216},[1153],[1100,4218],{"className":4219,"style":1540},[1157],[1100,4221,1136],{"className":4222},[1162,1163],[1100,4224],{"className":4225,"style":1169},[1168],[1100,4227,1294],{"className":4228},[1173],[1100,4230],{"className":4231,"style":1169},[1168],[1100,4233,4235,4239,4362,4365,4368,4371,4374,4377,4380],{"className":4234},[1153],[1100,4236],{"className":4237,"style":4238},[1157],"height:1.4539em;vertical-align:-0.345em;",[1100,4240,4242,4246,4359],{"className":4241},[1162],[1100,4243],{"className":4244},[1194,4245],"nulldelimiter",[1100,4247,4249],{"className":4248},[4130],[1100,4250,4252,4350],{"className":4251},[1708,1709],[1100,4253,4255,4347],{"className":4254},[1713],[1100,4256,4259,4275,4286],{"className":4257,"style":4258},[1717],"height:1.1089em;",[1100,4260,4262,4266],{"style":4261},"top:-2.655em;",[1100,4263],{"className":4264,"style":4265},[1725],"height:3em;",[1100,4267,4269],{"className":4268},[1730,1731,1732,1733],[1100,4270,4272],{"className":4271},[1162,1733],[1100,4273,1442],{"className":4274},[1162,1163,1733],[1100,4276,4278,4281],{"style":4277},"top:-3.23em;",[1100,4279],{"className":4280,"style":4265},[1725],[1100,4282],{"className":4283,"style":4285},[4284],"frac-line","border-bottom-width:0.04em;",[1100,4287,4289,4292],{"style":4288},"top:-3.485em;",[1100,4290],{"className":4291,"style":4265},[1725],[1100,4293,4295],{"className":4294},[1730,1731,1732,1733],[1100,4296,4298,4338,4341,4344],{"className":4297},[1162,1733],[1100,4299,4301,4304],{"className":4300},[1162,1733],[1100,4302,3261],{"className":4303,"style":3349},[1162,1163,1733],[1100,4305,4307],{"className":4306},[1704],[1100,4308,4310],{"className":4309},[1708],[1100,4311,4313],{"className":4312},[1713],[1100,4314,4317],{"className":4315,"style":4316},[1717],"height:0.8913em;",[1100,4318,4320,4324],{"style":4319},"top:-2.931em;margin-right:0.0714em;",[1100,4321],{"className":4322,"style":4323},[1725],"height:2.5em;",[1100,4325,4329],{"className":4326},[1730,4327,4328,1733],"reset-size3","size1",[1100,4330,4332,4335],{"className":4331},[1162,1733],[1100,4333,1957],{"className":4334},[1162,1733],[1100,4336,1871],{"className":4337},[1162,1733],[1100,4339,1133],{"className":4340},[1194,1733],[1100,4342,2290],{"className":4343,"style":1272},[1162,1163,1733],[1100,4345,1139],{"className":4346},[1201,1733],[1100,4348,1745],{"className":4349},[1744],[1100,4351,4353],{"className":4352},[1713],[1100,4354,4357],{"className":4355,"style":4356},[1717],"height:0.345em;",[1100,4358],{},[1100,4360],{"className":4361},[1201,4245],[1100,4363,1868],{"className":4364},[1919],[1100,4366],{"className":4367,"style":4042},[1168],[1100,4369],{"className":4370,"style":1923},[1168],[1100,4372,1226],{"className":4373,"style":1272},[1162,1163],[1100,4375],{"className":4376,"style":1169},[1168],[1100,4378,1294],{"className":4379},[1173],[1100,4381],{"className":4382,"style":1169},[1168],[1100,4384,4386,4389,4392,4395,4398],{"className":4385},[1153],[1100,4387],{"className":4388,"style":1817},[1157],[1100,4390,1675],{"className":4391,"style":1740},[1162,1163],[1100,4393],{"className":4394,"style":1331},[1168],[1100,4396,1957],{"className":4397},[1357],[1100,4399],{"className":4400,"style":1331},[1168],[1100,4402,4404,4407,4410,4413,4416],{"className":4403},[1153],[1100,4405],{"className":4406,"style":1540},[1157],[1100,4408,1136],{"className":4409},[1162,1163],[1100,4411],{"className":4412,"style":1169},[1168],[1100,4414,1294],{"className":4415},[1173],[1100,4417],{"className":4418,"style":1169},[1168],[1100,4420,4422,4425,4460,4463,4466,4469,4472,4475],{"className":4421},[1153],[1100,4423],{"className":4424,"style":3991},[1157],[1100,4426,4428,4431],{"className":4427},[1162],[1100,4429,2883],{"className":4430},[1162,1163],[1100,4432,4434],{"className":4433},[1704],[1100,4435,4437],{"className":4436},[1708],[1100,4438,4440],{"className":4439},[1713],[1100,4441,4443],{"className":4442,"style":3727},[1717],[1100,4444,4445,4448],{"style":3748},[1100,4446],{"className":4447,"style":1726},[1725],[1100,4449,4451],{"className":4450},[1730,1731,1732,1733],[1100,4452,4454,4457],{"className":4453},[1162,1733],[1100,4455,1957],{"className":4456},[1162,1733],[1100,4458,1871],{"className":4459},[1162,1733],[1100,4461,1133],{"className":4462},[1194],[1100,4464,1854],{"className":4465},[1162,1163],[1100,4467,1139],{"className":4468},[1201],[1100,4470],{"className":4471,"style":1331},[1168],[1100,4473,1957],{"className":4474},[1357],[1100,4476],{"className":4477,"style":1331},[1168],[1100,4479,4481,4484],{"className":4480},[1153],[1100,4482],{"className":4483,"style":4238},[1157],[1100,4485,4487,4490,4590],{"className":4486},[1162],[1100,4488],{"className":4489},[1194,4245],[1100,4491,4493],{"className