{"id":10004,"date":"2026-10-06T15:49:19","date_gmt":"2026-10-06T06:49:19","guid":{"rendered":"https:\/\/since2020.jp\/media\/?p=10004"},"modified":"2026-10-06T15:49:19","modified_gmt":"2026-10-06T06:49:19","slug":"mcmc-convergence-diagnostics","status":"publish","type":"post","link":"https:\/\/since2020.jp\/media\/mcmc-convergence-diagnostics\/","title":{"rendered":"\u305d\u306eMCMC\u3001\u672c\u5f53\u306b\u53ce\u675f\u3057\u3066\u308b\uff1f\u2500\u2500\u8a55\u4fa1\u6307\u6a19\u307e\u3068\u3081"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\"><strong>\u30a4\u30f3\u30c8\u30ed\u30c0\u30af\u30b7\u30e7\u30f3<\/strong><\/h2>\n\n\n\n<p>MCMC\uff08\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\uff09\u306f\u3001\u8907\u96d1\u306a\u78ba\u7387\u5206\u5e03\uff08\u591a\u304f\u306e\u5834\u5408\u306f\u30d9\u30a4\u30ba\u7d71\u8a08\u306e\u4e8b\u5f8c\u5206\u5e03\uff09\u304b\u3089\u76f4\u63a5\u30b5\u30f3\u30d7\u30eb\u3092\u751f\u6210\u3059\u308b\u305f\u3081\u306e\u624b\u6cd5\u3067\u3042\u308b\u3002\u56de\u5e30\u4fc2\u6570\u306e\u89e3\u6790\u89e3\u304c\u6c42\u307e\u3089\u306a\u3044\u3088\u3046\u306a\u30e2\u30c7\u30eb\u3067\u3082\u3001MCMC\u3092\u56de\u305b\u3070\u305d\u308c\u3089\u3057\u3044\u30b5\u30f3\u30d7\u30eb\u5217\u304c\u51fa\u529b\u3055\u308c\u308b\u3002\u3057\u304b\u3057\u3001\u3053\u3053\u306b\u5927\u304d\u306a\u843d\u3068\u3057\u7a74\u304c\u3042\u308b\u3002<strong>MCMC\u306f\u300c\u8a08\u7b97\u304c\u7d42\u308f\u3063\u305f\u300d\u3053\u3068\u3068\u300c\u6b63\u3057\u3044\u5206\u5e03\u306b\u53ce\u675f\u3057\u305f\u300d\u3053\u3068\u3092\u533a\u5225\u3057\u3066\u304f\u308c\u306a\u3044<\/strong>\u3002\u9014\u4e2d\u3067\u6b62\u3081\u3066\u3082\u3001\u4f55\u304b\u3057\u3089\u306e\u6570\u5217\u306f\u51fa\u529b\u3055\u308c\u7d9a\u3051\u308b\u304b\u3089\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u51fa\u529b\u3055\u308c\u305f\u30b5\u30f3\u30d7\u30eb\u304c\u3001\u672c\u5f53\u306b\u76ee\u7684\u306e\u5206\u5e03\u3092\u4ee3\u8868\u3057\u3066\u3044\u308b\u306e\u304b\u3002\u305d\u308c\u3068\u3082\u3001\u307e\u3060\u7279\u5b9a\u306e\u9818\u57df\u306b\u504f\u3063\u305f\u307e\u307e\u63a2\u7d22\u304c\u7d42\u308f\u3063\u3066\u3044\u306a\u3044\u306e\u304b\u3002\u3053\u308c\u3092\u5224\u65ad\u3059\u308b\u305f\u3081\u306b\u4f7f\u308f\u308c\u308b\u306e\u304c\u3001\u672c\u8a18\u4e8b\u3067\u7d39\u4ecb\u3059\u308b<strong>MCMC\u306e\u8a55\u4fa1\u6307\u6a19\uff08\u8a3a\u65ad\u6307\u6a19\uff09<\/strong>\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u30c8\u30ec\u30fc\u30b9\u30d7\u30ed\u30c3\u30c8\uff1a\u6700\u521d\u306b\u898b\u308b\u3079\u304