{"id":477963,"date":"2023-08-09T09:23:08","date_gmt":"2023-08-09T09:23:08","guid":{"rendered":""},"modified":"2023-09-05T11:15:45","modified_gmt":"2023-09-05T11:15:45","slug":"markov-chain-monte-carlo-mcmc","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/jp\/wiki\/markov-chain-monte-carlo-mcmc\/","title":{"rendered":"\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5 (MCMC)"},"content":{"rendered":"<p>\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed (MCMC) \u306f\u3001\u3055\u307e\u3056\u307e\u306a\u79d1\u5b66\u304a\u3088\u3073\u5de5\u5b66\u5206\u91ce\u3067\u8907\u96d1\u306a\u78ba\u7387\u5206\u5e03\u3092\u8abf\u67fb\u3057\u3001\u6570\u5024\u7a4d\u5206\u3092\u5b9f\u884c\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u5f37\u529b\u306a\u8a08\u7b97\u624b\u6cd5\u3067\u3059\u3002\u9ad8\u6b21\u5143\u7a7a\u9593\u3084\u6271\u3044\u306b\u304f\u3044\u78ba\u7387\u5206\u5e03\u3092\u6271\u3046\u5834\u5408\u306b\u7279\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002MCMC \u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u89e3\u6790\u5f62\u5f0f\u304c\u4e0d\u660e\u307e\u305f\u306f\u8a08\u7b97\u304c\u96e3\u3057\u3044\u5834\u5408\u3067\u3082\u3001\u30bf\u30fc\u30b2\u30c3\u30c8\u5206\u5e03\u304b\u3089\u30dd\u30a4\u30f3\u30c8\u3092\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u65b9\u6cd5\u306f\u3001\u30de\u30eb\u30b3\u30d5\u9023\u9396\u306e\u539f\u7406\u3092\u5229\u7528\u3057\u3066\u3001\u30bf\u30fc\u30b2\u30c3\u30c8\u5206\u5e03\u3092\u8fd1\u4f3c\u3059\u308b\u30b5\u30f3\u30d7\u30eb\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u751f\u6210\u3059\u308b\u305f\u3081\u3001\u30d9\u30a4\u30ba\u63a8\u5b9a\u3001\u7d71\u8a08\u30e2\u30c7\u30ea\u30f3\u30b0\u3001\u6700\u9069\u5316\u306e\u554f\u984c\u306b\u4e0d\u53ef\u6b20\u306a\u30c4\u30fc\u30eb\u3068\u306a\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n<h2>\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\uff08MCMC\uff09\u306e\u8d77\u6e90\u3068\u305d\u306e\u6700\u521d\u306e\u8a00\u53ca\u306e\u6b74\u53f2<\/h2>\n<p>MCMC \u306e\u8d77\u6e90\u306f 20 \u4e16\u7d00\u534a\u3070\u306b\u9061\u308a\u307e\u3059\u3002\u3053\u306e\u624b\u6cd5\u306e\u57fa\u790e\u306f\u30011940 \u5e74\u4ee3\u306b\u30b9\u30bf\u30cb\u30b9\u30ef\u30d5 \u30a6\u30e9\u30e0\u3068\u30b8\u30e7\u30f3 \u30d5\u30a9\u30f3 \u30ce\u30a4\u30de\u30f3\u306e\u7814\u7a76\u306b\u3088\u3063\u3066\u7d71\u8a08\u529b\u5b66\u306e\u5206\u91ce\u3067\u7bc9\u304b\u308c\u307e\u3057\u305f\u3002\u5f7c\u3089\u306f\u3001\u7269\u7406\u30b7\u30b9\u30c6\u30e0\u3092\u30e2\u30c7\u30eb\u5316\u3059\u308b\u65b9\u6cd5\u3068\u3057\u3066\u3001\u683c\u5b50\u4e0a\u306e\u30e9\u30f3\u30c0\u30e0 \u30a6\u30a9\u30fc\u30af \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u8abf\u67fb\u3057\u3066\u3044\u307e\u3057\u305f\u3002\u3057\u304b\u3057\u3001\u3053\u306e\u624b\u6cd5\u304c\u3088\u308a\u5e83\u304f\u6ce8\u76ee\u3055\u308c\u3001\u30e2\u30f3\u30c6 \u30ab\u30eb\u30ed\u6cd5\u3068\u95a2\u9023\u4ed8\u3051\u3089\u308c\u308b\u3088\u3046\u306b\u306a\u3063\u305f\u306e\u306f\u30011950 \u5e74\u4ee3\u3068 1960 \u5e74\u4ee3\u306b\u306a\u3063\u3066\u304b\u3089\u3067\u3057\u305f\u3002<\/p>\n<p>\u300c\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u300d\u3068\u3044\u3046\u7528\u8a9e\u81ea\u4f53\u306f\u3001\u7269\u7406\u5b66\u8005\u306e\u30cb\u30b3\u30e9\u30b9\u30fb\u30e1\u30c8\u30ed\u30dd\u30ea\u30b9\u3001\u30a2\u30ea\u30a2\u30ca\u30fb\u30ed\u30fc\u30bc\u30f3\u30d6\u30eb\u30fc\u30b9\u3001\u30de\u30fc\u30b7\u30e3\u30eb\u30fb\u30ed\u30fc\u30bc\u30f3\u30d6\u30eb\u30fc\u30b9\u3001\u30aa\u30fc\u30ac\u30b9\u30bf\u30fb\u30c6\u30e9\u30fc\u3001\u30a8\u30c9\u30ef\u30fc\u30c9\u30fb\u30c6\u30e9\u30fc\u304c\u30e1\u30c8\u30ed\u30dd\u30ea\u30b9\u30fb\u30d8\u30a4\u30b9\u30c6\u30a3\u30f3\u30b0\u30b9\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u767a\u8868\u3057\u305f 