{"id":4220,"date":"2025-07-12T22:10:12","date_gmt":"2025-07-12T13:10:12","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/?p=4220"},"modified":"2025-07-12T22:10:14","modified_gmt":"2025-07-12T13:10:14","slug":"uncertainty-unveiled-connecting-bayes-theory-with-bayesian-statistics","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/uncertainty-unveiled-connecting-bayes-theory-with-bayesian-statistics\/","title":{"rendered":"\u30d9\u30a4\u30ba\u306e\u7406\u8ad6\u304b\u3089\u30d9\u30a4\u30ba\u7d71\u8a08\u3078\uff1a\u4e0d\u78ba\u5b9f\u6027\u3092\u6271\u3046\u5f37\u529b\u306a\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af"},"content":{"rendered":"\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u79c1\u305f\u3061\u304c\u751f\u304d\u308b\u4e16\u754c\u306f\u4e0d\u78ba\u5b9f\u6027\u306b\u6e80\u3061\u3066\u3044\u308b\u3002\u660e\u65e5\u306e\u5929\u6c17\u3001\u65b0\u3057\u3044\u6cbb\u7642\u6cd5\u306e\u52b9\u679c\u3001\u30de\u30fc\u30b1\u30c6\u30a3\u30f3\u30b0\u30ad\u30e3\u30f3\u30da\u30fc\u30f3\u306e\u6210\u529f\u7387\u306a\u3069\u3001\u672a\u6765\u306e\u51fa\u6765\u4e8b\u3092\u5b8c\u5168\u306b\u4e88\u6e2c\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3002\u3057\u304b\u3057\u3001\u3053\u306e\u4e0d\u78ba\u5b9f\u6027\u3092\u6570\u5b66\u7684\u306b\u6349\u3048\u3001\u5408\u7406\u7684\u306a\u610f\u601d\u6c7a\u5b9a\u3092\u652f\u63f4\u3059\u308b\u5f37\u529b\u306a\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af\u304c\u5b58\u5728\u3059\u308b\u3002\u305d\u308c\u304c\u300c\u30d9\u30a4\u30ba\u306e\u7406\u8ad6\u300d\u3067\u3042\u308a\u3001\u305d\u3053\u304b\u3089\u767a\u5c55\u3057\u305f\u300c\u30d9\u30a4\u30ba\u7d71\u8a08\u300d\u3067\u3042\u308b\u3002\u672c\u8a18\u4e8b\u3067\u306f\u3001\u30d9\u30a4\u30ba\u306e\u7406\u8ad6\u306e\u6838\u5fc3\u304b\u3089\u30d9\u30a4\u30ba\u7d71\u8a08\u3078\u306e\u3064\u306a\u304c\u308a\u3001\u305d\u306e\u5fdc\u7528\u4f8b\u3001\u305d\u3057\u3066\u7c21\u5358\u306aR\u30b3\u30fc\u30c9\u3067\u306e\u8a08\u7b97\u4f8b\u307e\u3067\u3092\u5206\u304b\u308a\u3084\u3059\u304f\u89e3\u8aac\u3059\u308b\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\">\u30d9\u30a4\u30ba\u7406\u8ad6<\/h2>\n\n\n\n<p>\u30d9\u30a4\u30ba\u7406\u8ad6\u306e\u6839\u5e79\u3092\u306a\u3059\u306e\u306f\u300118\u4e16\u7d00\u306e\u7267\u5e2b\u3067\u3042\u308a\u6570\u5b66\u8005\u3067\u3042\u3063\u305f\u30c8\u30fc\u30de\u30b9\u30fb\u30d9\u30a4\u30ba\u306b\u3088\u3063\u3066\u5b9a\u5f0f\u5316\u3055\u308c\u305f<strong>\u30d9\u30a4\u30ba\u306e\u5b9a\u7406<\/strong>\u3067\u3042\u308b\u3002\u30d9\u30a4\u30ba\u306e\u5b9a\u7406\u306f\u3001<strong>\u65b0\u3057\u3044\u60c5\u5831\uff08\u30c7\u30fc\u30bf\uff09\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u306b\u3001\u3042\u308b\u4eee\u8aac\uff08\u307e\u305f\u306f\u4e8b\u8c61\uff09\u306e\u78ba\u7387\uff08\u4fe1\u5ff5\uff09\u3092\u3069\u306e\u3088\u3046\u306b\u66f4\u65b0\u3059\u3079\u304d\u304b<\/strong>\u3092\u793a\u3059\u3082\u306e\u3060\u3002<\/p>\n\n\n\n<p>$$ P(H\u2223E)=\\frac{P(E\u2223H)P(H)}{P(E)}\u200b $$<\/p>\n\n\n\n<p>\u3053\u306e\u5f0f\u3092\u69cb\u6210\u3059\u308b\u5404\u8981\u7d20\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3060\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>P(H\u2223E): <strong>\u4e8b\u5f8c\u78ba\u7387\uff08Posterior Probability\uff09<\/strong>\u3002\u4e8b\u8c61 E \u304c\u8d77\u304d\u305f\u5f8c\u3067\u306e\u4eee\u8aac H \u306e\u78ba\u7387\u3002\u79c1\u305f\u3061\u304c\u77e5\u308a\u305f\u3044\u300c\u66f4\u65b0\u3055\u308c\u305f\u4fe1\u5ff5\u300d\u3067\u3042\u308b\u3002<\/li>\n\n\n\n<li>P(E\u2223H): <strong>\u5c24\u5ea6\uff08Likelihood\uff09<\/strong>\u3002\u4eee\u8aac H \u304c\u771f\u3067\u3042\u308b\u3068\u3044\u3046\u6761\u4ef6\u4e0b\u3067\u3001\u4e8b\u8c61 E \u304c\u89b3\u5bdf\u3055\u308c\u308b\u78ba\u7387\u3002<\/li>\n\n\n\n<li>P(H): <strong>\u4e8b\u524d\u78ba\u7387\uff08Prior Probability\uff09<\/strong>\u3002\u4e8b\u8c61 E \u304c\u89b3\u5bdf\u3055\u308c\u308b\u524d\u306e\u4eee\u8aac H \u306e\u78ba\u7387\u3002\u3053\u308c\u306f\u79c1\u305f\u3061\u306e\u521d\u671f\u306e\u4fe1\u5ff5\u3084\u65e2\u5b58\u306e\u77e5\u8b58\u3092\u8868\u3059\u3002<\/li>\n\n\n\n<li>P(E): <strong>\u5468\u8fba\u5c24\u5ea6\uff08Marginal Likelihood\uff09<\/strong>\u3002\u4e8b\u8c61 E \u304c\u89b3\u5bdf\u3055\u308c\u308b\u78ba\u7387\u3002\u3053\u308c\u306f\u901a\u5e38\u3001\u3059\u3079\u3066\u306e\u53ef\u80fd\u306a\u4eee\u8aac\u306b\u3064\u3044\u3066\u5c24\u5ea6\u3068\u4e8b\u524d\u78ba\u7387\u3092\u5408\u8a08\uff08\u307e\u305f\u306f\u7a4d\u5206\uff09\u3059\u308b\u3053\u3068\u3067\u8a08\u7b97\u3055\u308c\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u7c21\u5358\u306b\u8a00\u3048\u3070\u3001\u30d9\u30a4\u30ba\u306e\u5b9a\u7406\u306f\u300c<strong>\u30c7\u30fc\u30bf\u3092\u898b\u308b\u524d\u306b\u62b1\u3044\u3066\u3044\u305f\u4fe1\u5ff5\uff08\u4e8b\u524d\u78ba\u7387\uff09\u3092\u3001\u65b0\u3057\u3044\u30c7\u30fc\u30bf\uff08\u5c24\u5ea6\uff09\u306b\u57fa\u3065\u3044\u3066\u66f4\u65b0\u3057\u3001\u3088\u308a\u78ba\u304b\u3089\u3057\u3044\u4fe1\u5ff5\uff08\u4e8b\u5f8c\u78ba\u7387\uff09\u3092\u5f97\u308b<\/strong>\u300d\u305f\u3081\u306e\u30eb\u30fc\u30eb\u306a\u306e\u3060\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u30d9\u30a4\u30ba\u7d71\u8a08<\/h2>\n\n\n\n<p>\u30d9\u30a4\u30ba\u7d71\u8a08\u306f\u3001\u3053\u306e\u30d9\u30a4\u30ba\u306e\u5b9a\u7406\u3092\u7d71\u8a08\u7684\u63a8\u8ad6\u306b\u5fdc\u7528\u3057\u305f\u3082\u306e\u3060\u3002\u5f93\u6765\u306e\u983b\u5ea6\u8ad6\u7d71\u8a08\u304c\u3001\u30c7\u30fc\u30bf\u304c\u7121