{"id":4208,"date":"2025-07-12T16:17:13","date_gmt":"2025-07-12T07:17:13","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/?p=4208"},"modified":"2025-07-12T22:11:01","modified_gmt":"2025-07-12T13:11:01","slug":"mastering-markov-chain-monte-carlo-mcmc-a-comprehensive-guide","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/mastering-markov-chain-monte-carlo-mcmc-a-comprehensive-guide\/","title":{"rendered":"\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5 (MCMC) \u3092\u5fb9\u5e95\u89e3\u8aac\uff01"},"content":{"rendered":"\n<p>\u300c\u306a\u3093\u3060\u304b\u8907\u96d1\u305d\u3046\u306a\u6570\u5f0f\u3084\u7406\u8ad6\u304c\u51fa\u3066\u304d\u305d\u3046\u2026\u300d\u305d\u3046\u601d\u308f\u308c\u305f\u65b9\u3082\u3044\u308b\u304b\u3082\u3057\u308c\u306a\u3044\u3002\u3057\u304b\u3057\u3001\u3054\u5b89\u5fc3\u3044\u305f\u3060\u304d\u305f\u3044\u3002\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001<strong>\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5 (MCMC)<\/strong> \u3068\u3044\u3046\u5f37\u529b\u306a\u7d71\u8a08\u7684\u624b\u6cd5\u306b\u3064\u3044\u3066\u3001\u305d\u306e\u57fa\u672c\u304b\u3089\u5fdc\u7528\u307e\u3067\u3092\u3001\u3067\u304d\u308b\u9650\u308a\u308f\u304b\u308a\u3084\u3059\u304f\u89e3\u8aac\u3059\u308b\u3002<\/p>\n\n\n\n<p>MCMC\u306f\u3001\u73fe\u4ee3\u306e\u30c7\u30fc\u30bf\u30b5\u30a4\u30a8\u30f3\u30b9\u306b\u304a\u3044\u3066\u6b20\u304b\u305b\u306a\u3044\u30c4\u30fc\u30eb\u3067\u3042\u308a\u3001\u7279\u306b<strong>\u30d9\u30a4\u30ba\u7d71\u8a08<\/strong>\u3084\u8907\u96d1\u306a\u30e2\u30c7\u30eb\u306e\u5206\u6790\u3067\u305d\u306e\u771f\u4fa1\u3092\u767a\u63ee\u3059\u308b\u3002\u96e3\u89e3\u306b\u601d\u3048\u308b\u3053\u306eMCMC\u304c\u3001\u3069\u306e\u3088\u3046\u306a\u539f\u7406\u3067\u52d5\u304d\u3001\u3069\u306e\u3088\u3046\u306a\u554f\u984c\u3092\u89e3\u6c7a\u3057\u3066\u304f\u308c\u308b\u306e\u304b\u3002\u3053\u306e\u8a18\u4e8b\u3092\u8aad\u307f\u7d42\u3048\u308b\u9803\u306b\u306f\u3001\u304d\u3063\u3068\u305d\u306e\u9b45\u529b\u306b\u6c17\u3065\u304d\u3001\u30c7\u30fc\u30bf\u5206\u6790\u306e\u65b0\u305f\u306a\u6249\u304c\u958b\u304b\u308c\u308b\u3053\u3068\u3067\u3042\u308d\u3046\u3002\u3055\u3042\u3001\u4e00\u7dd2\u306bMCMC\u306e\u4e16\u754c\u3078\u8e0f\u307f\u51fa\u305d\u3046\u3002<\/p>\n\n\n\n<!--more-->\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">MCMC\u306e\u6982\u8981<\/h2>\n\n\n\n<p>\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5 (MCMC) \u306f\u3001\u30d9\u30a4\u30ba\u7d71\u8a08\u3084\u8907\u96d1\u306a\u78ba\u7387\u5206\u5e03\u304b\u3089\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306b\u4e0d\u53ef\u6b20\u306a\u5f37\u529b\u306a\u8a08\u7b97\u624b\u6cd5\u3067\u3042\u308b\u3002\u7279\u306b\u3001\u89e3\u6790\u7684\u306b\u6271\u3046\u3053\u3068\u304c\u96e3\u3057\u3044\u9ad8\u6b21\u5143\u306e\u5206\u5e03\u3084\u3001\u5b9a\u6570\u90e8\u5206\u304c\u4e0d\u660e\u306a\u5206\u5e03\u304b\u3089\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306b\u305d\u306e\u771f\u4fa1\u3092\u767a\u63ee\u3059\u308b\u3002MCMC\u306f\u3001<strong>\u30de\u30eb\u30b3\u30d5\u9023\u9396<\/strong>\u306e\u6982\u5ff5\u3068<strong>\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5<\/strong>\u306e\u30a2\u30a4\u30c7\u30a2\u3092\u7d44\u307f\u5408\u308f\u305b\u308b\u3053\u3068\u3067\u3001\u5bfe\u8c61\u306e\u5206\u5e03\u306b\u5f93\u3046\u30b5\u30f3\u30d7\u30eb\u3092\u751f\u6210\u3057\u3001\u305d\u306e\u5206\u5e03\u306e\u7279\u6027\u3092\u8fd1\u4f3c\u7684\u306b