1950 \u5e74\u4ee3\u521d\u982d\u306b\u9020\u3089\u308c\u307e\u3057\u305f\u3002\u3053\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u7d71\u8a08\u529b\u5b66\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3067\u30dc\u30eb\u30c4\u30de\u30f3\u5206\u5e03\u3092\u52b9\u7387\u7684\u306b\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3059\u308b\u3088\u3046\u306b\u8a2d\u8a08\u3055\u308c\u3001MCMC \u306e\u73fe\u4ee3\u7684\u306a\u958b\u767a\u3078\u306e\u9053\u3092\u958b\u304d\u307e\u3057\u305f\u3002<\/p>\n<h2>\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5 (MCMC) \u306e\u8a73\u7d30\u60c5\u5831<\/h2>\n<p>MCMC \u306f\u3001\u5b9a\u5e38\u5206\u5e03\u304c\u76ee\u7684\u306e\u78ba\u7387\u5206\u5e03\u3067\u3042\u308b\u30de\u30eb\u30b3\u30d5\u9023\u9396\u3092\u751f\u6210\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u3001\u76ee\u6a19\u306e\u78ba\u7387\u5206\u5e03\u3092\u8fd1\u4f3c\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u30af\u30e9\u30b9\u3067\u3059\u3002MCMC \u306e\u80cc\u5f8c\u306b\u3042\u308b\u57fa\u672c\u7684\u306a\u8003\u3048\u65b9\u306f\u3001\u53cd\u5fa9\u56de\u6570\u304c\u7121\u9650\u306b\u8fd1\u3065\u304f\u306b\u3064\u308c\u3066\u76ee\u6a19\u306e\u5206\u5e03\u306b\u53ce\u675f\u3059\u308b\u30de\u30eb\u30b3\u30d5\u9023\u9396\u3092\u69cb\u7bc9\u3059\u308b\u3053\u3068\u3067\u3059\u3002<\/p>\n<h3>\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\uff08MCMC\uff09\u306e\u5185\u90e8\u69cb\u9020\u3068\u305d\u306e\u4ed5\u7d44\u307f<\/h3>\n<p>MCMC \u306e\u57fa\u672c\u7684\u306a\u8003\u3048\u65b9\u306f\u3001\u65b0\u3057\u3044\u72b6\u614b\u3092\u7e70\u308a\u8fd4\u3057\u63d0\u6848\u3057\u3001\u76f8\u5bfe\u7684\u306a\u78ba\u7387\u306b\u57fa\u3065\u3044\u3066\u53d7\u3051\u5165\u308c\u308b\u304b\u62d2\u5426\u3059\u308b\u304b\u3059\u308b\u3053\u3068\u3067\u3001\u30bf\u30fc\u30b2\u30c3\u30c8\u5206\u5e03\u306e\u72b6\u614b\u7a7a\u9593\u3092\u63a2\u7d22\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u3053\u306e\u30d7\u30ed\u30bb\u30b9\u306f\u3001\u6b21\u306e\u624b\u9806\u306b\u5206\u3051\u3089\u308c\u307e\u3059\u3002<\/p>\n<ol>\n<li>\n<p><strong>\u521d\u671f\u5316<\/strong>: \u30bf\u30fc\u30b2\u30c3\u30c8\u5206\u5e03\u304b\u3089\u306e\u521d\u671f\u72b6\u614b\u307e\u305f\u306f\u30b5\u30f3\u30d7\u30eb\u304b\u3089\u958b\u59cb\u3057\u307e\u3059\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u63d0\u6848\u30b9\u30c6\u30c3\u30d7<\/strong>: \u63d0\u6848\u5206\u5e03\u306b\u57fa\u3065\u3044\u3066\u5019\u88dc\u72b6\u614b\u3092\u751f\u6210\u3057\u307e\u3059\u3002\u3053\u306e\u5206\u5e03\u306f\u65b0\u3057\u3044\u72b6\u614b\u306e\u751f\u6210\u65b9\u6cd5\u3092\u6c7a\u5b9a\u3057\u3001MCMC \u306e\u52b9\u7387\u306b\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u627f\u8a8d\u30b9\u30c6\u30c3\u30d7<\/strong>: \u73fe\u5728\u306e\u72b6\u614b\u3068\u63d0\u6848\u3055\u308c\u305f\u72b6\u614b\u306e\u78ba\u7387\u3092\u8003\u616e\u3057\u305f\u53d7\u3051\u5165\u308c\u6bd4\u7387\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u3053\u306e\u6bd4\u7387\u306f\u3001\u63d0\u6848\u3055\u308c\u305f\u72b6\u614b\u3092\u53d7\u3051\u5165\u308c\u308b\u304b\u62d2\u5426\u3059\u308b\u304b\u3092\u6c7a\u5b9a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u66f4\u65b0\u624b\u9806<\/strong>: \u63d0\u6848\u3055\u308c\u305f\u72b6\u614b\u304c\u53d7\u3051\u5165\u308c\u3089\u308c\u305f\u5834\u5408\u306f\u3001\u73fe\u5728\u306e\u72b6\u614b\u3092\u65b0\u3057\u3044\u72b6\u614b\u306b\u66f4\u65b0\u3057\u307e\u3059\u3002\u305d\u308c\u4ee5\u5916\u306e\u5834\u5408\u306f\u3001\u73fe\u5728\u306e\u72b6\u614b\u3092\u5909\u66f4\u305b\u305a\u306b\u7dad\u6301\u3057\u307e\u3059\u3002<\/p>\n<\/li>\n<\/ol>\n<p>\u3053\u308c\u3089\u306e\u624b\u9806\u3092\u7e70\u308a\u8fd4\u3057\u5b9f\u884c\u3059\u308b\u3053\u3068\u3067\u3001\u30de\u30eb\u30b3\u30d5\u9023\u9396\u306f\u72b6\u614b\u7a7a\u9593\u3092\u63a2\u7d22\u3057\u3001\u5341\u5206\u306a\u56de\u6570\u306e\u53cd\u5fa9\u3092\u7d4c\u308b\u3068\u3001\u30b5\u30f3\u30d7\u30eb\u306f\u30bf\u30fc\u30b2\u30c3\u30c8\u5206\u5e03\u306b\u8fd1\u3065\u304d\u307e\u3059\u3002<\/p>\n<h2>\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5 (MCMC) \u306e\u4e3b\u306a\u7279\u5fb4\u306e\u5206\u6790<\/h2>\n<p>MCMC \u3092\u3055\u307e\u3056\u307e\u306a\u5206\u91ce\u3067\u4fa1\u5024\u3042\u308b\u30c4\u30fc\u30eb\u306b\u3059\u308b\u4e3b\u306a\u6a5f\u80fd\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n<ol>\n<li>\n<p><strong>\u8907\u96d1\u306a\u5206\u5e03\u304b\u3089\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0<\/strong>MCMC \u306f\u3001\u5206\u5e03\u306e\u8907\u96d1\u3055\u3084\u554f\u984c\u306e\u9ad8\u6b21\u5143\u6027\u306e\u305f\u3081\u306b\u3001\u30bf\u30fc\u30b2\u30c3\u30c8\u5206\u5e03\u304b\u3089\u306e\u76f4\u63a5\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u304c\u56f0\u96e3\u307e\u305f\u306f\u4e0d\u53ef\u80fd\u306a\u72b6\u6cc1\u3067\u7279\u306b\u52b9\u679c\u7684\u3067\u3059\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u30d9\u30a4\u30ba\u63a8\u8ad6<\/strong>MCMC \u306f\u3001\u30e2\u30c7\u30eb \u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u4e8b\u5f8c\u5206\u5e03\u306e\u63a8\u5b9a\u3092\u53ef\u80fd\u306b\u3059\u308b\u3053\u3068\u3067\u3001\u30d9\u30a4\u30ba\u7d71\u8a08\u5206\u6790\u306b\u9769\u547d\u3092\u3082\u305f\u3089\u3057\u307e\u3057\u305f\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u7814\u7a76\u8005\u306f\u4e8b\u524d\u306e\u77e5\u8b58\u3092\u53d6\u308a\u5165\u308c\u3001\u89b3\u6e2c\u3055\u308c\u305f\u30c7\u30fc\u30bf\u306b\u57fa\u3065\u3044\u3066\u4fe1\u5ff5\u3092\u66f4\u65b0\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u4e0d\u78ba\u5b9f\u6027\u306e\u5b9a\u91cf\u5316<\/strong>MCMC \u306f\u3001\u610f\u601d\u6c7a\u5b9a\u30d7\u30ed\u30bb\u30b9\u306b\u304a\u3044\u3066\u975e\u5e38\u306b\u91cd\u8981\u306a\u3001\u30e2\u30c7\u30eb\u4e88\u6e2c\u3068\u30d1\u30e9\u30e1\u30fc\u30bf\u63a8\u5b9a\u306b\u304a\u3051\u308b\u4e0d\u78ba\u5b9f\u6027\u3092\u5b9a\u91cf\u5316\u3059\u308b\u65b9\u6cd5\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u6700\u9069\u5316<\/strong>MCMC \u306f\u3001\u30bf\u30fc\u30b2\u30c3\u30c8\u5206\u5e03\u306e\u6700\u5927\u5024\u307e\u305f\u306f\u6700\u5c0f\u5024\u3092\u898b\u3064\u3051\u308b\u305f\u3081\u306e\u30b0\u30ed\u30fc\u30d0\u30eb\u6700\u9069\u5316\u624b\u6cd5\u3068\u3057\u3066\u4f7f\u7528\u3067\u304d\u308b\u305f\u3081\u3001\u8907\u96d1\u306a\u6700\u9069\u5316\u554f\u984c\u3067\u6700\u9069\u306a\u30bd\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u3092\u898b\u3064\u3051\u308b\u306e\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002<\/p>\n<\/li>\n<\/ol>\n<h2>\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5 (MCMC) \u306e\u7a2e\u985e<\/h2>\n<p>MCMC \u306b\u306f\u3001\u3055\u307e\u3056\u307e\u306a\u7a2e\u985e\u306e\u78ba\u7387\u5206\u5e03\u3092\u8abf\u67fb\u3059\u308b\u305f\u3081\u306b\u8a2d\u8a08\u3055\u308c\u305f\u8907\u6570\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002\u4e00\u822c\u7684\u306a MCMC \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u306f\u6b21\u306e\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ol>\n<li>\n<p><strong>\u30e1\u30c8\u30ed\u30dd\u30ea\u30b9\u30fb\u30d8\u30a4\u30b9\u30c6\u30a3\u30f3\u30b0\u30b9\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/strong>: \u6700\u3082\u521d\u671f\u304b\u3064\u5e83\u304f\u4f7f\u7528\u3055\u308c\u3066\u3044\u308b MCMC \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e 1 \u3064\u3067\u3001\u6b63\u898f\u5316\u3055\u308c\u3066\u3044\u306a\u3044\u5206\u5e03\u304b\u3089\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u30ae\u30d6\u30b9\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0<\/strong>: \u6761\u4ef6\u4ed8\u304d\u5206\u5e03\u304b\u3089\u53cd\u5fa9\u7684\u306b\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u7d50\u5408\u5206\u5e03\u304b\u3089\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3059\u308b\u305f\u3081\u306b\u7279\u5225\u306b\u8a2d\u8a08\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u30cf\u30df\u30eb\u30c8\u30f3\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed (HMC)<\/strong>: \u30cf\u30df\u30eb\u30c8\u30f3\u529b\u5b66\u306e\u539f\u7406\u3092\u5229\u7528\u3057\u3066\u3001\u3088\u308a\u52b9\u7387\u7684\u3067\u76f8\u95a2\u306e\u5c11\u306a\u3044\u30b5\u30f3\u30d7\u30eb\u3092\u5b9f\u73fe\u3059\u308b\u3001\u3088\u308a\u6d17\u7df4\u3055\u308c\u305f MCMC \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u30ce\u30fcU\u30bf\u30fc\u30f3\u30b5\u30f3\u30d7\u30e9\u30fc\uff08NUTS\uff09<\/strong>: \u6700\u9069\u306a\u8ecc\u9053\u9577\u3092\u81ea\u52d5\u7684\u306b\u6c7a\u5b9a\u3057\u3001HMC \u306e\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u3092\u5411\u4e0a\u3055\u305b\u308b HMC \u306e\u62e1\u5f35\u6a5f\u80fd\u3002<\/p>\n<\/li>\n<\/ol>\n<h2>\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\uff08MCMC\uff09\u306e\u4f7f\u7528\u65b9\u6cd5\u3001\u4f7f\u7528\u306b\u95a2\u9023\u3059\u308b\u554f\u984c\u3068\u305d\u306e\u89e3\u6c7a\u7b56<\/h2>\n<p>MCMC \u306f\u3055\u307e\u3056\u307e\u306a\u5206\u91ce\u3067\u5fdc\u7528\u3055\u308c\u3066\u304a\u308a\u3001\u4e00\u822c\u7684\u306a\u4f7f\u7528\u4f8b\u306b\u306f\u6b21\u306e\u3088\u3046\u306a\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ol>\n<li>\n<p><strong>\u30d9\u30a4\u30ba\u63a8\u8ad6<\/strong>MCMC \u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u7814\u7a76\u8005\u306f\u30d9\u30a4\u30ba\u7d71\u8a08\u5206\u6790\u306b\u304a\u3051\u308b\u30e2\u30c7\u30eb \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306e\u4e8b\u5f8c\u5206\u5e03\u3092\u63a8\u5b9a\u3067\u304d\u307e\u3059\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u8907\u96d1\u306a\u5206\u5e03\u304b\u3089\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0<\/strong>\u8907\u96d1\u306a\u5206\u5e03\u3084\u9ad8\u6b21\u5143\u306e\u5206\u5e03\u3092\u6271\u3046\u5834\u5408\u3001MCMC \u306f\u4ee3\u8868\u7684\u306a\u30b5\u30f3\u30d7\u30eb\u3092\u62bd\u51fa\u3059\u308b\u52b9\u679c\u7684\u306a\u624b\u6bb5\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u6700\u9069\u5316<\/strong>MCMC \u306f\u3001\u30b0\u30ed\u30fc\u30d0\u30eb\u306a\u6700\u5927\u5024\u307e\u305f\u306f\u6700\u5c0f\u5024\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u96e3\u3057\u3044\u30b0\u30ed\u30fc\u30d0\u30eb\u6700\u9069\u5316\u554f\u984c\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u6a5f\u68b0\u5b66\u7fd2<\/strong>MCMC \u306f\u3001\u30d9\u30a4\u30ba\u6a5f\u68b0\u5b66\u7fd2\u3067\u30e2\u30c7\u30eb\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u4e8b\u5f8c\u5206\u5e03\u3092\u63a8\u5b9a\u3057\u3001\u4e0d\u78ba\u5b9f\u6027\u3092\u4f34\u3046\u4e88\u6e2c\u3092\u884c\u3046\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n<\/li>\n<\/ol>\n<h3>\u8ab2\u984c\u3068\u89e3\u6c7a\u7b56:<\/h3>\n<ol>\n<li>\n<p><strong>\u53ce\u675f<\/strong>: \u6b63\u78ba\u306a\u63a8\u5b9a\u5024\u3092\u63d0\u4f9b\u3059\u308b\u306b\u306f\u3001MCMC \u30c1\u30a7\u30fc\u30f3\u304c\u30bf\u30fc\u30b2\u30c3\u30c8\u5206\u5e03\u306b\u53ce\u675f\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u53ce\u675f\u306e\u8a3a\u65ad\u3068\u6539\u5584\u306f\u56f0\u96e3\u306a\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u89e3\u6c7a\u7b56: \u30c8\u30ec\u30fc\u30b9 \u30d7\u30ed\u30c3\u30c8\u3001\u81ea\u5df1\u76f8\u95a2\u30d7\u30ed\u30c3\u30c8\u3001\u53ce\u675f\u57fa\u6e96 (Gelman-Rubin \u7d71\u8a08\u306a\u3069) \u306a\u3069\u306e\u8a3a\u65ad\u306f\u3001\u53ce\u675f\u3092\u78ba\u5b9f\u306b\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><strong>\u63d0\u6848\u914d\u5e03\u306e\u9078\u629e<\/strong>MCMC \u306e\u52b9\u7387\u306f\u3001\u63d0\u6848\u5206\u5e03\u306e\u9078\u629e\u306b\u5927\u304d\u304f\u4f9d\u5b58\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u89e3\u6c7a\u7b56: \u9069\u5fdc\u578b MCMC \u30e1\u30bd\u30c3\u30c9\u306f\u3001\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u4e2d\u306b\u63d0\u6848\u5206\u5e03\u3092\u52d5\u7684\u306b\u8abf\u6574\u3057\u3066\u3001\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u3092\u5411\u4e0a\u3055\u305b\u307e\u3059\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><strong>\u9ad8\u6b21\u5143\u6027<\/strong>\u9ad8\u6b21\u5143\u7a7a\u9593\u3067\u306f\u3001\u72b6\u614b\u7a7a\u9593\u306e\u63a2\u7d22\u304c\u3088\u308a\u56f0\u96e3\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u89e3\u6c7a\u7b56: HMC \u3084 NUTS \u306a\u3069\u306e\u9ad8\u5ea6\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u9ad8\u6b21\u5143\u7a7a\u9593\u3067\u3088\u308a\u52b9\u679c\u7684\u3067\u3059\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<h2>\u4e3b\u306a\u7279\u5fb4\u3068\u985e\u4f3c\u7528\u8a9e\u3068\u306e\u6bd4\u8f03<\/h2>\n<table>\n<thead>\n<tr>\n<th><strong>\u7279\u6027<\/strong><\/th>\n<th><strong>\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5 (MCMC)<\/strong><\/th>\n<th><strong>\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>\u30e1\u30bd\u30c3\u30c9\u306e\u7a2e\u985e<\/strong><\/td>\n<td>\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u30d9\u30fc\u30b9<\/td>\n<td>\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u30d9\u30fc\u30b9<\/td>\n<\/tr>\n<tr>\n<td><strong>\u30b4\u30fc\u30eb<\/strong><\/td>\n<td>\u304a\u304a\u3088\u305d\u306e\u30bf\u30fc\u30b2\u30c3\u30c8\u5206\u5e03<\/td>\n<td>\u78ba\u7387\u3092\u63a8\u5b9a\u3059\u308b<\/td>\n<\/tr>\n<tr>\n<td><strong>\u4f7f\u7528\u4f8b<\/strong><\/td>\n<td>\u30d9\u30a4\u30ba\u63a8\u8ad6\u3001\u6700\u9069\u5316\u3001\