d\u30b0\u30e9\u30d5<\/strong><\/h2>\n\n\n\n<p>\u6700\u3082\u57fa\u672c\u7684\u306a\u8a3a\u65ad\u306f\u3001\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306e\u53cd\u5fa9\u56de\u6570\u3092\u6a2a\u8ef8\u306b\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u5024\u3092\u7e26\u8ef8\u306b\u3068\u3063\u305f<strong>\u30c8\u30ec\u30fc\u30b9\u30d7\u30ed\u30c3\u30c8<\/strong>\u3092\u76ee\u3067\u898b\u308b\u3053\u3068\u3067\u3042\u308b\u3002\u3088\u304f\u6df7\u5408\u3057\u3066\u3044\u308b\u30c1\u30a7\u30fc\u30f3\u306f\u3001\u7279\u5b9a\u306e\u5024\u306e\u5468\u308a\u3092\u9ad8\u901f\u306b\u3001\u6bdb\u866b\u306e\u3088\u3046\u306b\u30e9\u30f3\u30c0\u30e0\u306b\u884c\u304d\u6765\u3059\u308b\u3002\u9006\u306b\u6df7\u5408\u304c\u60aa\u3044\u30c1\u30a7\u30fc\u30f3\u306f\u3001\u540c\u3058\u5024\u306e\u5468\u8fba\u306b\u9577\u304f\u7559\u307e\u3063\u305f\u308a\u3001\u3086\u3063\u304f\u308a\u3068\u3057\u304b\u5024\u304c\u5909\u5316\u3057\u306a\u304b\u3063\u305f\u308a\u3059\u308b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"976\" height=\"480\" src=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/10\/image-11.png\" alt=\"\" class=\"wp-image-10006\" srcset=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/10\/image-11.png 976w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/10\/image-11-300x148.png 300w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/10\/image-11-768x378.png 768w\" sizes=\"(max-width: 976px) 100vw, 976px\" \/><\/figure>\n\n\n\n<p>\u56f31: \u5de6\u306f\u5024\u306e\u5468\u308a\u3092\u9ad8\u901f\u306b\u5f80\u5fa9\u3057\u3066\u304a\u308a\u3001\u63a2\u7d22\u304c\u3046\u307e\u304f\u3044\u3063\u3066\u3044\u308b\u3002\u53f3\u306f\u540c\u3058\u5024\u306b\u9577\u304f\u7559\u307e\u3063\u3066\u304b\u3089\u5225\u306e\u5024\u306b\u98db\u3093\u3067\u304a\u308a\u3001\u53ce\u675f\u3084\u6df7\u5408\u306b\u554f\u984c\u304c\u3042\u308b\u5146\u5019\u3002<\/p>\n\n\n\n<p>\u30c8\u30ec\u30fc\u30b9\u30d7\u30ed\u30c3\u30c8\u306f\u76f4\u611f\u7684\u3060\u304c\u3001\u3042\u304f\u307e\u3067\u76ee\u8996\u306b\u3088\u308b\u78ba\u8a8d\u306b\u3059\u304e\u306a\u3044\u3002\u305d\u3053\u3067\u3001\u6570\u5024\u3068\u3057\u3066\u5b9a\u91cf\u5316\u3059\u308b\u6307\u6a19\u304c\u5fc5\u8981\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>R-hat\uff08Gelman-Rubin\u7d71\u8a08\u91cf\uff09<\/strong><\/h2>\n\n\n\n<p>\u5b9f\u52d9\u3067\u306f\u3001\u521d\u671f\u5024\u3092\u5909\u3048\u305f\u8907\u6570\u306e\u30c1\u30a7\u30fc\u30f3\uff08\u4f8b\u3048\u30704\u672c\uff09\u3092\u4e26\u5217\u306b\u8d70\u3089\u305b\u308b\u306e\u304c\u4e00\u822c\u7