\u628a\u63e1\u3059\u308b\u3053\u3068\u3092\u53ef\u80fd\u306b\u3059\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u30de\u30eb\u30b3\u30d5\u9023\u9396\u3068\u306f<\/h2>\n\n\n\n<p>\u30de\u30eb\u30b3\u30d5\u9023\u9396\u306f\u3001\u5c06\u6765\u306e\u72b6\u614b\u304c\u73fe\u5728\u306e\u72b6\u614b\u306e\u307f\u306b\u4f9d\u5b58\u3057\u3001\u305d\u308c\u4ee5\u524d\u306e\u72b6\u614b\u306b\u306f\u4f9d\u5b58\u3057\u306a\u3044\u3068\u3044\u3046\u7279\u6027\u3092\u6301\u3064\u78ba\u7387\u904e\u7a0b\u3067\u3042\u308b\u3002\u3053\u308c\u3092\u300c\u30de\u30eb\u30b3\u30d5\u6027\u300d\u3068\u547c\u3076\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u78ba\u7387\u904e\u7a0b<\/strong>: \u6642\u9593\u306e\u7d4c\u904e\u3068\u3068\u3082\u306b\u5909\u5316\u3059\u308b\u78ba\u7387\u5909\u6570\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u6307\u3059\u3002<\/li>\n\n\n\n<li><strong>\u9077\u79fb\u6838<\/strong>: \u3042\u308b\u72b6\u614b\u304b\u3089\u5225\u306e\u72b6\u614b\u3078\u9077\u79fb\u3059\u308b\u78ba\u7387\u3092\u8868\u3059\u3002\u4f8b\u3048\u3070\u3001\u73fe\u5728\u306e\u72b6\u614b\u304c x \u3067\u3042\u3063\u305f\u3068\u304d\u306b\u3001\u6b21\u306e\u72b6\u614b\u304c y \u306b\u306a\u308b\u78ba\u7387\u3092 P(y\u2223x) \u306e\u3088\u3046\u306b\u8868\u3059\u3002<\/li>\n\n\n\n<li><strong>\u5b9a\u5e38\u5206\u5e03<\/strong>: \u30de\u30eb\u30b3\u30d5\u9023\u9396\u304c\u5341\u5206\u306b\u9577\u3044\u6642\u9593\u9032\u884c\u3057\u305f\u5f8c\u306b\u5230\u9054\u3059\u308b\u3001\u5909\u5316\u3057\u306a\u3044\u78ba\u7387\u5206\u5e03\u306e\u3053\u3068\u3067\u3042\u308b\u3002\u5b9a\u5e38\u5206\u5e03\u306b\u5230\u9054\u3059\u308b\u3068\u3001\u5404\u72b6\u614b\u306b\u3044\u308b\u78ba\u7387\u304c\u6642\u9593\u3068\u3068\u3082\u306b\u5909\u5316\u3057\u306a\u304f\u306a\u308b\u3002MCMC\u3067\u306f\u3001\u3053\u306e\u5b9a\u5e38\u5206\u5e03\u304c\u79c1\u305f\u3061\u304c\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3057\u305f\u3044\u30bf\u30fc\u30b2\u30c3\u30c8\u306e\u5206\u5e03\u3068\u306a\u308b\u3088\u3046\u306b\u30de\u30eb\u30b3\u30d5\u9023\u9396\u3092\u8a2d\u8a08\u3059\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<div id=\"biost-587969348\" class=\"biost- biost-entity-placement\"><p style=\"text-align: center;\"><span style=\"font-size: 20px;\"><strong><a href=\"https:\/\/best-biostatistics.com\/kmhl\">\uff1e\uff1e\u3082\u3046\u7d71\u8a08\u3067\u60a9\u3080\u306e\u306f\u7d42\u308f\u308a\u306b\u3057\u307e\u305b\u3093\u304b\uff1f\u00a0<\/a><\/strong><\/span><\/p>\r\n<a href=\"https:\/\/best-biostatistics.com\/kmhl\"><img class=\"aligncenter wp-image-2794 size-full\" src=\"https:\/\/best-biostatistics.com\/wp\/wp-content\/uploads\/2023\/11\/bn_r_03.png\" alt=\"\" width=\"500\" height=\"327\" \/><\/a>\r\n<p style=\"text-align: center;\"><span style=\"color: #ff0000; font-size: 20px;\"><strong><span class=\"marker2\">\u21911\u4e07\u4eba\u4ee5\u4e0a\u306e\u533b\u7642\u5f93\u4e8b\u8005\u304c\u8cfc\u8aad\u4e2d<\/span><\/strong><\/span><\/p><\/div><h2 