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0<\/td>\n<td>\u7d71\u5408\u3001\u63a8\u5b9a<\/td>\n<\/tr>\n<tr>\n<td><strong>\u30b5\u30f3\u30d7\u30eb\u3078\u306e\u4f9d\u5b58<\/strong><\/td>\n<td>\u30b7\u30fc\u30b1\u30f3\u30b7\u30e3\u30eb\u3001\u30de\u30eb\u30b3\u30d5\u9023\u9396\u52d5\u4f5c<\/td>\n<td>\u72ec\u7acb\u3057\u305f\u30e9\u30f3\u30c0\u30e0\u30b5\u30f3\u30d7\u30eb<\/td>\n<\/tr>\n<tr>\n<td><strong>\u9ad8\u6b21\u5143\u3067\u306e\u52b9\u7387<\/strong><\/td>\n<td>\u666e\u901a\u304b\u3089\u826f\u3044<\/td>\n<td>\u975e\u52b9\u7387\u7684\u306a<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\uff08MCMC\uff09\u306b\u95a2\u3059\u308b\u5c06\u6765\u306e\u5c55\u671b\u3068\u6280\u8853<\/h2>\n<p>\u30c6\u30af\u30ce\u30ed\u30b8\u30fc\u304c\u9032\u6b69\u3059\u308b\u306b\u3064\u308c\u3066\u3001MCMC \u306f\u3044\u304f\u3064\u304b\u306e\u65b9\u5411\u306b\u9032\u5316\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ol>\n<li>\n<p><strong>\u4e26\u5217\u304a\u3088\u3073\u5206\u6563MCMC<\/strong>: \u4e26\u5217\u304a\u3088\u3073\u5206\u6563\u30b3\u30f3\u30d4\u30e5\u30fc\u30c6\u30a3\u30f3\u30b0 \u30ea\u30bd\u30fc\u30b9\u3092\u6d3b\u7528\u3057\u3066\u3001\u5927\u898f\u6a21\u306a\u554f\u984c\u306e MCMC \u8a08\u7b97\u3092\u9ad8\u901f\u5316\u3057\u307e\u3059\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u5909\u5206\u63a8\u8ad6<\/strong>: MCMC \u3068\u5909\u5206\u63a8\u8ad6\u6280\u8853\u3092\u7d44\u307f\u5408\u308f\u305b\u3066\u3001\u30d9\u30a4\u30ba\u8a08\u7b97\u306e\u52b9\u7387\u3068\u30b9\u30b1\u30fc\u30e9\u30d3\u30ea\u30c6\u30a3\u3092\u5411\u4e0a\u3055\u305b\u307e\u3059\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u30cf\u30a4\u30d6\u30ea\u30c3\u30c9\u65b9\u5f0f<\/strong>: MCMC \u3092\u6700\u9069\u5316\u6cd5\u307e\u305f\u306f\u5909\u5206\u6cd5\u3068\u7d71\u5408\u3057\u3066\u3001\u305d\u308c\u305e\u308c\u306e\u5229\u70b9\u3092\u6d3b\u7528\u3057\u307e\u3059\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u30a2\u30af\u30bb\u30e9\u30ec\u30fc\u30b7\u30e7\u30f3<\/strong>: GPU \u3084 TPU \u306a\u3069\u306e\u7279\u6b8a\u306a\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u3092\u6d3b\u7528\u3057\u3066\u3001MCMC \u8a08\u7b97\u3092\u3055\u3089\u306b\u9ad8\u901f\u5316\u3057\u307e\u3059\u3002<\/p>\n<\/li>\n<\/ol>\n<h2>\u30d7\u30ed\u30ad\u30b7 \u30b5\u30fc\u30d0\u30fc\u3092\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed (MCMC) \u3067\u4f7f\u7528\u3059\u308b\u65b9\u6cd5\u307e\u305f\u306f\u95a2\u9023\u4ed8\u3051\u308b\u65b9\u6cd5<\/h2>\n<p>\u30d7\u30ed\u30ad\u30b7 \u30b5\u30fc\u30d0\u30fc\u306f\u3001\u7279\u306b\u5fc5\u8981\u306a\u8a08\u7b97\u30ea\u30bd\u30fc\u30b9\u304c\u5927\u91cf\u3067\u3042\u308b\u5834\u5408\u306b\u3001MCMC \u8a08\u7b97\u3092\u9ad8\u901f\u5316\u3059\u308b\u4e0a\u3067\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002\u8907\u6570\u306e\u30d7\u30ed\u30ad\u30b7 \u30b5\u30fc\u30d0\u30fc\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u3055\u307e\u3056\u307e\u306a\u30ce\u30fc\u30c9\u306b\u8a08\u7b97\u3092\u5206\u6563\u3057\u3001MCMC \u30b5\u30f3\u30d7\u30eb\u306e\u751f\u6210\u306b\u304b\u304b\u308b\u6642\u9593\u3092\u77ed\u7e2e\u3067\u304d\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u30d7\u30ed\u30ad\u30b7 \u30b5\u30fc\u30d0\u30fc\u3092\u4f7f\u7528\u3057\u3066\u30ea\u30e2\u30fc\u30c8 \u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306b\u30a2\u30af\u30bb\u30b9\u3057\u3001\u3088\u308a\u5e83\u7bc4\u3067\u591a\u69d8\u306a\u30c7\u30fc\u30bf\u3092\u5206\u6790\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u30d7\u30ed\u30ad\u30b7 \u30b5\u30fc\u30d0\u30fc\u306f\u3001MCMC \u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u4e2d\u306e\u30bb\u30ad\u30e5\u30ea\u30c6\u30a3\u3068\u30d7\u30e9\u30a4\u30d0\u30b7\u30fc\u3092\u5f37\u5316\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u30d7\u30ed\u30ad\u30b7 \u30b5\u30fc\u30d0\u30fc\u306f\u3001\u30e6\u30fc\u30b6\u30fc\u306e\u5b9f\u969b\u306e\u5834\u6240\u3068 ID \u3092\u96a0\u3059\u3053\u3068\u3067\u3001\u6a5f\u5bc6\u30c7\u30fc\u30bf\u3092\u4fdd\u8b77\u3057\u3001\u533f\u540d\u6027\u3092\u7dad\u6301\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u500b\u4eba\u60c5\u5831\u3092\u6271\u3046\u30d9\u30a4\u30ba\u63a8\u8ad6\u3067\u306f\u7279\u306b\u91cd\u8981\u3067\u3059\u3002<\/p>\n<h2>\u95a2\u9023\u30ea\u30f3\u30af<\/h2>\n<p>\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed (MCMC) \u306e\u8a73\u7d30\u306b\u3064\u3044\u3066\u306f\u3001\u6b21\u306e\u30ea\u30bd\u30fc\u30b9\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<ol>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Metropolis%E2%80%93Hastings_algorithm\" target=\"_new\" rel=\"noopener nofollow\">\u30e1\u30c8\u30ed\u30dd\u30ea\u30b9\u30fb\u30d8\u30a4\u30b9\u30c6\u30a3\u30f3\u30b0\u30b9\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Gibbs_sampling\" target=\"_new\" rel=\"noopener nofollow\">\u30ae\u30d6\u30b9\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Hamiltonian_Monte_Carlo\" target=\"_new\" rel=\"noopener nofollow\">\u30cf\u30df\u30eb\u30c8\u30f3\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed (HMC)<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/No-U-Turn_Sampler\" target=\"_new\" rel=\"noopener nofollow\">\u30ce\u30fcU\u30bf\u30fc\u30f3\u30b5\u30f3\u30d7\u30e9\u30fc\uff08NUTS\uff09<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Adaptive_Metropolis%E2%80%93Hastings_algorithm\" target=\"_new\" rel=\"noopener nofollow\">\u9069\u5fdc\u578bMCMC<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Variational_Bayesian_methods\" target=\"_new\" rel=\"noopener nofollow\">\u5909\u5206\u63a8\u8ad6<\/a><\/li>\n<\/ol>\n<p>\u7d50\u8ad6\u3068\u3057\u3066\u3001\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5 (MCMC) \u306f\u3001\u30d9\u30a4\u30ba\u7d71\u8a08\u3001\u6a5f\u68b0\u5b66\u7fd2\u3001\u6700\u9069\u5316\u306a\u3069\u3001\u3055\u307e\u3056\u307e\u306a\u5206\u91ce\u306b\u9769\u547d\u3092\u3082\u305f\u3089\u3057\u305f\u591a\u7528\u9014\u3067\u5f37\u529b\u306a\u624b\u6cd5\u3067\u3059\u3002MCMC \u306f\u7814\u7a76\u306e\u6700\u524d\u7dda\u306b\u3042\u308a\u7d9a\u3051\u3001\u5c06\u6765\u306e\u30c6\u30af\u30ce\u30ed\u30b8\u30fc\u3068\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3092\u5f62\u6210\u3059\u308b\u4e0a\u3067\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3059\u3053\u3068\u306f\u9593\u9055\u3044\u3042\u308a\u307e\u305b\u3093\u3002<\/p>","protected":false},"featured_media":468867,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-477963","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about <mark>Markov Chain Monte Carlo (MCMC): Exploring Probabilistic Landscapes<\/mark>","faq_items":[{"question":"What is Markov Chain Monte Carlo (MCMC)?","answer":"<p>Markov Chain Monte Carlo (MCMC) is a powerful computational technique used to explore complex probability distributions and perform numerical integration. It allows for sampling from a target distribution, even when its analytical form is unknown or difficult to compute. MCMC is widely employed in Bayesian inference, statistical modeling, and optimization problems.