684\u3067\u3042\u308b\u3002\u3082\u3057\u5168\u3066\u306e\u30c1\u30a7\u30fc\u30f3\u304c\u540c\u3058\u5206\u5e03\u306b\u53ce\u675f\u3057\u3066\u3044\u308c\u3070\u3001<strong>\u30c1\u30a7\u30fc\u30f3\u5185\u306e\u3070\u3089\u3064\u304d<\/strong>\u3068<strong>\u30c1\u30a7\u30fc\u30f3\u9593\u306e\u3070\u3089\u3064\u304d<\/strong>\u306f\u307b\u307c\u540c\u3058\u306b\u306a\u308b\u306f\u305a\u3067\u3042\u308b\u3002\u9006\u306b\u3001\u30c1\u30a7\u30fc\u30f3\u3054\u3068\u306b\u9055\u3046\u5834\u6240\u3092\u3046\u308d\u3064\u3044\u3066\u3044\u308b\u306a\u3089\u3001\u30c1\u30a7\u30fc\u30f3\u9593\u306e\u3070\u3089\u3064\u304d\u306e\u65b9\u304c\u5927\u304d\u304f\u306a\u308b\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u8003\u3048\u65b9\u3092\u6307\u6a19\u306b\u3057\u305f\u306e\u304c<strong>$\\widehat{R}$\uff08R-hat\u3001potential scale reduction factor\uff09<\/strong>\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"has-text-align-center\">$\\widehat{R} = \\sqrt{ {\\widehat{V} \\over W} }$<\/p>\n\n\n\n<p>\u3053\u3053\u3067 $W$ \u306f\u30c1\u30a7\u30fc\u30f3\u5185\u5206\u6563\u306e\u5e73\u5747\u3001$\\widehat{V}$ \u306f\u30c1\u30a7\u30fc\u30f3\u5185\u5206\u6563\u3068\u30c1\u30a7\u30fc\u30f3\u9593\u5206\u6563\u3092\u7d44\u307f\u5408\u308f\u305b\u305f\u5206\u6563\u306e\u63a8\u5b9a\u5024\u3067\u3042\u308b\u3002\u5168\u30c1\u30a7\u30fc\u30f3\u304c\u540c\u3058\u5206\u5e03\u304b\u3089\u6765\u3066\u3044\u308b\u306a\u3089 $\\widehat{R}$ \u306f1\u306b\u8fd1\u3065\u304d\u3001\u53ce\u675f\u3057\u3066\u3044\u306a\u3051\u308c\u30701\u3088\u308a\u5927\u304d\u304f\u306a\u308b\u3002<\/p>\n\n\n\n<p>\u5b9f\u52d9\u4e0a\u306e\u76ee\u5b89\u3068\u3057\u3066\u3001Vehtari et al.\uff082021\uff09\u306f\u3001\u5c11\u306a\u304f\u3068\u30824\u672c\u306e\u30c1\u30a7\u30fc\u30f3\u3092\u8d70\u3089\u305b\u305f\u4e0a\u3067\u3001<strong>$\\widehat{R} \\lt 1.01$<\/strong> \u306e\u3068\u304d\u306b\u3060\u3051\u305d\u306e\u30b5\u30f3\u30d7\u30eb\u3092\u4f7f\u3046\u3053\u3068\u3092\u63a8\u5968\u3057\u3066\u3044\u308b\u3002\u3053\u308c\u306f Gelman and Rubin\uff081992\uff09\u00a0\u306e\u63a8\u5968\u3088\u308a\u3082\u5927\u5e45\u306b\u53b3\u3057\u3044\u57fa\u6e96\u3067\u3001\u5f93\u6765\u306f <strong>$\\widehat{R} \\lt 