":4492},[4130],[1100,4494,4496,4582],{"className":4495},[1708,1709],[1100,4497,4499,4579],{"className":4498},[1713],[1100,4500,4502,4516,4524],{"className":4501,"style":4258},[1717],[1100,4503,4504,4507],{"style":4261},[1100,4505],{"className":4506,"style":4265},[1725],[1100,4508,4510],{"className":4509},[1730,1731,1732,1733],[1100,4511,4513],{"className":4512},[1162,1733],[1100,4514,1442],{"className":4515},[1162,1163,1733],[1100,4517,4518,4521],{"style":4277},[1100,4519],{"className":4520,"style":4265},[1725],[1100,4522],{"className":4523,"style":4285},[4284],[1100,4525,4526,4529],{"style":4288},[1100,4527],{"className":4528,"style":4265},[1725],[1100,4530,4532],{"className":4531},[1730,1731,1732,1733],[1100,4533,4535,4570,4573,4576],{"className":4534},[1162,1733],[1100,4536,4538,4541],{"className":4537},[1162,1733],[1100,4539,3261],{"className":4540,"style":3349},[1162,1163,1733],[1100,4542,4544],{"className":4543},[1704],[1100,4545,4547],{"className":4546},[1708],[1100,4548,4550],{"className":4549},[1713],[1100,4551,4553],{"className":4552,"style":4316},[1717],[1100,4554,4555,4558],{"style":4319},[1100,4556],{"className":4557,"style":4323},[1725],[1100,4559,4561],{"className":4560},[1730,4327,4328,1733],[1100,4562,4564,4567],{"className":4563},[1162,1733],[1100,4565,1957],{"className":4566},[1162,1733],[1100,4568,1871],{"className":4569},[1162,1733],[1100,4571,1133],{"className":4572},[1194,1733],[1100,4574,2290],{"className":4575,"style":1272},[1162,1163,1733],[1100,4577,1139],{"className":4578},[1201,1733],[1100,4580,1745],{"className":4581},[1744],[1100,4583,4585],{"className":4584},[1713],[1100,4586,4588],{"className":4587,"style":4356},[1717],[1100,4589],{},[1100,4591],{"className":4592},[1201,4245],[1096,4594,4595,4596,1202,4624,4652],{},"得到 ",[1100,4597,4599,4612],{"className":4598},[1103],[1100,4600,4602],{"className":4601},[1107],[1109,4603,4604],{"xmlns":1111},[1113,4605,4606,4610],{},[1116,4607,4608],{},[1119,4609,1136],{},[1141,4611,1136],{"encoding":1143},[1100,4613,4615],{"className":4614,"ariaHidden":1149},[1148],[1100,4616,4618,4621],{"className":4617},[1153],[1100,4619],{"className":4620,"style":1540},[1157],[1100,4622,1136],{"className":4623},[1162,1163],[1100,4625,4627,4640],{"className":4626},[1103],[1100,4628,4630],{"className":4629},[1107],[1109,4631,4632],{"xmlns":1111},[1113,4633,4634,4638],{},[1116,4635,4636],{},[1119,4637,1226],{},[1141,4639,1226],{"encoding":1143},[1100,4641,4643],{"className":4642,"ariaHidden":1149},[1148],[1100,4644,4646,4649],{"className":4645},[1153],[1100,4647],{"className":4648,"style":1570},[1157],[1100,4650,1226],{"className":4651,"style":1272},[1162,1163]," 的表达式",[1619,4654,4656],{"id":4655},"_4-验证覆盖率","4: 验证覆盖率",[4658,4659,4660,4693],"ul",{},[4661,4662,4663,4664,4692],"li",{},"模拟目标：检查构造的置信区间覆盖真实 ",[1100,4665,4667,4680],{"className":4666},[1103],[1100,4668,4670],{"className":4669},[1107],[1109,4671,4672],{"xmlns":1111},[1113,4673,4674,4678],{},[1116,4675,4676],{},[1119,4677,1226],{},[1141,4679,1226],{"encoding":1143},[1100,4681,4683],{"className":4682,"ariaHidden":1149},[1148],[1100,4684,4686,4689],{"className":4685},[1153],[1100,4687],{"className":4688,"style":1570},[1157],[1100,4690,1226],{"className":4691,"style":1272},[1162,1163]," 的概率是否接近 95%",[4661,4694,4695],{},"步骤：",[1096,4697,4698,4699],{},"生成观测数据：从分布生成一对观测值 ",[1100,4700,4702,4724],{"className":4701},[1103],[1100,4703,4705],{"className":4704},[1107],[1109,4706,4707],{"xmlns":1111},[1113,4708,4709,4721],{},[1116,4710,4711,4713,4715,4717,4719],{},[1123,4712,1133],{"stretchy":1132},[1119,4714,1291],{},[1123,4716,1868],{"separator":1149},[1119,4718,1433],{},[1123,4720,1139],{"stretchy":1132},[1141,4722,4723],{"encoding":1143},"(Y,W)",[1100,4725,4727],{"className":4726,"ariaHidden":1149},[1148],[1100,4728,4730,4733,4736,4739,4742,4745,4748],{"className":4729},[1153],[1100,4731],{"className":4732,"style":1183},[1157],[1100,4734,1133],{"className":4735},[1194],[1100,4737,1291],{"className":4738,"style":1331},[1162,1163],[1100,4740,1868],{"className":4741},[1919],[1100,4743],{"className":4744,"style":1923},[1168],[1100,4746,1433],{"className":4747,"style":1465},[1162,1163],[1100,4749,1139],{"className":4750},[1201],[1096,4752,4753,4754,4805,4806,4861,4862],{},"对于固定 ",[1100,4755,4757,4778],{"className":4756},[1103],[1100,4758,4760],{"className":4759},[1107],[1109,4761,4762],{"xmlns":1111},[1113,4763,4764,4776],{},[1116,4765,4766,4768,4770,4772,4774],{},[1123,4767,1133],{"stretchy":1132},[1119,4769,1291],{},[1123,4771,1868],{"separator":1149},[1119,4773,1433],{},[1123,4775,1139],{"stretchy":1132},[1141,4777,4723],{"encoding":1143},[1100,4779,4781],{"className":4780,"ariaHidden":1149},[1148],[1100,4782,4784,4787,4790,4793,4796,4799,4802],{"className":4783},[1153],[1100,4785],{"className":4786,"style":1183},[1157],[1100,4788,1133],{"className":4789},[1194],[1100,4791,1291],{"className":4792,"style":1331},[1162,1163],[1100,4794,1868],{"className":4795},[1919],[1100,4797],{"className":4798,"style":1923},[1168],[1100,4800,1433],{"className":4801,"style":1465},[1162,1163],[1100,4803,1139],{"className":4804},[1201],"，生成大量样本（如 ",[1100,4807,4809,4829],{"className":4808},[1103],[1100,4810,4812],{"className":4811},[1107],[1109,4813,4814],{"xmlns":1111},[1113,4815,4816,4826],{},[1116,4817,4818,4821,4823],{},[1119,4819,4820],{},"N",[1123,4822,1294],{},[1863,4824,4825],{},"10000",[1141,4827,4828],{"encoding":1143},"N=10000",[1100,4830,4832,4851],{"className":4831,"ariaHidden":1149},[1148],[1100,4833,4835,4838,4842,4845,4848],{"className":4834},[1153],[1100,4836],{"className":4837,"style":1158},[1157],[1100,4839,4820],{"className":4840,"style":4841},[1162,1163],"margin-right:0.109em;",[1100,4843],{"className":4844,"style":1169},[1168],[1100,4846,1294],{"className":4847},[1173],[1100,4849],{"className":4850,"style":1169},[1168],[1100,4852,4854,4858],{"className":4853},[1153],[1100,4855],{"className":4856,"style":4857},[1157],"height:0.6444em;",[1100,4859,4825],{"className":4860},[1162]," 个）的 ",[1100,4863,4865,4913],{"className":4864},[1103],[1100,4866,4868],{"className":4867},[1107],[1109,4869,4870],{"xmlns":1111},[1113,4871,4872,4910],{},[1116,4873,4874,4876,4878,4880,4882,4888,4890,4896,4898,4900,4902,4904,4906,4908],{},[1119,4875,1854],{},[1123,4877,1868],{"separator":1149},[1119,4879,2290],{},[1123,4881,1868],{"separator":1149},[1668,4883,4884,4886],{},[1119,4885,2206],{},[1863,4887,1871],{},[1123,4889,1868],{"separator":1149},[1668,4891,4892,4894],{},[1119,4893,2206],{},[1863,4895,2616],{},[1123,4897,1125],{},[1127,4899,1859],{},[1123,4901,1133],{"stretchy":1132},[1863,4903,1865],{},[1123,4905,1868],{"separator":1149},[1863,4907,1871],{},[1123,4909,1139],{"stretchy":1132},[1141,4911,4912],{"encoding":1143},"u, v, w_1, w_2 \\sim \\text{Uniform}(0,1)",[1100,4914,4916,5035],{"className":4915,"ariaHidden":1149},[1148],[1100,4917,4919,4922,4925,4928,4931,4934,4937,4940,4980,4983,4986,5026,5029,5032],{"className":4918},[1153],[1100,4920],{"className":4921,"style":1570},[1157],[1100,4923,1854],{"className":4924},[1162,1163],[1100,4926,1868],{"className":4927},[1919],[1100,4929],{"className":4930,"style":1923},[1168],[1100,4932,2290],{"className":4933,"style":1272},[1162,1163],[1100,4935,1868],{"className":4936},[1919],[1100,4938],{"className":4939,"style":1923},[1168],[1100,4941,4943,4946],{"className":4942},[1162],[1100,4944,2206],{"className":4945,"style":2271},[1162,1163],[1100,4947,4949],{"className":4948},[1704],[1100,4950,4952,4972],{"className":4951},[1708,1709],[1100,4953,4955,4969],{"className":4954},[1713],[1100,4956,4958],{"className":4957,"style":2661},[1717],[1100,4959,4960,4963],{"style":2664},[1100,4961],{"className":4962,"style":1726},[1725],[1100,4964,4966],{"className":4965},[1730,1731,1732,1733],[1100,4967,1871],{"className":4968},[1162,1733],[1100,4970,1745],{"className":4971},[1744],[1100,4973,4975],{"className":4974},[1713],[1100,4976,4978],{"className":4977,"style":1752},[1717],[1100,4979],{},[1100,4981,1868],{"className":4982},[1919],[1100,4984],{"className":4985,"style":1923},[1168],[1100,4987,4989,4992],{"className":4988},[1162],[1100,4990,2206],{"className":4991,"style":2271},[1162,1163],[1100,4993,4995],{"className":4994},[1704],[1100,4996,4998,5018],{"className":4997},[1708,1709],[1100,4999,5001,5015],{"className":5000},[1713],[1100,5002,5004],{"className":5003,"style":2661},[1717],[1100,5005,5006,5009],{"style":2664},[1100,5007],{"className":5008,"style":1726},[1725],[1100,5010,5012],{"className":5011},[1730,1731,1732,1733],[1100,5013,2616],{"className":5014},[1162,1733],[1100,5016,1745],{"className":5017},[1744],[1100,5019,5021],{"className":5020},[1713],[1100,5022,5024],{"className":5023,"style":1752},[1717],[1100,5025],{},[1100,5027],{"className":5028,"style":1169},[1168],[1100,5030,1125],{"className":5031},[1173],[1100,5033],{"className":5034,"style":1169},[1168],[1100,5036,5038,5041,5047,5050,5053,5056,5059,5062],{"className":5037},[1153],[1100,5039],{"className":5040,"style":1183},[1157],[1100,5042,5044],{"className":5043},[1162,1187],[1100,5045,1859],{"className":5046},[1162],[1100,5048,1133],{"className":5049},[1194],[1100,5051,1865],{"className":5052},[1162],[1100,5054,1868],{"className":5055},[1919],[1100,5057],{"className":5058,"style":1923},[1168],[1100,5060,1871],{"className":5061},[1162],[1100,5063,1139],{"className":5064},[1201],[1096,5066,5067,5068,5096,5097],{},"计算 ",[1100,5069,5071,5084],{"className":5070},[1103],[1100,5072,5074],{"className":5073},[1107],[1109,5075,5076],{"xmlns":1111},[1113,5077,5078,5082],{},[1116,5079,5080],{},[1119,5081,1226],{},[1141,5083,1226],{"encoding":1143},[1100,5085,5087],{"className":5086,"ariaHidden":1149},[1148],[1100,5088,5090,5093],{"className":5089},[1153],[1100,5091],{"className":5092,"style":1570},[1157],[1100,5094,1226],{"className":5095,"style":1272},[1162,1163]," 的候选值：对于每个样本，计算 ",[1100,5098,5100,5161],{"className":5099},[1103],[1100,5101,5103],{"className":5102},[1107],[1109,5104,5105],{"xmlns":1111},[1113,5106,5107,5158],{},[1116,5108,5109,5116,5118,5128,5130,5132,5134,5136],{},[1668,5110,5111,5113],{},[1119,5112,1226],{},[1127,5114,5115],{},"candidate",[1123,5117,1294],{},[3705,5119,5120,5122],{},[1119,5121,2883],{},[1116,5123,5124,5126],{},[1123,5125,1957],{},[1863,5127,1871],{},[1123,5129,1133],{"stretchy":1132},[1119,5131,1854],{},[1123,5133,1139],{"stretchy":1132},[1123,5135,1957],{},[4130,5137,5138,5156],{},[1116,5139,5140,5150,5152,5154],{},[3705,5141,5142,5144],{},[1119,5143,3261],{},[1116,5145,5146,5148],{},[1123,5147,1957],{},[1863,5149,1871],{},[1123,5151,1133],{"stretchy":1132},[1119,5153,2290],{},[1123,5155,1139],{"stretchy":1132},[1119,5157,1442],{},[1141,5159,5160],{"encoding":1143},"q_{\\text{candidate}} = G^{-1}(u) - \\frac{H^{-1}(v)}{m}",[1100,5162,5164,5226,5285],{"className":5163,"ariaHidden":1149},[1148],[1100,5165,5167,5170,5217,5220,5223],{"className":5166},[1153],[1100,5168],{"className":5169,"style":1570},[1157],[1100,5171,5173,5176],{"className":5172},[1162],[1100,5174,1226],{"className":5175,"style":1272},[1162,1163],[1100,5177,5179],{"className":5178},[1704],[1100,5180,5182,5209],{"className":5181},[1708,1709],[1100,5183,5185,5206],{"className":5184},[1713],[1100,5186,5188],{"className":5187,"style":1718},[1717],[1100,5189,5191,5194],{"style":5190},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1100,5192],{"className":5193,"style":1726},[1725],[1100,5195,5197],{"className":5196},[1730,1731,1732,1733],[1100,5198,5200],{"className":5199},[1162,1733],[1100,5201,5203],{"className":5202},[1162,1187,1733],[1100,5204,5115],{"className":5205},[1162,1733],[1100,5207,1745],{"className":5208},[1744],[1100,5210,5212],{"className":5211},[1713],[1100,5213,5215],{"className":5214,"style":1752},[1717],[1100,5216],{},[1100,5218],{"className":5219,"style":1169},[1168],[1100,5221,1294],{"className":5222},[1173],[1100,5224],{"className":5225,"style":1169},[1168],[1100,5227,5229,5232,5267,5270,5273,5276,5279,5282],{"className":5228},[1153],[1100,5230],{"className":5231,"style":3991},[1157],[1100,5233,5235,5238],{"className":5234},[1162],[1100,5236,2883],{"className":5237},[1162,1163],[1100,5239,5241],{"className":5240},[1704],[1100,5242,5244],{"className":5243},[1708],[1100,5245,5247],{"className":5246},[1713],[1100,5248,5250],{"className":5249,"style":3727},[1717],[1100,5251,5252,5255],{"style":3748},[1100,5253],{"className":5254,"style":1726},[1725],[1100,5256,5258],{"className":5257},[1730,1731,1732,1733],[1100,5259,5261,5264],{"className":5260},[1162,1733],[1100,5262,1957],{"className":5263},[1162,1733],[1100,5265,1871],{"className":5266},[1162,1733],[1100,5268,1133],{"className":5269},[1194],[1100,5271,1854],{"className":5272},[1162,1163],[1100,5274,1139],{"className":5275},[1201],[1100,5277],{"className":5278,"style":1331},[1168],[1100,5280,1957],{"className":5281},[1357],[1100,5283],{"className":5284,"style":1331},[1168],[1100,5286,5288,5291],{"className":5287},[1153],[1100,5289],{"className":5290,"style":4238},[1157],[1100,5292,5294,5297,5397],{"className":5293},[1162],[1100,5295],{"className":5296},[1194,4245],[1100,5298,5300],{"className":5299},[4130],[1100,5301,5303,5389],{"className":5302},[1708,1709],[1100,5304,5306,5386],{"className":5305},[1713],[1100,5307,5309,5323,5331],{"className":5308,"style":4258},[1717],[1100,5310,5311,5314],{"style":4261},[1100,5312],{"className":5313,"style":4265},[1725],[1100,5315,5317],{"className":5316},[1730,1731,1732,1733],[1100,5318,5320],{"className":5319},[1162,1733],[1100,5321,1442],{"className":5322},[1162,1163,1733],[1100,5324,5325,5328],{"style":4277},[1100,5326],{"className":5327,"style":4265},[1725],[1100,5329],{"className":5330,"style":4285},[4284],[1100,5332,5333,5336],{"style":4288},[1100,5334],{"className":5335,"style":4265},[1725],[1100,5337,5339],{"className":5338},[1730,1731,1732,1733],[1100,5340,5342,5377,5380,5383],{"className":5341},[1162,1733],[1100,5343,5345,5348],{"className":5344},[1162,1733],[1100,5346,3261],{"className":5347,"style":3349},[1162,1163,1733],[1100,5349,5351],{"className":5350},[1704],[1100,5352,5354],{"className":5353},[1708],[1100,5355,5357],{"className":5356},[1713],[1100,5358,5360],{"className":5359,"style":4316},[1717],[1100,5361,5362,5365],{"style":4319},[1100,5363],{"className":5364,"style":4323},[1725],[1100,5366,5368],{"className":5367},[1730,4327,4328,1733],[1100,5369,5371,5374],{"className":5370},[1162,1733],[1100,5372,1957],{"className":5373},[1162,1733],[1100,5375,1871],{"className":5376},[1162,1733],[1100,5378,1133],{"className":5379},[1194,1733],[1100,5381,2290],{"className":5382,"style":1272},[1162,1163,1733],[1100,5384,1139],{"className":5385},[1201,1733],[1100,5387,1745],{"className":5388},[1744],[1100,5390,5392],{"className":5391},[1713],[1100,5393,5395],{"className":5394,"style":4356},[1717],[1100,5396],{},[1100,5398],{"className":5399},[1201,4245],[1096,5401,5402,5403],{},"构造置信区间：从 