<\/p>"},{"question":"How did Markov Chain Monte Carlo (MCMC) originate?","answer":"<p>The origins of MCMC can be traced back to the mid-20th century, with its foundations laid in the field of statistical mechanics by Stanislaw Ulam and John von Neumann. The term \"Markov Chain Monte Carlo\" was coined in the 1950s when physicists introduced the Metropolis-Hastings algorithm to efficiently sample the Boltzmann distribution in simulations.<\/p>"},{"question":"How does Markov Chain Monte Carlo (MCMC) work?","answer":"<p>MCMC constructs a Markov chain whose stationary distribution is the target probability distribution. The process involves proposing new states, accepting or rejecting them based on their probabilities, and updating the chain iteratively. After a sufficient number of iterations, the samples approximate the target distribution.<\/p>"},{"question":"What are the key features of Markov Chain Monte Carlo (MCMC)?","answer":"<p>MCMC is renowned for its ability to sample from complex distributions, perform Bayesian inference, quantify uncertainty in predictions, and tackle optimization problems. It provides a robust approach to dealing with high-dimensional spaces and exploring intricate probability landscapes.<\/p>"},{"question":"What types of Markov Chain Monte Carlo (MCMC) exist?","answer":"<p>There are several MCMC algorithms, including the Metropolis-Hastings Algorithm, Gibbs Sampling, Hamiltonian Monte Carlo (HMC), and No-U-Turn Sampler (NUTS). Each algorithm is tailored to explore different types of probability distributions.<\/p>"},{"question":"How can Markov Chain Monte Carlo (MCMC) be used, and what are some common challenges?","answer":"<p>MCMC finds applications in Bayesian inference, optimization, and sampling from complex distributions. Common challenges include ensuring convergence, selecting suitable proposal distributions, and addressing high-dimensional problems. Adaptive methods and diagnostics help address these challenges.<\/p>"},{"question":"What does the future hold for Markov Chain Monte Carlo (MCMC)?","answer":"<p>The future of MCMC involves parallel and distributed computing, hybrid methods with other inference techniques, and hardware acceleration. These advancements will lead to more efficient and scalable MCMC computations for complex problems.<\/p>"},{"question":"How are proxy servers associated with Markov Chain Monte Carlo (MCMC)?","answer":"<p>Proxy servers can enhance MCMC computations by distributing the workload across multiple nodes, reducing computation time. Additionally, they offer added security and privacy during simulations by anonymizing users' identities and locations.<\/p>"}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/jp\/wp-json\/wp\/v2\/wiki\/477963","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/jp\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/jp\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":0,"href":"https:\/\/oneproxy.pro\/jp\/wp-json\/wp\/v2\/wiki\/477963\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/jp\/wp-json\/wp\/v2\/media\/468867"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/jp\/wp-json\/wp\/v2\/media?parent=477963"}],"curies":[{"name":"\u3046\u30fc\u3093","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}