\u9650\u306b\u7e70\u308a\u8fd4\u3055\u308c\u308b\u4e2d\u3067\u300c\u771f\u306e\u5024\u300d\u304c\u5b58\u5728\u3059\u308b\u3068\u4eee\u5b9a\u3057\u3001\u305d\u306e\u5024\u304c\u300c\u6709\u610f\u300d\u3067\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u65ad\u3059\u308b\u306e\u306b\u5bfe\u3057\u3001\u30d9\u30a4\u30ba\u7d71\u8a08\u306f<strong>\u672a\u77e5\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\uff08\u4f8b\u3048\u3070\u3001\u3042\u308b\u30b0\u30eb\u30fc\u30d7\u306e\u5e73\u5747\u3084\u6bd4\u7387\u306a\u3069\uff09\u81ea\u4f53\u3092\u78ba\u7387\u5909\u6570\u3068\u3057\u3066\u6349\u3048\u308b<\/strong>\u3002<\/p>\n\n\n\n<p>\u30d9\u30a4\u30ba\u7d71\u8a08\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u30b9\u30c6\u30c3\u30d7\u3067\u63a8\u8ad6\u3092\u9032\u3081\u308b\u3002<\/p>\n\n\n\n<ul start=\"1\" class=\"wp-block-list\">\n<li><strong>\u4e8b\u524d\u5206\u5e03\u306e\u8a2d\u5b9a<\/strong>: \u5206\u6790\u8005\u304c\u30c7\u30fc\u30bf\u3092\u898b\u308b\u524d\u306b\u6301\u3063\u3066\u3044\u308b\u3001\u672a\u77e5\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306b\u95a2\u3059\u308b\u77e5\u8b58\u3084\u4fe1\u5ff5\u3092\u78ba\u7387\u5206\u5e03\u3068\u3057\u3066\u8868\u73fe\u3059\u308b\u3002\u3053\u308c\u304c<mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-swl-deep-01-color\">\u4e8b\u524d\u5206\u5e03\uff08Prior Distribution\uff09<\/mark>\u3060\u3002<\/li>\n\n\n\n<li><strong>\u5c24\u5ea6\u306e\u5b9a\u7fa9<\/strong>: \u30c7\u30fc\u30bf\u3092\u751f\u6210\u3059\u308b\u78ba\u7387\u30e2\u30c7\u30eb\uff08\u4f8b\u3048\u3070\u3001\u6b63\u898f\u5206\u5e03\u3084\u4e8c\u9805\u5206\u5e03\u306a\u3069\uff09\u3092\u4eee\u5b9a\u3057\u3001\u672a\u77e5\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306e\u7279\u5b9a\u306e\u5024\u306e\u3082\u3068\u3067\u305d\u306e\u30c7\u30fc\u30bf\u304c\u89b3\u5bdf\u3055\u308c\u308b\u78ba\u7387\uff08<strong>\u5c24\u5ea6\u95a2\u6570<\/strong>\uff09\u3092\u5b9a\u7fa9\u3059\u308b\u3002<\/li>\n\n\n\n<li><strong>\u4e8b\u5f8c\u5206\u5e03\u306e\u8a08\u7b97<\/strong>: \u30d9\u30a4\u30ba\u306e\u5b9a\u7406\u3092\u7528\u3044\u3066\u3001\u4e8b\u524d\u5206\u5e03\u3068\u5c24\u5ea6\u95a2\u6570\u3092\u7d50\u5408\u3057\u3001\u65b0\u3057\u3044\u30c7\u30fc\u30bf\u304c\u4e0e\u3048\u3089\u308c\u305f\u5f8c\u306e\u672a\u77e5\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306b\u95a2\u3059\u308b\u4fe1\u5ff5\u3092\u66f4\u65b0\u3059\u308b\u3002\u3053\u308c\u304c<mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-swl-deep-01-color\">\u4e8b\u5f8c\u5206\u5e03\uff08Posterior