10000 个 q 值中取分位数，得到置信区间 ",[1100,5404,5406,5442],{"className":5405},[1103],[1100,5407,5409],{"className":5408},[1107],[1109,5410,5411],{"xmlns":1111},[1113,5412,5413,5439],{},[1116,5414,5415,5418,5420,5424,5427,5429,5431,5433,5436],{},[1123,5416,5417],{"stretchy":1132},"[",[1119,5419,1226],{},[1119,5421,5423],{"mathvariant":5422},"normal","_",[1863,5425,5426],{},"0.025",[1123,5428,1868],{"separator":1149},[1119,5430,1226],{},[1119,5432,5423],{"mathvariant":5422},[1863,5434,5435],{},"0.975",[1123,5437,5438],{"stretchy":1132},"]",[1141,5440,5441],{"encoding":1143},"[q\\_{0.025}, q\\_{0.975}]",[1100,5443,5445],{"className":5444,"ariaHidden":1149},[1148],[1100,5446,5448,5452,5455,5458,5461,5467,5470,5473,5476,5479,5485],{"className":5447},[1153],[1100,5449],{"className":5450,"style":5451},[1157],"height:1.06em;vertical-align:-0.31em;",[1100,5453,5417],{"className":5454},[1194],[1100,5456,1226],{"className":5457,"style":1272},[1162,1163],[1100,5459,5423],{"className":5460,"style":1740},[1162],[1100,5462,5464],{"className":5463},[1162],[1100,5465,5426],{"className":5466},[1162],[1100,5468,1868],{"className":5469},[1919],[1100,5471],{"className":5472,"style":1923},[1168],[1100,5474,1226],{"className":5475,"style":1272},[1162,1163],[1100,5477,5423],{"className":5478,"style":1740},[1162],[1100,5480,5482],{"className":5481},[1162],[1100,5483,5435],{"className":5484},[1162],[1100,5486,5438],{"className":5487},[1201],[1096,5489,5490,5491,5543,5544,5595,5596,5624,5625],{},"检查覆盖率：重复步骤 2-5 多次（ ",[1100,5492,5494,5513],{"className":5493},[1103],[1100,5495,5497],{"className":5496},[1107],[1109,5498,5499],{"xmlns":1111},[1113,5500,5501,5510],{},[1116,5502,5503,5506,5508],{},[1119,5504,5505],{},"M",[1123,5507,1294],{},[1863,5509,4825],{},[1141,5511,5512],{"encoding":1143},"M=10000",[1100,5514,5516,5534],{"className":5515,"ariaHidden":1149},[1148],[1100,5517,5519,5522,5525,5528,5531],{"className":5518},[1153],[1100,5520],{"className":5521,"style":1158},[1157],[1100,5523,5505],{"className":5524,"style":4841},[1162,1163],[1100,5526],{"className":5527,"style":1169},[1168],[1100,5529,1294],{"className":5530},[1173],[1100,5532],{"className":5533,"style":1169},[1168],[1100,5535,5537,5540],{"className":5536},[1153],[1100,5538],{"className":5539,"style":4857},[1157],[1100,5541,4825],{"className":5542},[1162]," 次），每次生成新的 ",[1100,5545,5547,5568],{"className":5546},[1103],[1100,5548,5550],{"className":5549},[1107],[1109,5551,5552],{"xmlns":1111},[1113,5553,5554,5566],{},[1116,5555,5556,5558,5560,5562,5564],{},[1123,5557,1133],{"stretchy":1132},[1119,5559,1291],{},[1123,5561,1868],{"separator":1149},[1119,5563,1433],{},[1123,5565,1139],{"stretchy":1132},[1141,5567,4723],{"encoding":1143},[1100,5569,5571],{"className":5570,"ariaHidden":1149},[1148],[1100,5572,5574,5577,5580,5583,5586,5589,5592],{"className":5573},[1153],[1100,5575],{"className":5576,"style":1183},[1157],[1100,5578,1133],{"className":5579},[1194],[1100,5581,1291],{"className":5582,"style":1331},[1162,1163],[1100,5584,1868],{"className":5585},[1919],[1100,5587],{"className":5588,"style":1923},[1168],[1100,5590,1433],{"className":5591,"style":1465},[1162,1163],[1100,5593,1139],{"className":5594},[1201],"，计算区间覆盖真实 ",[1100,5597,5599,5612],{"className":5598},[1103],[1100,5600,5602],{"className":5601},[1107],[1109,5603,5604],{"xmlns":1111},[1113,5605,5606,5610],{},[1116,5607,5608],{},[1119,5609,1226],{},[1141,5611,1226],{"encoding":1143},[1100,5613,5615],{"className":5614,"ariaHidden":1149},[1148],[1100,5616,5618,5621],{"className":5617},[1153],[1100,5619],{"className":5620,"style":1570},[1157],[1100,5622,1226],{"className":5623,"style":1272},[1162,1163]," 的比例覆盖率 ",[1100,5626,5628,5649],{"className":5627},[1103],[1100,5629,5631],{"className":5630},[1107],[1109,5632,5633],{"xmlns":1111},[1113,5634,5635,5646],{},[1116,5636,5637,5639],{},[1123,5638,1294],{},[4130,5640,5641,5644],{},[1127,5642,5643],{},"覆盖次数",[1119,5645,5505],{},[1141,5647,5648],{"encoding":1143},"= 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numpy as np\nimport pandas