1.1$<\/strong> \u304c\u53ce\u675f\u306e\u76ee\u5b89\u3068\u3057\u3066\u6271\u308f\u308c\u3066\u3044\u305f\u3002\u540c\u8ad6\u6587\u306f\u30011.01\u3068\u3044\u3046\u6570\u5024\u306f\u3042\u304f\u307e\u3067\u6700\u521d\u306e\u30c1\u30a7\u30c3\u30af\u3068\u3057\u3066\u306e\u76ee\u6a19\u5024\u3067\u3042\u308a\u3001\u7528\u9014\u306b\u5fdc\u3058\u3066\u8abf\u6574\u3059\u3079\u304d\u3060\u3068\u3082\u8ff0\u3079\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u6709\u52b9\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\uff08ESS\uff09<\/strong><\/h2>\n\n\n\n<p>MCMC\u304c\u751f\u6210\u3059\u308b\u30b5\u30f3\u30d7\u30eb\u306f\u3001\u96a3\u308a\u5408\u3046\u53cd\u5fa9\u540c\u58eb\u304c\u4f3c\u305f\u5024\u306b\u306a\u308a\u3084\u3059\u3044\uff08\u81ea\u5df1\u76f8\u95a2\u3092\u6301\u3064\uff09\u3002\u305d\u306e\u305f\u3081\u3001\u305f\u3068\u30481\u4e07\u500b\u30b5\u30f3\u30d7\u30eb\u3092\u53d6\u3063\u3066\u3082\u3001\u72ec\u7acb\u306a\u30b5\u30f3\u30d7\u30eb1\u4e07\u500b\u5206\u306e\u60c5\u5831\u91cf\u304c\u3042\u308b\u3068\u306f\u9650\u3089\u306a\u3044\u3002<strong>\u6709\u52b9\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\uff08Effective Sample Size, ESS\uff09<\/strong>\u306f\u3001\u300c\u81ea\u5df1\u76f8\u95a2\u3092\u8003\u616e\u3059\u308b\u3068\u3001\u5b9f\u8cea\u7684\u306b\u72ec\u7acb\u306a\u30b5\u30f3\u30d7\u30eb\u304c\u4f55\u500b\u5206\u306b\u76f8\u5f53\u3059\u308b\u304b\u300d\u3092\u8868\u3059\u6307\u6a19\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"has-text-align-center\">$\\mathrm{ESS} = \\dfrac{n}{1 + 2\\sum_{k=1}^{\\infty}\\rho_k}$<\/p>\n\n\n\n<p>\u3053\u3053\u3067 $n$ \u306f\u5168\u30b5\u30f3\u30d7\u30eb\u6570\u3001$\\rho_k$ \u306f\u30e9\u30b0 $k$ \u306e\u81ea\u5df1\u76f8\u95a2\u3067\u3042\u308b\u3002\u81ea\u5df1\u76f8\u95a2\u304c\u3059\u3050\u306b0\u306b\u8fd1\u3065\u304f\u30c1\u30a7\u30fc\u30f3\u307b\u3069\u3001ESS\u306f\u30b5\u30f3\u30d7\u30eb\u6570 $n$ \u306b\u8fd1\u3065\u304f\u3002\u81ea\u5df1\u76f8\u95a2\u304c\u306a\u304b\u306a\u304b\u6e1b\u8870\u3057\u306a\u3044\u30c1\u30a7\u30fc\u30f3\u307b\u3069\u3001ESS\u306f $n$ \u3088\u308a\u305a\u3063\u3068\u5c0f\u3055\u304f\u306a\u308b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"952\" height=\"510\" src=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/10\/image-10.png\" alt=\"\" class=\"wp-image-10005\" srcset=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/10\/image-10.png 952w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/10\/image-10-300x161.png 300w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/10\/image-10-768x411.png 768w\" sizes=\"(max-width: 952px) 100vw, 952px\" \/><\/figure>\n\n\n\n<p>\u56f32: \u7dd1\u306f\u81ea\u5df1\u76f8\u95a2\u304c\u3059\u3050\u306b\u5c0f\u3055\u304f\u306a\u308a\u3001\u5c11\u306a\u3044\u30b5\u30f3\u30d7\u30eb\u3067\u3082\u5b9f\u8cea\u7684\u306a\u60c5\u5831\u91cf\u304c\u591a\u3044\u3002\u8d64\u306f\u81ea\u5df1\u76f8\u95a2\u304c\u9577\u304f\u6b8b\u308a\u3001\u540c\u3058\u30b5\u30f3\u30d7\u30eb\u6570\u3067\u3082\u5b9f\u8cea\u7684\u306a\u60c5\u5831\u91cf\uff08ESS\uff09\u304c\u5c11\u306a\u3044\u3002<\/p>\n\n\n\n<p>\u306a\u304a\u8fd1\u5e74\u3067\u306f\u3001\u4e8b\u5f8c\u5206\u5e03\u306e\u4e2d\u5fc3\u4ed8\u8fd1\u3060\u3051\u3067\u306a\u304f\u3001\u88fe\uff08\u5206\u4f4d\u70b9\uff09\u306e\u63a8\u5b9a\u7cbe\u5ea6\u3082\u5225\u306b\u78ba\u8a8d\u3059\u308b\u305f\u3081\u3001<strong>bulk-ESS<\/strong>\uff08\u5206\u5e03\u306e\u4e2d\u5fc3\u4ed8\u8fd1\u306e\u63a8\u5b9a\u306b\u95a2\u3059\u308bESS\uff09\u3068<strong>tail-ESS<\/strong>\uff08\u5206\u5e03\u306e\u7aef\u306e\u63a8\u5b9a\u306b\u95a2\u3059\u308bESS\uff09\u3092\u5206\u3051\u3066\u5831\u544a\u3059\u308b\u3053\u3068\u304c\u63a8\u5968\u3055\u308c\u3066\u3044\u308b\u3002\u76ee\u5b89\u3068\u3057\u3066\u3001Vehtari et al.\uff082021\uff09\u306f\u3001\u9806\u4f4d\u6b63\u898f\u5316\u3057\u305fESS\u304c400\u3092\u8d85\u3048\u308b\u3053\u3068\u3092\u63a8\u5968\u3057\u3066\u3044\u308b\uff08\u5b89\u5b9a\u3057\u305fMCSE\u306e\u63a8\u5b9a\u306b\u901a\u5e38\u5341\u5206\u306a\u5024\u3068\u3057\u3066\u3001\u7d4c\u9a13\u3068\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u304b\u3089\u9078\u3093\u3060\u6570\u5b57\u3060\u3068\u8aac\u660e\u3055\u308c\u3066\u3044\u308b\uff09\u3002tail-ESS\u306b\u3064\u3044\u3066\u3082\u3001\u540c\u3058400\u304c\u63a8\u5968\u6c34\u6e96\u3068\u3057\u3066\u793a\u3055\u308c\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6a19\u6e96\u8aa4\u5dee\uff08MCSE\uff09<\/strong><\/h2>\n\n\n\n<p>\u4e8b\u5f8c\u5206\u5e03\u306e\u5e73\u5747\u3092\u63a8\u5b9a\u3059\u308b\u3068\u304d\u3001\u79c1\u305f\u3061\u304c\u5b9f\u969b\u306b\u4f7f\u3048\u308b\u306e\u306f\u6709\u9650\u500b\u306eMCMC\u30b5\u30f3\u30d7\u30eb\u304b\u3089\u8a08\u7b97\u3057\u305f\u6a19\u672c\u5e73\u5747\u3067\u3042\u308b\u3002\u3053\u306e\u6a19\u672c\u5e73\u5747\u306b\u306f\u3001\u6709\u9650\u30b5\u30f3\u30d7\u30eb\u3067\u3042\u308b\u3053\u3068\u306b\u8d77\u56e0\u3059\u308b\u8aa4\u5dee\u304c\u4e57\u308b\u3002\u3053\u306e\u8aa4\u5dee\u306e\u5927\u304d\u3055\u3092\u8868\u3059\u306e\u304c<strong>\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6a19\u6e96\u8aa4\u5dee\uff08Monte Carlo Standard Error, MCSE\uff09<\/strong>\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"has-text-align-center\">$\\mathrm{MCSE} = {\\mathrm{SD}(\\theta\\mid y) \\over \\sqrt{\\mathrm{ESS}}}$<\/p>\n\n\n\n<p>ESS\u304c\u5927\u304d\u3044\u307b\u3069MCSE\u306f\u5c0f\u3055\u304f\u306a\u308a\u3001\u5831\u544a\u3059\u308b\u63a8\u5b9a\u5024\uff08\u4e8b\u5f8c\u5e73\u5747\u306a\u3069\uff09\u306e\u6841\u6570\u3092\u3069\u3053\u307e\u3067\u4fe1\u3058\u3066\u3088\u3044\u304b\u306e\u76ee\u5b89\u306b\u306a\u308b\u3002\u300c\u5c0f\u6570\u70b9\u4ee5\u4e0b2\u6841\u307e\u3067\u5831\u544a\u3057\u3066\u3044\u308b\u304c\u3001MCSE\u3092\u8a08\u7b97\u3059\u308b\u3068\u305d\u306e\u6841\u306f\u8aa4\u5dee\u306b\u57cb\u3082\u308c\u3066\u3044\u308b\u300d\u3068\u3044\u3063\u305f\u3053\u3068\u306f\u5b9f\u52d9\u3067\u3082\u3088\u304f\u8d77\u304d\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u30c0\u30a4\u30d0\u30fc\u30b8\u30a7\u30f3\u30b9\uff08HMC\u30fbNUTS\u7279\u6709\u306e\u8a3a\u65ad\uff09<\/strong><\/h2>\n\n\n\n<p>Stan\u3084PyMC\u306a\u3069\u3067\u4f7f\u308f\u308c\u308b\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\uff08HMC\uff09\u3084NUTS\u3068\u3044\u3046\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u306f\u3001\u4ed6\u306b\u306f\u306a\u3044\u5c02\u7528\u306e\u8a3a\u65ad\u6307\u6a19\u304c\u3042\u308b\u3002\u305d\u308c\u304c<strong>\u30c0\u30a4\u30d0\u30fc\u30b8\u30a7\u30f3\u30b9\uff08divergent transitions\uff09<\/strong>\u3067\u3042\u308b\u3002\u4e8b\u5f8c\u5206\u5e03\u306e\u4e2d\u306b\u6975\u7aef\u306b\u66f2\u7387\u306e\u9ad8\u3044\u9818\u57df\uff08\u6025\u306b\u72ed\u304f\u306a\u308b\u8c37\u306a\u3069\uff09\u304c\u3042\u308b\u3068\u3001\u6570\u5024\u7a4d\u5206\u304c\u305d\u306e\u9818\u57df\u3092\u3046\u307e\u304f\u518d\u73fe\u3067\u304d\u305a\u3001\u8b66\u544a\u3068\u3057\u3066\u8a18\u9332\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<p>$\\widehat{R}$\u3084ESS\u304c\u826f\u597d\u3067\u3082\u3001\u30c0\u30a4\u30d0\u30fc\u30b8\u30a7\u30f3\u30b9\u304c\u591a\u6570\u5831\u544a\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u306f\u8981\u6ce8\u610f\u3067\u3042\u308b\u3002\u4e8b\u5f8c\u5206\u5e03\u306e\u7279\u5b9a\u306e\u9818\u57df\u304c\u6b63\u3057\u304f\u63a2\u7d22\u3067\u304d\u3066\u3044\u306a\u3044\u53ef\u80fd\u6027\u304c\u3042\u308a\u3001\u30e2\u30c7\u30eb\u306e\u518d\u30d1\u30e9\u30e1\u30fc\u30bf\u5316\uff08\u4f8b\u3048\u3070\u968e\u5c64\u30e2\u30c7\u30eb\u306e\u975e\u4e2d\u5fc3\u5316\u30d1\u30e9\u30e1\u30fc\u30bf\u5316\uff09\u306a\u3069\u306e\u5bfe\u51e6\u304c\u5fc5\u8981\u306b\u306a\u308b\u3053\u3068\u304c\u591a\u3044\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u5b9f\u52d9\u3067\u306e\u30c1\u30a7\u30c3\u30af\u30ea\u30b9\u30c8<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u6307\u6a19<\/th><th>\u898b\u308b\u30dd\u30a4\u30f3\u30c8<\/th><th>\u76ee\u5b89<\/th><\/tr><\/thead><tbody><tr><td>\u30c8\u30ec\u30fc\u30b9\u30d7\u30ed\u30c3\u30c8<\/td><td>\u8907\u6570\u30c1\u30a7\u30fc\u30f3\u304c