class=\"wp-block-heading\">\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\u3068\u306f<\/h2>\n\n\n\n<p>\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\u306f\u3001\u4e71\u6570\u3092\u7528\u3044\u3066\u6570\u5024\u7684\u306a\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u624b\u6cd5\u306e\u7dcf\u79f0\u3067\u3042\u308b\u3002\u7279\u306b\u3001\u78ba\u7387\u7684\u306a\u73fe\u8c61\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3057\u305f\u308a\u3001\u8907\u96d1\u306a\u7a4d\u5206\u3092\u8fd1\u4f3c\u7684\u306b\u8a08\u7b97\u3057\u305f\u308a\u3059\u308b\u969b\u306b\u7528\u3044\u3089\u308c\u308b\u3002\u4f8b\u3048\u3070\u3001\u5186\u5468\u7387\u3092\u6c42\u3081\u308b\u305f\u3081\u306b\u30e9\u30f3\u30c0\u30e0\u306a\u70b9\u3092\u6b63\u65b9\u5f62\u5185\u306b\u30d7\u30ed\u30c3\u30c8\u3057\u3001\u5186\u306e\u5185\u5074\u306b\u5165\u3063\u305f\u70b9\u306e\u5272\u5408\u304b\u3089\u5186\u5468\u7387\u3092\u63a8\u5b9a\u3059\u308b\u3068\u3044\u3063\u305f\u65b9\u6cd5\u3082\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\u306e\u4e00\u3064\u3067\u3042\u308b\u3002\u7d71\u8a08\u5b66\u306b\u304a\u3044\u3066\u306f\u3001\u3042\u308b\u5206\u5e03\u304b\u3089\u306e\u30b5\u30f3\u30d7\u30eb\u3092\u5927\u91cf\u306b\u751f\u6210\u3057\u3001\u305d\u308c\u3089\u306e\u30b5\u30f3\u30d7\u30eb\u3092\u7528\u3044\u3066\u671f\u5f85\u5024\u3084\u5206\u6563\u306a\u3069\u3092\u63a8\u5b9a\u3059\u308b\u969b\u306b\u3088\u304f\u5229\u7528\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u30de\u30eb\u30b3\u30d5\u9023\u9396\u3068\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\u3092\u7d50\u3073\u3064\u3051\u308b\u610f\u7fa9<\/h2>\n\n\n\n<p>MCMC\u306e\u6838\u5fc3\u306f\u3001<strong>\u5bfe\u8c61\u3068\u3057\u305f\u3044\u78ba\u7387\u5206\u5e03\u3092\u5b9a\u5e38\u5206\u5e03\u3068\u3057\u3066\u6301\u3064\u30de\u30eb\u30b3\u30d5\u9023\u9396\u3092\u69cb\u7bc9\u3059\u308b\u3053\u3068<\/strong>\u306b\u3042\u308b\u3002\u4e00\u5ea6\u3053\u306e\u3088\u3046\u306a\u30de\u30eb\u30b3\u30d5\u9023\u9396\u304c\u69cb\u7bc9\u3055\u308c\u308c\u3070\u3001\u305d\u306e\u9023\u9396\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\u3057\u7d9a\u3051\u308b\u3053\u3068\u3067\u3001\u6700\u7d42\u7684\u306b\u5b9a\u5e38\u5206\u5e03\uff08\u3059\u306a\u308f\u3061\u3001\u30bf\u30fc\u30b2\u30c3\u30c8\u306e\u5206\u5e03\uff09\u306b\u5f93\u3046\u30b5\u30f3\u30d7\u30eb\u3092\u751f\u6210\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p>\u306a\u305c\u3053\u308c\u304c\u91cd\u8981\u306a\u306e\u304b\u3002\u591a\u304f\u306e\u7d71\u8a08\u30e2\u30c7\u30eb\u3001\u7279\u306b\u30d9\u30a4\u30ba\u7d71\u8a08\u30e2\u30c7\u30eb\u3067\u306f\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u306e<strong>\u4e8b\u5f8c\u5206\u5e03<\/strong>\u304c\u975e\u5e38\u306b\u8907\u96d1\u3067\u3001\u76f4\u63a5\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3057\u305f\u308a\u3001\u89e3\u6790\u7684\u306b\u8a08\u7b97\u3057\u305f\u308a\u3059\u308b\u3053\u3068\u304c\u56f0\u96e3\u306a\u5834\u5408\u304c\u3042\u308b\u3002MCMC\u306f\u3001\u3053\u306e\u3088\u3046\u306a<strong>\u76f4\u63a5\u7684\u306a\u8a08\u7b97\u304c\u96e3\u3057\u3044\u5206\u5e03\u304b\u3089\u3067\u3082\u3001\u305d\u306e\u5206\u5e03\u306b\u5f93\u3046\u30b5\u30f3\u30d7\u30eb\u3092\u300c\u9593\u63a5\u7684\u306b\u300d\u751f\u6210\u3059\u308b\u9053\u3092\u958b\u304f<\/strong>\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3055\u308c\u305f\u30c7\u30fc\u30bf\u3092\u4f7f\u3063\u3066\u3001\u5bfe\u8c61\u3068\u306a\u308b\u5206\u5e03\u306e\u5f62\u72b6\u3092\u63a8\u5b9a\u3057\u305f\u308a\u3001\u69d8\u3005\u306a\u7d71\u8a08\u91cf\u3092\u8a08\u7b97\u3057\u305f\u308a\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e8b\u524d\u5206\u5e03\u3068\u4e8b\u5f8c\u5206\u5e03<\/h3>\n\n\n\n<p>\u3053\u3053\u3067\u3001\u30d9\u30a4\u30ba\u7d71\u8a08\u306b\u304a\u3051\u308b\u91cd\u8981\u306a\u6982\u5ff5\u3067\u3042\u308b\u300c\u4e8b\u524d\u5206\u5e03\u300d\u3068\u300c\u4e8b\u5f8c\u5206\u5e03\u300d\u306b\u3064\u3044\u3066\u89e3\u8aac\u3059\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u4e8b\u524d\u5206\u5e03 (Prior Distribution)<\/strong>: \u30c7\u30fc\u30bf\u3092\u5f97\u308b<strong>\u524d<\/strong>\u306b\u3001\u79c1\u305f\u3061\u304c\u77e5\u308a\u305f\u3044\u30d1\u30e9\u30e1\u30fc\u30bf $ \\theta $ \u304c\u3069\u306e\u3088\u3046\u306a\u5024\u3092\u53d6\u308b\u304b\u306b\u3064\u3044\u3066\u306e\u4fe1\u5ff5\u3084\u77e5\u8b58\u3092\u8868\u3059\u78ba\u7387\u5206\u5e03\u3067\u3042\u308b\u3002\u3053\u308c\u306f\u3001\u904e\u53bb\u306e\u7814\u7a76\u7d50\u679c\u3001\u5c02\u9580\u5bb6\u306e\u610f\u898b\u3001\u3042\u308b\u3044\u306f\u5358\u306a\u308b\u7121\u60c5\u5831\u306a\u4eee\u5b9a\uff08\u4f8b\u3048\u3070\u3001\u3059\u3079\u3066\u306e\u5024\u304c\u7b49\u3057\u3044\u78ba\u7387\u3067\u8d77\u3053\u308a\u3046\u308b\u3068\u4eee\u5b9a\u3059\u308b\u4e00\u69d8\u5206\u5e03\u306a\u3069\uff09\u306b\u57fa\u3065\u3044\u3066\u8a2d\u5b9a\u3055\u308c\u308b\u3002\u4e8b\u524d\u5206\u5e03\u306f\u3001$ P(\\theta) $ \u3068\u8868\u8a18\u3055\u308c\u308b\u3002<\/li>\n\n\n\n<li><strong>\u4e8b\u5f8c\u5206\u5e03 (Posterior Distribution)<\/strong>: \u65b0\u3057\u3044\u30c7\u30fc\u30bf D \u3092\u89b3\u6e2c\u3057\u305f<strong>\u5f8c<\/strong>\u306b\u3001\u30d1\u30e9\u30e1\u30fc\u30bf $ \\theta $ \u304c\u3069\u306e\u3088\u3046\u306a\u5024\u3092\u53d6\u308b\u304b\u306b\u3064\u3044\u3066\u306e\u66f4\u65b0\u3055\u308c\u305f\u4fe1\u5ff5\u3092\u8868\u3059\u78ba\u7387\u5206\u5e03\u3067\u3042\u308b\u3002\u3053\u308c\u306f\u3001\u4e8b\u524d\u5206\u5e03\u3068\u30c7\u30fc\u30bf\u304b\u3089\u5f97\u3089\u308c\u305f\u60c5\u5831\uff08\u5c24\u5ea6\uff09\u3092\u7d44\u307f\u5408\u308f\u305b\u308b\u3053\u3068\u3067\u5f97\u3089\u308c\u308b\u3002\u4e8b\u5f8c\u5206\u5e03\u306f\u3001\u30d9\u30a4\u30ba\u306e\u5b9a\u7406\u306b\u3088\u3063\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3055\u308c\u308b\u3002<br>$$ P(\\theta | D) = \\frac{P(D|\\theta)P(\\theta)}{P(D)} $$<br>\u200b\u3053\u3053\u3067\u3001$ P(D\u2223\\theta) $ \u306f<strong>\u5c24\u5ea6 (Likelihood)<\/strong> \u3068\u547c\u3070\u308c\u3001\u7279\u5b9a\u306e\u30d1\u30e9\u30e1\u30fc\u30bf $ \\theta $ \u306e\u3082\u3068\u3067\u3001\u89b3\u6e2c\u3055\u308c\u305f\u30c7\u30fc\u30bf D \u304c\u5f97\u3089\u308c\u308b\u78ba\u7387\u3092\u793a\u3059\u3002P(D) \u306f\u30c7\u30fc\u30bf\u306e\u5468\u8fba\u78ba\u7387\u3067\u3001\u6b63\u898f\u5316\u5b9a\u6570\u3068\u3057\u3066\u6a5f\u80fd\u3057\u3001\u3059\u3079\u3066\u306e $\\theta $ \u306b\u3064\u3044\u3066 $ P(D\u2223\\theta)P(\\theta) $ \u3092\u7a4d\u5206\uff08\u307e\u305f\u306f\u5408\u8a08\uff09\u3059\u308b\u3053\u3068\u3067\u5f97\u3089\u308c\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u4e8b\u5f8c\u5206\u5e03 $ P(\\theta\u2223D) $ \u306f\u3001\u30c7\u30fc\u30bf D \u3092\u8003\u616e\u306b\u5165\u308c\u305f\u4e0a\u3067\u306e\u3001\u30d1\u30e9\u30e1\u30fc\u30bf $ \\theta $ \u306b\u95a2\u3059\u308b\u6700\u3082\u5305\u62ec\u7684\u306a\u60c5\u5831\u3092\u63d0\u4f9b\u3059\u308b\u3002\u3057\u304b\u3057\u3001\u7279\u306b\u9ad8\u6b21\u5143\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u7a7a\u9593\u3084\u8907\u96d1\u306a\u5c24\u5ea6\u95a2\u6570\u3001\u4e8b\u524d\u5206\u5e03\u306e\u5834\u5408\u3001P(D) \u306e\u8a08\u7b97\uff08\u3064\u307e\u308a\u3001\u5206\u6bcd\u306e\u7a4d\u5206\uff09\u304c\u975e\u5e38\u306b\u56f0\u96e3\u306b\u306a\u308b\u3053\u3068\u304c\u3088\u304f\u3042\u308b\u3002MCMC\u306f\u3001\u3053\u306e\u56f0\u96e3\u306a\u7a4d\u5206\u3092\u76f4\u63a5\u8a08\u7b97\u3059\u308b\u3053\u3068\u306a\u304f\u3001<strong>\u4e8b\u5f8c\u5206\u5e03 $ P(\\theta\u2223D) $ \u304b\u3089\u76f4\u63a5\u30b5\u30f3\u30d7\u30eb\u3092\u751f\u6210\u3059\u308b<\/strong>\u3053\u3068\u3092\u53ef\u80fd\u306b\u3059\u308b\u3002\u3053\u308c\u304c\u3001MCMC\u304c\u30d9\u30a4\u30ba\u7d71\u8a08\u306b\u304a\u3044\u3066\u4e0d\u53ef\u6b20\u306a\u30c4\u30fc\u30eb\u3068\u306a\u3063\u3066\u3044\u308b\u7406\u7531\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">MCMC\u306e\u4f7f\u3044\u6240<\/h2>\n\n\n\n<p>MCMC\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u5834\u9762\u3067\u975e\u5e38\u306b\u6709\u52b9\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u30d9\u30a4\u30ba\u7d71\u8a08\u63a8\u8ad6<\/strong>: \u4e8b\u5f8c\u5206\u5e03\u304b\u3089\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306b\u5fc5\u9808\u3067\u3042\u308b\u3002\u7279\u306b\u3001\u8907\u96d1\u306a\u968e\u5c64\u30e2\u30c7\u30eb\u3084\u30b0\u30e9\u30d5\u30a3\u30ab\u30eb\u30e2\u30c7\u30eb\u306b\u304a\u3044\u3066\u5a01\u529b\u3092\u767a\u63ee\u3059\u308b\u3002<\/li>\n\n\n\n<li><strong>\u9ad8\u6b21\u5143\u306e\u7a4d\u5206<\/strong>: \u9ad8\u6b21\u5143\u306e\u8907\u96d1\u306a\u95a2\u6570\u3092\u7a4d\u5206\u3059\u308b\u969b\u306b\u3001\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u7a4d\u5206\u306e\u52b9\u7387\u3092\u5411\u4e0a\u3055\u305b\u308b\u3002<\/li>\n\n\n\n<li><strong>\u7269\u7406\u5b66\u3084\u5316\u5b66\u306b\u304a\u3051\u308b\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3<\/strong>: \u7d71\u8a08\u529b\u5b66\u306b\u304a\u3051\u308b\u76f8\u8ee2\u79fb\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u306a\u3069\u3001\u591a\u69d8\u306a\u7cfb\u3067\u5229\u7528\u3055\u308c\u308b\u3002<\/li>\n\n\n\n<li><strong>\u6a5f\u68b0\u5b66\u7fd2<\/strong>: \u78ba\u7387\u7684\u30b0\u30e9\u30d5\u30a3\u30ab\u30eb\u30e2\u30c7\u30eb\u306e\u5b66\u7fd2\u3084\u63a8\u8ad6\u306b\u7528\u3044\u3089\u308c\u308b\u3053\u3068\u304c\u3042\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u5177\u4f53\u4f8b\u3068 R \u306e\u8a08\u7b97\u4f8b\u30fb\u53ef\u8996\u5316<\/h2>\n\n\n\n<p>\u3053\u3053\u3067\u306f\u3001\u6700\u3082\u57fa\u672c\u7684\u306aMCMC\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u4e00\u3064\u3067\u3042\u308b<strong>\u30e1\u30c8\u30ed\u30dd\u30ea\u30b9\u30fb\u30d8\u30a4\u30b9\u30c6\u30a3\u30f3\u30b0\u30b9\u6cd5<\/strong>\u3092\u7528\u3044\u3066\u3001\u6b63\u898f\u5206\u5e03\u304b\u3089\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3092\u8a66\u307f\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n<p>\u30bf\u30fc\u30b2\u30c3\u30c8\u3068\u3059\u308b\u5206\u5e03\u3092\u5e73\u57470\u3001\u6a19\u6e96\u504f\u5dee1\u306e\u6a19\u6e96\u6b63\u898f\u5206\u5e03 N(0,1) \u3068\u3059\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">R \u8a08\u7b97\u4f8b<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code># \u30bf\u30fc\u30b2\u30c3\u30c8\u3068\u306a\u308b\u5206\u5e03 (\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570)\ntarget_density &lt;- function(x) {\n    dnorm(x, mean = 0, sd = 1)\n}\n\n# \u30e1\u30c8\u30ed\u30dd\u30ea\u30b9\u30fb\u30d8\u30a4\u30b9\u30c6\u30a3\u30f3\u30b0\u30b9\u6cd5\u306e\u5b9f\u88c5\nmcmc_mh &lt;- function(n_iter, initial_x, proposal_sd) {\n    # \u30b5\u30f3\u30d7\u30eb\u3092\u4fdd\u5b58\u3059\u308b\u30d9\u30af\u30c8\u30eb\n    samples &lt;- rep(NA, n_iter)\n    current_x &lt;- initial_x\n\n    for (i in 1:n_iter) {\n        # \u63d0\u6848\u5206\u5e03\u304b\u3089\u65b0\u3057\u3044\u5019\u88dc\u3092\u751f\u6210 (\u3053\u3053\u3067\u306f\u6b63\u898f\u5206\u5e03\u3092\u4f7f\u7528)\n        proposed_x &lt;- rnorm(1, mean = current_x, sd = proposal_sd)\n\n        # \u53d7\u5bb9\u78ba\u7387\u306e\u8a08\u7b97\n        # \u03b1 = min(1, (\u30bf\u30fc\u30b2\u30c3\u30c8\u5bc6\u5ea6(\u63d0\u6848) \/ \u30bf\u30fc\u30b2\u30c3\u30c8\u5bc6\u5ea6(\u73fe\u5728)) * (\u63d0\u6848\u5206\u5e03(\u73fe\u5728|\u63d0\u6848) \/ \u63d0\u6848\u5206\u5e03(\u63d0\u6848|\u73fe\u5728)))\n        # \u63d0\u6848\u5206\u5e03\u304c\u5bfe\u79f0 (N(current, sigma) -> N(proposed, sigma)) \u306a\u306e\u3067\u3001\u5f8c\u534a\u306f1\u306b\u306a\u308b\n        acceptance_ratio &lt;- target_density(proposed_x) \/ target_density(current_x)\n        alpha &lt;- min(1, acceptance_ratio)\n\n        # \u4e71\u6570\u3092\u751f\u6210\u3057\u3001\u53d7\u5bb9\u3059\u308b\u304b\u3069\u3046\u304b\u3092\u6c7a\u5b9a\n        if (runif(1) &lt; alpha) {\n            current_x &lt;- proposed_x # \u53d7\u5bb9\n        }\n        samples&#91;i] &lt;- current_x # \u73fe\u5728\u306e\u72b6\u614b\u3092\u30b5\u30f3\u30d7\u30eb\u3068\u3057\u3066\u8a18\u9332\n    }\n    return(samples)\n}\n\n# MCMC\u306e\u5b9f\u884c\nset.seed(123) # \u518d\u73fe\u6027\u306e\u305f\u3081\u306b\u30b7\u30fc\u30c9\u3092\u8a2d\u5b9a\nn_iterations &lt;- 5000 # \u7e70\u308a\u8fd4\u3057\u56de\u6570\ninitial_value &lt;- 0 # \u521d\u671f\u5024\nproposal_sd_value &lt;- 1 # \u63d0\u6848\u5206\u5e03\u306e\u6a19\u6e96\u504f\u5dee\n\nmcmc_samples &lt;- mcmc_mh(n_iterations, initial_value, proposal_sd_value)\n\n# \u7d50\u679c\u306e\u53ef\u8996\u5316\nhist(mcmc_samples&#91;1001:n_iterations], # \u30d0\u30fc\u30f3\u30a4\u30f3\u671f\u9593\u3092\u9664\u5916\n    freq = FALSE,\n    main = \"MCMC\u30b5\u30f3\u30d7\u30eb\u306b\u3088\u308b\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u306e\u8fd1\u4f3c\",\n    xlab = \"\u5024\",\n    ylab = \"\u5bc6\u5ea6\",\n    col = \"lightblue\",\n    border = \"white\"\n)\n\n# \u771f\u306e\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u306e\u5bc6\u5ea6\u66f2\u7dda\u3092\u91cd\u306d\u3066\u63cf\u753b\ncurve(dnorm(x, mean = 0, sd = 1), add = TRUE, col = \"red\", lwd = 2)\n\n# \u30b5\u30f3\u30d7\u30eb\u306e\u63a8\u79fb\uff08\u30c8\u30ec\u30fc\u30b9\u30d7\u30ed\u30c3\u30c8\uff09\nplot(mcmc_samples, type = \"l\", main = \"MCMC\u30b5\u30f3\u30d7\u30eb\u306e\u63a8\u79fb (\u30c8\u30ec\u30fc\u30b9\u30d7\u30ed\u30c3\u30c8)\", xlab = \"\u30a4\u30c6\u30ec\u30fc\u30b7\u30e7\u30f3\", ylab = \"\u5024\")\nabline(h = mean(mcmc_samples&#91;1001:n_iterations]), col = \"blue\", lty = 2) # \u30b5\u30f3\u30d7\u30eb\u306e\u5e73\u5747\u5024\nabline(h = 0, col = \"green\", lty = 2) # \u771f\u306e\u5e73\u5747\u5024\n<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">\u53ef\u8996\u5316\u306e\u89e3\u91c8<\/h3>\n\n\n\n<p>\u4e0a\u306eR\u30b3\u30fc\u30c9\u3092\u5b9f\u884c\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e2\u3064\u306e\u30b0\u30e9\u30d5\u304c\u5f97\u3089\u308c\u308b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"683\" height=\"1024\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/image-683x1024.png\" alt=\"\" class=\"wp-image-4210\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/image-683x1024.png 683w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/image-200x300.png 200w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/image-768x1152.png 768w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/image.png 800w\" sizes=\"(max-width: 