as pd\nfrom scipy.stats import poisson, gamma\nfrom scipy.optimize import brentq\nimport matplotlib.pyplot as plt\nimport seaborn as sns\nfrom tqdm import tqdm\nimport warnings\nwarnings.filterwarnings('ignore')\n\n\n# 设置全局字体为 SimHei (黑体) 或其他中文字体\nplt.rcParams['font.sans-serif'] = ['SimHei']\nplt.rcParams['axes.unicode_minus'] = False\n\nclass PoissonSignalInference:\n    \"\"\"\n    基于随机加权IM方法的泊松信号推断类\n    用于估计背景率b、信号率q和尺度参数m\n    \"\"\"\n\n    def __init__(self, b_true=None, q_true=None, m_true=None):\n        \"\"\"\n        初始化真实参数值\n        \"\"\"\n        self.b_true = b_true\n        self.q_true = q_true\n        self.m_true = m_true\n        self.STA_true = b_true + q_true if b_true is not None and q_true is not None else None\n\n    def generate_data(self, n_samples=1):\n        \"\"\"\n\n        生成观测数据Y和W\n\n        当前有不可观测的泊松过程 B ∼ Poisson(b) 和 S ∼ Poisson(q)\n        可观测对象有 Y = B + S ∼ Poisson(b + q) 和辅助变量 W ∼ Poisson(m · b)\n        目标是估计参数 b、q 和可能的 m\n\n        \"\"\"\n        if self.b_true is None or self.q_true is None or self.m_true is None:\n            raise ValueError(\"必须先设置真实参数值\")\n\n        if self.STA_true is None:\n            self.STA_true = self.b_true + self.q_true\n\n        Y = np.random.poisson(self.STA_true, n_samples)\n        W = np.random.poisson(self.m_true * self.b_true, n_samples)\n\n        return Y, W\n\n    def poisson_cdf(self, k, theta):\n        \"\"\"\n        计算泊松分布的累积分布函数\n        \"\"\"\n        return poisson.cdf(k, theta) #泊松分布的CDF公式，参数为 k 和 theta\n\n    def solve_G_inverse(self, u, Y, w1, bracket_low=0, bracket_high=100):\n        \"\"\"\n        求解方程 G(STA) = u 的逆函数，得到STA\n        使用二分法求解 G(STA): w_1 F_{STA}(Y-1) + (1-w_1) F_{STA}(Y) = u\n\n        计算泊松混合分布的累积分布函数值与目标值的差值\n\n        该函数计算一个泊松混合分布的CDF值，该混合分布由两个泊松分布组成，权重分别为w1和(1-w1)，\n        然后减去目标值u，通常用于求解分位数或进行概率计算\n        参数:\n            Y (int or array-like): 观测值，泊松分布的计数变量\n            STA (float or array-like): 泊松分布的参数λ（均值）\n            w1 (float): 第一个泊松分布的权重，取值范围[0,1]\n            u (float): 目标概率值，用于比较或求解\n        返回:\n        \"\"\"\n        def equation(STA): #返回值:(float or array-like): 泊松混合分布的CDF值与目标值u的差值\n            if Y == 0:\n                # 当Y=0时，F_STA(-1)=0，方程简化为F_STA(0)=u\n                return self.poisson_cdf(0, STA) - u\n            else:\n                return w1 * self.poisson_cdf(Y-1, STA) + (1-w1) * self.poisson_cdf(Y, STA) - u\n                # 求加权泊松混合分布\n                # 第一项：权重w1乘以P(X \u003C= Y-1)的概率\n                # 第二项：权重(1-w1)乘以P(X \u003C= Y)的概率\n                # 最后减去目标值u\n\n        try:\n            \"\"\"\n            使用二分法求解 G(STA) = u 方程中的 STA 值\n            \"\"\"\n            # 设置上下界来初始化搜索区间\n            low = max(0.00001, bracket_low) #bracket_low下界（）\n            high = max(10 * Y, bracket_high) if Y > 0 else bracket_high #bracket_high上界，根据观测值 Y 调整上界\n\n            # 检查边界值\n            f_low = equation(low)\n            f_high = equation(high)\n\n\n            if f_low * f_high > 0:\n                # 如果 f_low * f_high > 0（同号），则自动扩大搜索区间\n                attempts = 0\n                while f_low * f_high > 0 and attempts \u003C 10:\n                    high *= 2 #最多尝试10次，每次将上界翻倍：high *= 2\n                    f_high = equation(high)\n                    attempts += 1\n\n            STA_solution = brentq(equation, low, high, xtol=1e-6)\n            \"\"\"\n            参数为要求解的方程（加权泊松混合分布），上下区间，精度\n            使用 brentq 函数进行二分法求根\n            求解 w1 * self.poisson_cdf(Y-1, STA) + (1-w1) * self.poisson_cdf(Y, STA) - u = 0\n\n            即求解方程 G(STA) = u\n            得到STA\n\n            \"\"\"\n\n            return STA_solution #返回求解得到的 STA 值\n        except (ValueError, RuntimeError):\n            # 如果求解失败，返回保守估计\n            print(\"ERR solve_G_inverse 求解失败，返回保守估计\")\n            return max(0.001, Y)\n\n    def solve_H_inverse(self, v, W, w2, m, bracket_low=0, bracket_high=100):\n        \"\"\"\n        求解方程 H(mb) = v 的逆函数，得到mb\n\n        H(mb): w_2 F_{mb}(W-1) + (1-w_2) F_{mb}(W) = v\n\n        \"\"\"\n        def equation(mb):\n            if W == 0:\n                return self.poisson_cdf(0, mb) - v\n            else:\n                return w2 * self.poisson_cdf(W-1, mb) + (1-w2) * self.poisson_cdf(W, mb) - v\n\n        try:\n            low = max(0.001, bracket_low)\n            high = max(10 * W, bracket_high) if W > 0 else bracket_high\n\n            f_low = equation(low)\n            f_high = equation(high)\n\n            if f_low * f_high > 0:\n                attempts = 0\n                while f_low * f_high > 0 and attempts \u003C 10:\n                    high *= 2\n                    f_high = equation(high)\n                    attempts += 1\n\n            mb_solution = brentq(equation, low, high, xtol=1e-6)\n            return mb_solution\n        except (ValueError, RuntimeError):\n            return max(0.001, W)\n\n    def estimate_parameters_IM(self, Y_obs, W_obs, m_known=True, n_inner_samples=10000):\n        \"\"\"\n        使用随机加权IM方法估计三个参数q、b和STA\n        Y_obs：观测值Y\n        W_obs：观测值W\n        m_known：一个布尔值，表示参数m是否已知\n        n_inner_samples：内部采样次数，默认为10000\n\n        \"\"\"\n        if not m_known:\n            raise NotImplementedError(\"m未知\")\n\n        # 创建三个列表存储候选参数值\n        q_candidates = []\n        b_candidates = []\n        STA_candidates = []\n\n        for _ in range(n_inner_samples):\n            # 生成4个均匀分布的随机权重（u, v, w1, w2）\n            u = np.random.uniform(0, 1)\n            v = np.random.uniform(0, 1)\n            w1 = np.random.uniform(0, 1)\n            w2 = np.random.uniform(0, 1)\n\n            # 使用solve_G_inverse和solve_H_inverse方法计算STA和mb的估计值\n            STA_est = self.solve_G_inverse(u, Y_obs, w1)\n            mb_est = self.solve_H_inverse(v, W_obs, w2, self.m_true)\n            # G(STA): w_1 F_{STA}(Y-1) + (1-w_1) F_{STA}(Y) = u ==> 求解STA\n            # H(mb): w_2 F_{mb}(W-1) + (1-w_2) F_{mb}(W) = v ==> 求解mb\n            # 可以得到\n            # STA = G⁻¹(u), mb = H⁻¹(v)\n            # 计算b和q\n            # b = H⁻¹(v)\u002Fm\n            # q = STA - b = G⁻¹(u) - H⁻¹(v)\u002Fm\n            if self.m_true is None:\n                raise ValueError(\"参数 m_true 未设置，无法计算 b_est\")\n            b_est = mb_est \u002F self.m_true\n            q_est = STA_est - b_est\n\n            # 确保非负\n            q_est = max(0, q_est)\n            b_est = max(0, b_est)\n\n            #每次计算出新的 q_est 值后，会将其添加到 q_candidates 列表中\n            q_candidates.append(q_est)\n            b_candidates.append(b_est)\n            STA_candidates.append(STA_est)\n\n        return {\n            'q_candidates': np.array(q_candidates),\n            'b_candidates': np.array(b_candidates),\n            'STA_candidates': np.array(STA_candidates)\n        }\n\n    def calculate_confidence_intervals(self, candidates_dict, alpha=0.05):\n        \"\"\"\n        计算参数的置信区间\n        \"\"\"\n        intervals = {}\n\n        for param, values in candidates_dict.items():\n            # 移除'_candidates'后缀，使键名简化\n            simple_param = param.replace('_candidates', '')\n            lower = np.quantile(values, alpha\u002F2)\n            upper = np.quantile(values, 1 - alpha\u002F2)\n            intervals[simple_param] = (lower, upper)\n\n        return intervals\n\n    def coverage_simulation(self, n_outer_trials=1000, n_inner_samples=1000, alpha=0.05):\n        \"\"\"\n        进行覆盖率模拟验证\n        \"\"\"\n        coverage_results = {\n            'q': 0.0,\n            'b': 0.0,\n            'STA': 0.0\n        }\n\n        interval_lengths = {\n            'q': [],\n            'b': [],\n            'STA': []\n        }\n\n        print(\"正在进行覆盖率模拟...\")\n        for i in tqdm(range(n_outer_trials)):\n            # 生成新的观测数据\n            Y_obs, W_obs = self.generate_data(1)\n            Y_obs, W_obs = Y_obs[0], W_obs[0]\n\n            # 估计参数\n            candidates_dict = self.estimate_parameters_IM(Y_obs, W_obs,\n                                                         n_inner_samples=n_inner_samples)\n\n            # 计算置信区间\n            intervals = self.calculate_confidence_intervals(candidates_dict, alpha)\n\n            # 检查覆盖率\n            if intervals['q'][0] \u003C= self.q_true \u003C= intervals['q'][1]:\n                coverage_results['q'] += 1\n            if intervals['b'][0] \u003C= self.b_true \u003C= intervals['b'][1]:\n                coverage_results['b'] += 1\n            if intervals['STA'][0] \u003C= self.STA_true \u003C= intervals['STA'][1]:\n                coverage_results['STA'] += 1\n\n            # 记录区间长度\n            interval_lengths['q'].append(intervals['q'][1] - intervals['q'][0])\n            interval_lengths['b'].append(intervals['b'][1] - intervals['b'][0])\n            interval_lengths['STA'].append(intervals['STA'][1] - intervals['STA'][0])\n\n        # 计算覆盖率\n        for param in coverage_results:\n            coverage_results[param] = coverage_results[param] \u002F n_outer_trials\n\n        return coverage_results, interval_lengths\n\n    def plot_results(self, candidates_dict, intervals, Y_obs, W_obs):\n        \"\"\"\n        可视化结果\n        \"\"\"\n        fig, axes = plt.subplots(2, 2, figsize=(15, 10))\n\n        # q的分布\n        axes[0, 0].hist(candidates_dict['q_candidates'], bins=50, alpha=0.7, density=True)\n        axes[0, 0].axvline(self.q_true, color='red', linestyle='--', linewidth=2, label=f'真实 q = {self.q_true}')\n        axes[0, 