\u540c\u3058\u7bc4\u56f2\u3092\u7d20\u65e9\u304f\u5f80\u5fa9\u3057\u3066\u3044\u308b\u304b<\/td><td>\u76ee\u8996\u3067\u300c\u6bdb\u866b\u300d\u72b6\u306b\u306a\u3063\u3066\u3044\u308b\u304b<\/td><\/tr><tr><td>$\\widehat{R}$<\/td><td>\u30c1\u30a7\u30fc\u30f3\u9593\u30fb\u30c1\u30a7\u30fc\u30f3\u5185\u306e\u3070\u3089\u3064\u304d\u304c\u540c\u7a0b\u5ea6\u304b<\/td><td>1.01\u672a\u6e80<\/td><\/tr><tr><td>ESS\uff08bulk \/ tail\uff09<\/td><td>\u81ea\u5df1\u76f8\u95a2\u3092\u8003\u616e\u3057\u305f\u5b9f\u8cea\u7684\u306a\u30b5\u30f3\u30d7\u30eb\u6570<\/td><td>\u305d\u308c\u305e\u308c400\u4ee5\u4e0a<\/td><\/tr><tr><td>MCSE<\/td><td>\u63a8\u5b9a\u5024\u306e\u3069\u306e\u6841\u307e\u3067\u4fe1\u983c\u3067\u304d\u308b\u304b<\/td><td>\u5831\u544a\u3059\u308b\u6841\u6570\u3088\u308a\u5341\u5206\u5c0f\u3055\u3044\u304b<\/td><\/tr><tr><td>\u30c0\u30a4\u30d0\u30fc\u30b8\u30a7\u30f3\u30b9\uff08HMC\/NUTS\uff09<\/td><td>\u6570\u5024\u7a4d\u5206\u304c\u5931\u6557\u3057\u305f\u56de\u6570<\/td><td>0\u306b\u8fd1\u3044\u3053\u3068\u304c\u671b\u307e\u3057\u3044<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u307e\u3068\u3081<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>MCMC\u306f\u300c\u6b62\u3081\u305f\u6642\u70b9\u300d\u3068\u300c\u53ce\u675f\u3057\u305f\u6642\u70b9\u300d\u304c\u4e00\u81f4\u3059\u308b\u4fdd\u8a3c\u304c\u306a\u304f\u3001\u5c02\u7528\u306e\u8a3a\u65ad\u6307\u6a19\u3067\u78ba\u8a8d\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002<\/li>\n\n\n\n<li>\u30c8\u30ec\u30fc\u30b9\u30d7\u30ed\u30c3\u30c8\u306f\u6700\u3082\u57fa\u672c\u7684\u306a\u76ee\u8996\u8a3a\u65ad\u3067\u3001\u8907\u6570\u30c1\u30a7\u30fc\u30f3\u306e\u6df7\u5408\u5177\u5408\u3092\u78ba\u8a8d\u3059\u308b\u3002<\/li>\n\n\n\n<li>$\\widehat{R}$\u306f\u3001\u30c1\u30a7\u30fc\u30f3\u9593\u3068\u30c1\u30a7\u30fc\u30f3\u5185\u306e\u3070\u3089\u3064\u304d\u3092\u6bd4\u8f03\u3057\u3001\u8907\u6570\u30c1\u30a7\u30fc\u30f3\u304c\u540c\u3058\u5206\u5e03\u306b\u53ce\u675f\u3057\u3066\u3044\u308b\u304b\u3092\u6570\u5024\u5316\u3059\u308b\u3002<\/li>\n\n\n\n<li>ESS\u306f\u81ea\u5df1\u76f8\u95a2\u3092\u8003\u616e\u3057\u305f\u5b9f\u8cea\u7684\u306a\u30b5\u30f3\u30d7\u30eb\u6570\u3067\u3042\u308a\u3001MCSE\uff08\u63a8\u5b9a\u5024\u306e\u8aa4\u5dee\uff09\u306e\u8a08\u7b97\u306b\u3082\u4f7f\u308f\u308c\u308b\u3002<\/li>\n\n\n\n<li>HMC\/NUTS\u7cfb\u306e\u30b5\u30f3\u30d7\u30e9\u30fc\u3067\u306f\u3001\u30c0\u30a4\u30d0\u30fc\u30b8\u30a7\u30f3\u30b9\u3068\u3044\u3046\u5c02\u7528\u306e\u8b66\u544a\u3082\u4f75\u305b\u3066\u78ba\u8a8d\u3059\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u53c2\u8003\u6587\u732e<\/strong><\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., &amp; B\u00fcrkner, P.