Distribution\uff09<\/mark>\u3067\u3042\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u5f97\u3089\u308c\u305f\u4e8b\u5f8c\u5206\u5e03\u306f\u3001\u672a\u77e5\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306b\u95a2\u3059\u308b\u79c1\u305f\u3061\u306e\u6700\u65b0\u304b\u3064\u6700\u3082\u5305\u62ec\u7684\u306a\u60c5\u5831\u6e90\u3068\u306a\u308b\u3002\u3053\u306e\u5206\u5e03\u304b\u3089\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306e\u6700\u3082\u78ba\u304b\u3089\u3057\u3044\u5024\uff08\u4e8b\u5f8c\u5e73\u5747\u3084\u4e8b\u5f8c\u4e2d\u592e\u5024\uff09\u3001\u4fe1\u983c\u533a\u9593\u306b\u76f8\u5f53\u3059\u308b<mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-swl-deep-01-color\">\u4fe1\u7528\u533a\u9593\uff08Credible Interval\uff09<\/mark>\u306a\u3069\u3092\u5c0e\u304d\u51fa\u3057\u3001\u610f\u601d\u6c7a\u5b9a\u306b\u5f79\u7acb\u3066\u308b\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div id=\"biost-3542712436\" 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\">\u7406\u8ad6\u304b\u3089\u7d71\u8a08\u3078\u306e\u3064\u306a\u304c\u308a<\/h2>\n\n\n\n<p>\u30d9\u30a4\u30ba\u7406\u8ad6\u304c\u300c\u4fe1\u5ff5\u3092\u66f4\u65b0\u3059\u308b\u305f\u3081\u306e\u4e00\u822c\u7684\u306a\u6570\u5b66\u7684\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af\u300d\u3067\u3042\u308b\u306e\u306b\u5bfe\u3057\u3001\u30d9\u30a4\u30ba\u7d71\u8a08\u306f\u300c<strong>\u305d\u306e\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af\u3092\u7d71\u8a08\u7684\u63a8\u8ad6\u3001\u3064\u307e\u308a\u30c7\u30fc\u30bf\u304b\u3089\u672a\u77e5\u306e\u4e8b\u67c4\u3092\u63a8\u6e2c\u3059\u308b\u30d7\u30ed\u30bb\u30b9\u306b\u5fdc\u7528\u3057\u305f\u3082\u306e<\/strong>\u300d\u3068\u8a00\u3048\u308b\u3002<\/p>\n\n\n\n<p>\u5177\u4f53\u7684\u306b\u306f\u3001\u30d9\u30a4\u30ba\u306e\u5b9a\u7406\u306eH\u3092\u300c<strong>\u672a\u77e5\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306e\u5024<\/strong>\u300d\u3068\u307f\u306a\u3057\u3001E\u3092\u300c<strong>\u89b3\u6e2c\u3055\u308c\u305f\u30c7\u30fc\u30bf<\/strong>\u300d\u3068\u307f\u306a\u3059\u3053\u3068\u3067\u3001\u30d9\u30a4\u30ba\u7d71\u8a08\u304c\u69cb\u7bc9\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>P(H): \u672a\u77e5\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306b\u95a2\u3059\u308b<strong>\u4e8b\u524d\u5206\u5e03<\/strong><\/li>\n\n\n\n<li>P(E\u2223H): \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306e\u5024\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u306b\u30c7\u30fc\u30bf\u304c\u89b3\u5bdf\u3055\u308c\u308b<strong>\u5c24\u5ea6\u95a2\u6570<\/strong><\/li>\n\n\n\n<li>P(H\u2223E): \u30c7\u30fc\u30bf\u304c\u89b3\u5bdf\u3055\u308c\u305f\u5f8c\u306e\u672a\u77e5\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306b\u95a2\u3059\u308b<strong>\u4e8b\u5f8c\u5206\u5e03<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\u3053\u306e\u3088\u3046\u306b\u3001\u30d9\u30a4\u30ba\u306e\u5b9a\u7406\u3068\u3044\u3046<