0].axvline(intervals['q'][0], color='green', linestyle='--', linewidth=1, label=f'{100*(1-0.05)}% CI')\n        axes[0, 0].axvline(intervals['q'][1], color='green', linestyle='--', linewidth=1)\n        axes[0, 0].set_xlabel('q')\n        axes[0, 0].set_ylabel('密度')\n        axes[0, 0].set_title('q的后验分布')\n        axes[0, 0].legend()\n\n        # b的分布\n        axes[0, 1].hist(candidates_dict['b_candidates'], bins=50, alpha=0.7, density=True)\n        axes[0, 1].axvline(self.b_true, color='red', linestyle='--', linewidth=2, label=f'真实 b = {self.b_true}')\n        axes[0, 1].axvline(intervals['b'][0], color='green', linestyle='--', linewidth=1, label=f'{100*(1-0.05)}% CI')\n        axes[0, 1].axvline(intervals['b'][1], color='green', linestyle='--', linewidth=1)\n        axes[0, 1].set_xlabel('b')\n        axes[0, 1].set_ylabel('密度')\n        axes[0, 1].set_title('b的后验分布')\n        axes[0, 1].legend()\n\n        # STA的分布\n        axes[1, 0].hist(candidates_dict['STA_candidates'], bins=50, alpha=0.7, density=True)\n        axes[1, 0].axvline(self.STA_true, color='red', linestyle='--', linewidth=2, label=f'真实 STA = {self.STA_true}')\n        axes[1, 0].axvline(intervals['STA'][0], color='green', linestyle='--', linewidth=1, label=f'{100*(1-0.05)}% CI')\n        axes[1, 0].axvline(intervals['STA'][1], color='green', linestyle='--', linewidth=1)\n        axes[1, 0].set_xlabel('STA')\n        axes[1, 0].set_ylabel('密度')\n        axes[1, 0].set_title('STA的后验分布')\n        axes[1, 0].legend()\n\n        # 观测数据信息\n        axes[1, 1].axis('off')\n        text_str = f'观测数据:\\nY = {Y_obs}\\nW = {W_obs}\\n\\n真实参数:\\nb = {self.b_true}\\nq = {self.q_true}\\nm = {self.m_true}\\nSTA = {self.STA_true}'\n        axes[1, 1].text(0.1, 0.9, text_str, transform=axes[1, 1].transAxes, fontsize=12,\n                    verticalalignment='top', bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.5))\n\n        plt.tight_layout()\n        plt.show()\n\ndef main():\n    \"\"\"\n    主函数：演示完整的推断流程\n    \"\"\"\n    # 设置真实参数\n    b_true = 3.0  # b\n    q_true = 2.0  # q\n    m_true = 0.8  # 尺度参数（已知）\n    STA_true = b_true + q_true\n\n    print(\"=== 泊松推断演示 ===\")\n    print(f\"真实参数: b={b_true}, q={q_true}, m={m_true}, STA={STA_true}\")\n\n    # 初始化推断器\n    inference = PoissonSignalInference(b_true, q_true, m_true)\n\n    # 生成单次观测数据\n    Y_obs, W_obs = inference.generate_data(1)\n    Y_obs, W_obs = Y_obs[0], W_obs[0]\n    print(f\"\\n生成的观测数据: Y={Y_obs}, W={W_obs}\")\n\n    # 使用IM方法进行参数估计\n    print(\"\\n正在进行参数估计...\")\n    candidates_dict = inference.estimate_parameters_IM(Y_obs, W_obs, n_inner_samples=10000)\n\n    # 计算置信区间\n    alpha = 0.05  # 0.95置信区间\n    intervals = inference.calculate_confidence_intervals(candidates_dict, alpha)\n\n    print(\"\\n=== 估计结果 ===\")\n    for param, (lower, upper) in intervals.items():\n        true_value = getattr(inference, f\"{param.replace('_candidates', '')}_true\", None)\n        if true_value is not None:\n            print(f\"{param}: [{lower:.3f}, {upper:.3f}] (真实值: {true_value:.3f})\")\n        else:\n            print(f\"{param}: [{lower:.3f}, {upper:.3f}]\")\n\n    # 可视化结果\n    print(\"\\n生成可视化图表...\")\n    inference.plot_results(candidates_dict, intervals, Y_obs, W_obs)\n\n    # 进行覆盖率模拟（样本量较小以加快演示速度）\n    print(\"\\n正在进行覆盖率模拟...\")\n    coverage_results, interval_lengths = inference.coverage_simulation(\n        n_outer_trials=500,  # 减少试验次数以加快演示\n        n_inner_samples=1000,  # 减少内部样本数\n        alpha=0.05\n    )\n\n    print(\"\\n=== 覆盖率结果 ===\")\n    for param, coverage in coverage_results.items():\n        print(f\"{param}的覆盖率: {coverage:.3f} (目标: {1-alpha:.3f})\")\n\n    # 绘制区间长度分布\n    plt.figure(figsize=(12, 4))\n    for i, (param, lengths) in enumerate(interval_lengths.items()):\n        plt.subplot(1, 3, i+1)\n        plt.hist(lengths, bins=30, alpha=0.7)\n        plt.xlabel(f'{param}区间长度')\n        plt.ylabel('频数')\n        plt.title(f'{param}置信区间长度分布')\n    plt.tight_layout()\n    plt.show()\nif __name__ == \"__main__\":\n    main()\n","python","",[5758,5759,5754],"code",{"__ignoreMap":5756},{"title":5756,"searchDepth":5761,"depth":5761,"links":5762},4,[5763],{"id":1093,"depth":5764,"text":1094,"children":5765},2,[5766,5768],{"id":1581,"depth":5767,"text":1581},3,{"id":1617,"depth":5767,"text":1617,"children":5769},[5770,5771,5772,5773,5774],{"id":1621,"depth":5761,"text":1622},{"id":2585,"depth":5761,"text":2586},{"id":3836,"depth":5761,"text":3837},{"id":4655,"depth":5761,"text":4656},{"id":5748,"depth":5761,"text":5748},"md",true,{"uuid":5778,"slots":5779},"2cdb1e00-ba46-11f0-ac4e-2d8de9a9d9de",{},{"title":1085,"description":5756},"posts\u002F2025\u002F2025-11-05-基于随机加权推断模型（IM）的参数估计算法",[109,115,108,116],"zFy02_4AG6Ys1aF8d5WUsPWScntMzOoHhkFbmAHSIrM",1790443288027]