683px) 100vw, 683px\" \/><\/figure>\n\n\n\n<ul start=\"1\" class=\"wp-block-list\">\n<li><strong>MCMC\u30b5\u30f3\u30d7\u30eb\u306b\u3088\u308b\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u306e\u8fd1\u4f3c<\/strong>: \u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u304c\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u306e\u5bc6\u5ea6\u66f2\u7dda\uff08\u8d64\u7dda\uff09\u306b\u8fd1\u4f3c\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002\u3053\u308c\u306f\u3001MCMC\u304c\u76ee\u7684\u306e\u5206\u5e03\u304b\u3089\u30b5\u30f3\u30d7\u30eb\u3092\u52b9\u7387\u7684\u306b\u751f\u6210\u3067\u304d\u3066\u3044\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"683\" height=\"1024\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/image-1-683x1024.png\" alt=\"\" class=\"wp-image-4211\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/image-1-683x1024.png 683w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/image-1-200x300.png 200w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/image-1-768x1152.png 768w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/image-1.png 800w\" sizes=\"(max-width: 683px) 100vw, 683px\" \/><\/figure>\n\n\n\n<ul start=\"1\" class=\"wp-block-list\">\n<li><strong>MCMC\u30b5\u30f3\u30d7\u30eb\u306e\u63a8\u79fb (\u30c8\u30ec\u30fc\u30b9\u30d7\u30ed\u30c3\u30c8)<\/strong>: \u30b5\u30f3\u30d7\u30eb\u304c\u3069\u306e\u3088\u3046\u306b\u63a8\u79fb\u3057\u3066\u3044\u3063\u305f\u304b\u3092\u793a\u3057\u3066\u3044\u308b\u3002\u9023\u9396\u304c\u5341\u5206\u306b\u6df7\u5408\u3057\u3001\u7279\u5b9a\u306e\u5024\u306b\u56fa\u307e\u3089\u305a\u306b\u5206\u5e03\u5168\u4f53\u3092\u63a2\u7d22\u3067\u304d\u3066\u3044\u308b\u304b\u3092\u78ba\u8a8d\u3067\u304d\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u7d50\u679c\u89e3\u91c8<\/h3>\n\n\n\n<p>MCMC\u306b\u3088\u308b\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u304c\u6210\u529f\u3057\u3066\u3044\u308c\u3070\u3001\u751f\u6210\u3055\u308c\u305f\u30b5\u30f3\u30d7\u30eb\u306f\u30bf\u30fc\u30b2\u30c3\u30c8\u306e\u5206\u5e03\u306b\u5f93\u3046\u3068\u898b\u306a\u305b\u308b\u3002\u3053\u308c\u3089\u306e\u30b5\u30f3\u30d7\u30eb\u3092\u7528\u3044\u3066\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u5206\u6790\u304c\u53ef\u80fd\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u671f\u5f85\u5024\u306e\u63a8\u5b9a<\/strong>: \u30b5\u30f3\u30d7\u30eb\u306e\u5e73\u5747\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3067\u3001\u30bf\u30fc\u30b2\u30c3\u30c8\u5206\u5e03\u306e\u671f\u5f85\u5024\u3092\u63a8\u5b9a\u3067\u304d\u308b\u3002<\/li>\n\n\n\n<li><strong>\u4fe1\u983c\u533a\u9593\uff08\u4fe1\u7528\u533a\u9593\uff09\u306e\u8a08\u7b97<\/strong>: \u30b5\u30f3\u30d7\u30eb\u306e\u30d1\u30fc\u30bb\u30f3\u30bf\u30a4\u30eb\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3067\u3001\u4fe1\u983c\u533a\u9593\uff08\u30d9\u30a4\u30ba\u7d71\u8a08\u3067\u306f\u4fe1\u7528\u533a\u9593\uff09\u3092\u63a8\u5b9a\u3067\u304d\u308b\u3002<\/li>\n\n\n\n<li><strong>\u5206\u5e03\u306e\u5f62\u72b6\u306e\u7406\u89e3<\/strong>: \u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3084\u5bc6\u5ea6\u30d7\u30ed\u30c3\u30c8\u3092\u4f5c\u6210\u3059\u308b\u3053\u3068\u3067\u3001\u30bf\u30fc\u30b2\u30c3\u30c8\u5206\u5e03\u306e\u5f62\u72b6\u3001\u975e\u5bfe\u79f0\u6027\u3001\u30e2\u30fc\u30c9\u306a\u3069\u3092\u8996\u899a\u7684\u306b\u7406\u89e3\u3067\u304d\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u4e0a\u8a18\u306e\u4f8b\u3067\u306f\u3001\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u304b\u3089\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3092\u884c\u3063\u305f\u304c\u3001\u5b9f\u969b\u306b\u306f\u3088\u308a\u8907\u96d1\u306a\u591a\u5cf0\u6027\u5206\u5e03\u3084\u975e\u5bfe\u79f0\u306a\u5206\u5e03\u304b\u3089\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306bMCMC\u306f\u7528\u3044\u3089\u308c\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u307e\u3068\u3081<\/h2>\n\n\n\n<p>\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5 (MCMC) \u306f\u3001<strong>\u8907\u96d1\u306a\u78ba\u7387\u5206\u5e03\u304b\u3089\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3092\u53ef\u80fd\u306b\u3059\u308b\u5f37\u529b\u306a\u30c4\u30fc\u30eb<\/strong>\u3067\u3042\u308b\u3002\u30de\u30eb\u30b3\u30d5\u9023\u9396\u306e<strong>\u5b9a\u5e38\u5206\u5e03<\/strong>\u3068\u3001\u4e71\u6570\u3092\u7528\u3044\u305f<strong>\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5<\/strong>\u306e\u30a2\u30a4\u30c7\u30a2\u3092\u7d44\u307f\u5408\u308f\u305b\u308b\u3053\u3068\u3067\u3001\u76f4\u63a5\u8a08\u7b97\u304c\u96e3\u3057\u3044\u554f\u984c\u306b\u5bfe\u3057\u3066\u3082\u3001\u7d71\u8a08\u7684\u306a\u63a8\u8ad6\u3092\u884c\u3046\u9053\u3092\u958b\u304f\u3002<\/p>\n\n\n\n<p>\u30d9\u30a4\u30ba\u7d71\u8a08\u63a8\u8ad6\u306e\u767a\u5c55\u306b\u5927\u304d\u304f\u8ca2\u732e\u3057\u3001\u73fe\u5728\u3067\u306f\u7d71\u8a08\u5b66\u3001\u6a5f\u68b0\u5b66\u7fd2\u3001\u7269\u7406\u5b66\u306a\u3069\u3001\u5e45\u5e83\u3044\u5206\u91ce\u3067\u4e0d\u53ef\u6b20\u306a\u624b\u6cd5\u3068\u306a\u3063\u3066\u3044\u308b\u3002MCMC\u3092\u7406\u89e3\u3057\u6d3b\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u3088\u308a\u9ad8\u5ea6\u306a\u30c7\u30fc\u30bf\u5206\u6790\u3084\u30e2\u30c7\u30ea\u30f3\u30b0\u304c\u53ef\u80fd\u306b\u306a\u308b\u3060\u308d\u3046\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n","protected":false},"excerpt":{"rendered":"<p>\u300c\u306a\u3093\u3060\u304b\u8907\u96d1\u305d\u3046\u306a\u6570\u5f0f\u3084\u7406\u8ad6\u304c\u51fa\u3066\u304d\u305d\u3046\u2026\u300d\u305d\u3046\u601d\u308f\u308c\u305f\u65b9\u3082\u3044\u308b\u304b\u3082\u3057\u308c\u306a\u3044\u3002\u3057\u304b\u3057\u3001\u3054\u5b89\u5fc3\u3044\u305f\u3060\u304d\u305f\u3044\u3002\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5 (MCMC) \u3068\u3044\u3046\u5f37\u529b\u306a\u7d71\u8a08\u7684\u624b\u6cd5\u306b\u3064\u3044\u3066\u3001\u305d\u306e\u57fa\u672c\u304b\u3089\u5fdc\u7528\u307e\u3067\u3092\u3001 [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":4210,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[152],"tags":[],"class_list":["post-4208","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mcmc"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/image.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4208","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/comments?post=4208"}],"version-history":[{"count":3,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4208\/revisions"}],"predecessor-version":[{"id":4213,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4208\/revisions\/4213"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media\/4210"}],"wp:attachment":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media?parent=4208"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/categories?post=4208"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/tags?post=4208"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}