-C. (2021). Rank-normalization, folding, and localization: An improved R\u0302 for assessing convergence of MCMC (with discussion).&nbsp;<em>Bayesian Analysis<\/em>, 16(2), 667\u2013718.&nbsp;<a href=\"https:\/\/doi.org\/10.1214\/20-BA1221\">https:\/\/doi.org\/10.1214\/20-BA1221<\/a><\/li>\n\n\n\n<li>Gelman, A., &amp; Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences.&nbsp;<em>Statistical Science<\/em>, 7(4), 457\u2013472.&nbsp;<a href=\"https:\/\/doi.org\/10.1214\/ss\/1177011136\">https:\/\/doi.org\/10.1214\/ss\/1177011136<\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u30a4\u30f3\u30c8\u30ed\u30c0\u30af\u30b7\u30e7\u30f3 MCMC\uff08\u30de\u30eb\u30b3\u30d5\u9023\u9396\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\uff09\u306f\u3001\u8907\u96d1\u306a\u78ba\u7387\u5206\u5e03\uff08\u591a\u304f\u306e\u5834\u5408\u306f\u30d9\u30a4\u30ba\u7d71\u8a08\u306e\u4e8b\u5f8c\u5206\u5e03\uff09\u304b\u3089\u76f4\u63a5\u30b5\u30f3\u30d7\u30eb\u3092\u751f\u6210\u3059\u308b\u305f\u3081\u306e\u624b\u6cd5\u3067\u3042\u308b\u3002\u56de\u5e30\u4fc2\u6570\u306e\u89e3\u6790\u89e3\u304c\u6c42\u307e\u3089\u306a\u3044\u3088\u3046\u306a\u30e2\u30c7\u30eb\u3067\u3082\u3001MCMC\u3092\u56de\u305b\u3070\u305d [&hellip;]<\/p>\n","protected":false},"author":77,"featured_media":10008,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"content-type":"","swell_btn_cv_data":"","footnotes":"","_wp_rev_ctl_limit":""},"categories":[1251],"tags":[39,419,35],"class_list":["post-10004","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-data-analysis","tag-39","tag-419","tag-35"],"_links":{"self":[{"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/posts\/10004","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/users\/77"}],"replies":[{"embeddable":true,"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/comments?post=10004"}],"version-history":[{"count":21,"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/posts\/10004\/revisions"}],"predecessor-version":[{"id":10028,"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/posts\/10004\/revisions\/10028"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/media\/10008"}],"wp:attachment":[{"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/media?parent=10004"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/categories?post=10004"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/tags?post=10004"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}