strong>\u7406\u8ad6\u7684\u306a\u67f1<\/strong>\u3092\u57fa\u76e4\u3068\u3057\u3066\u3001\u30c7\u30fc\u30bf\u304b\u3089\u5b66\u7fd2\u3057\u3001\u4e0d\u78ba\u5b9f\u6027\u3092\u5b9a\u91cf\u5316\u3057\u3001\u4fe1\u5ff5\u3092\u66f4\u65b0\u3059\u308b\u3068\u3044\u3046<strong>\u7d71\u8a08\u7684\u306a\u5b9f\u8df5<\/strong>\u304c\u53ef\u80fd\u306b\u306a\u308b\u306e\u3060\u3002\u983b\u5ea6\u8ad6\u7d71\u8a08\u304c\u300c\u4eee\u8aac\u691c\u5b9a\u300d\u3092\u901a\u3058\u3066\u7d50\u8ad6\u3092\u51fa\u3059\u306e\u306b\u5bfe\u3057\u3001\u30d9\u30a4\u30ba\u7d71\u8a08\u306f\u300c<strong>\u78ba\u7387\u5206\u5e03\u3068\u3057\u3066\u4e0d\u78ba\u5b9f\u6027\u3092\u8868\u73fe\u3057\u3001\u610f\u601d\u6c7a\u5b9a\u306e\u6750\u6599\u3068\u3059\u308b<\/strong>\u300d\u3068\u3044\u3046\u70b9\u3067\u7570\u306a\u308b\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u30d9\u30a4\u30ba\u7d71\u8a08\u306e\u4f7f\u3044\u6240<\/h2>\n\n\n\n<p>\u30d9\u30a4\u30ba\u7d71\u8a08\u306f\u3001\u7279\u306b\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u5834\u9762\u3067\u305d\u306e\u771f\u4fa1\u3092\u767a\u63ee\u3059\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u30c7\u30fc\u30bf\u304c\u5c11\u306a\u3044\u5834\u5408<\/strong>: \u983b\u5ea6\u8ad6\u7d71\u8a08\u3067\u306f\u5341\u5206\u306a\u30c7\u30fc\u30bf\u304c\u306a\u3044\u3068\u5b89\u5b9a\u3057\u305f\u7d50\u679c\u304c\u5f97\u3089\u308c\u306b\u304f\u3044\u304c\u3001\u30d9\u30a4\u30ba\u7d71\u8a08\u306f\u4e8b\u524d\u60c5\u5831\u3092\u6d3b\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u5c11\u306a\u3044\u30c7\u30fc\u30bf\u304b\u3089\u3067\u3082\u5408\u7406\u7684\u306a\u63a8\u8ad6\u304c\u53ef\u80fd\u3060\u3002<\/li>\n\n\n\n<li><strong>\u4e8b\u524d\u60c5\u5831\u304c\u5b58\u5728\u3059\u308b\u5834\u5408<\/strong>: \u904e\u53bb\u306e\u7814\u7a76\u7d50\u679c\u3001\u5c02\u9580\u5bb6\u306e\u610f\u898b\u3001\u5e38\u8b58\u306a\u3069\u3001\u4f55\u3089\u304b\u306e\u4e8b\u524d\u77e5\u8b58\u304c\u3042\u308b\u5834\u5408\u306b\u3001\u305d\u308c\u3092\u5206\u6790\u306b\u7d44\u307f\u8fbc\u3080\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/li>\n\n\n\n<li><strong>\u4e0d\u78ba\u5b9f\u6027\u3092\u660e\u793a\u7684\u306b\u6271\u3044\u305f\u3044\u5834\u5408<\/strong>: \u63a8\u5b9a\u5024\u306e\u70b9\u63a8\u5b9a\u3060\u3051\u3067\u306a\u304f\u3001\u305d\u306e\u5024\u304c\u53d6\u308a\u3046\u308b\u7bc4\u56f2\uff08\u4fe1\u7528\u533a\u9593\uff09\u3084\u78ba\u7387\u5206\u5e03\u5168\u4f53\u3092\u77e5\u308a\u305f\u3044\u5834\u5408\u306b\u6709\u52b9\u3060\u3002<\/li>\n\n\n\n<li><strong>\u610f\u601d\u6c7a\u5b9a\u652f\u63f4<\/strong>: \u63a8\u5b9a\u7d50\u679c\u3092\u78ba\u7387\u7684\u306a\u8a00\u8449\u3067\u8868\u73fe\u3067\u304d\u308b\u305f\u3081\u3001\u30ea\u30b9\u30af\u3092\u8003\u616e\u3057\u305f\u610f\u601d\u6c7a\u5b9a\u306b\u5f79\u7acb\u3064\u3002<\/li>\n\n\n\n<li><strong>\u8907\u96d1\u306a\u968e\u5c64\u69cb\u9020\u3092\u6301\u3064\u30c7\u30fc\u30bf<\/strong>: \u533b\u7642\u30c7\u30fc\u30bf\u3084\u6559\u80b2\u30c7\u30fc\u30bf\u306a\u3069\u3001\u500b\u4f53\u3001\u30b0\u30eb\u30fc\u30d7\u3001\u5730\u57df\u3068\u3044\u3063\u305f\u968e\u5c64\u69cb\u9020\u3092\u6301\u3064\u30c7\u30fc\u30bf\u306b\u5bfe\u3057\u3066\u3001<strong>\u968e\u5c64\u30d9\u30a4\u30ba\u30e2\u30c7\u30eb<\/strong>\u304c\u5f37\u529b\u306a\u30c4\u30fc\u30eb\u3068\u306a\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u5177\u4f53\u4f8b\u3068\u7c21\u5358\u306a R \u8a08\u7b97\u4f8b<\/h2>\n\n\n\n<p>\u3042\u308b\u65b0\u85ac\u304c\u7279\u5b9a\u306e\u75be\u60a3\u306b\u52b9\u679c\u304c\u3042\u308b\u304b\u3092\u78ba\u8a8d\u3059\u308b\u81e8\u5e8a\u8a66\u9a13\u3092\u8003\u3048\u3066\u307f\u3088\u3046\u3002\u3053\u306e\u75be\u60a3\u306e\u6a19\u6e96\u6cbb\u7642\u306b\u5bfe\u3059\u308b\u65b0\u85ac\u306e\u6709\u52b9\u6027\u3092\u8a55\u4fa1\u3057\u305f\u3044\u3068\u3059\u308b\u3002<\/p>\n\n\n\n<p><strong>\u30b7\u30ca\u30ea\u30aa<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u904e\u53bb\u306e\u7d4c\u9a13\u304b\u3089\u3001\u3053\u306e\u75be\u60a3\u306e\u6a19\u6e96\u6cbb\u7642\u3067\u306f<mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-swl-deep-01-color\">\u7d0420%<\/mark>\u306e\u60a3\u8005\u306b\u52b9\u679c\u304c\u3042\u308b\u3068\u77e5\u3089\u308c\u3066\u3044\u308b\u3002<\/li>\n\n\n\n<li>\u65b0\u85ac\u309210\u4eba\u306e\u60a3\u8005\u306b\u6295\u4e0e\u3057\u305f\u3068\u3053\u308d\u3001<strong>4\u4eba<\/strong>\u306b\u52b9\u679c\u304c\u898b\u3089\u308c\u305f\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u3053\u306e\u30c7\u30fc\u30bf\u304b\u3089\u3001\u65b0\u85ac\u306e\u6709\u52b9\u6027\uff08\u52b9\u679c\u304c\u3042\u308b\u78ba\u7387 p\uff09\u304c\u6a19\u6e96\u6cbb\u7642\u3088\u308a\u3082\u9ad8\u3044\u3068\u8a00\u3048\u308b\u3060\u308d\u3046\u304b\uff1f<\/p>\n\n\n\n<p>\u30d9\u30a4\u30ba\u7d71\u8a08\u3067\u306f\u3001\u3053\u306e<strong>\u52b9\u679c\u304c\u3042\u308b\u78ba\u7387 p \u3092\u78ba\u7387\u5909\u6570\u3068\u3057\u3066\u6271\u3046<\/strong>\u3002<\/p>\n\n\n\n<ul start=\"1\" class=\"wp-block-list\">\n<li>\u4e8b\u524d\u5206\u5e03\u306e\u8a2d\u5b9a:\u65b0\u85ac\u306e\u52b9\u679c p \u306b\u3064\u3044\u3066\u3001\u30c7\u30fc\u30bf\u3092\u898b\u308b\u524d\u306e\u79c1\u305f\u3061\u306e\u4fe1\u5ff5\u3092\u8868\u3059\u5206\u5e03\u3092\u8a2d\u5b9a\u3059\u308b\u3002\u4eca\u56de\u306f\u3001\u904e\u53bb\u306e\u7d4c\u9a13\u304b\u3089\u300c\u6a19\u6e96\u6cbb\u7642\u3067\u306f20%\u300d\u3068\u3044\u3046\u60c5\u5831\u304c\u3042\u308b\u305f\u3081\u3001p\u304c0.2\u4ed8\u8fd1\u306b\u3042\u308b\u53ef\u80fd\u6027\u304c\u9ad8\u3044\u3068\u3044\u3046\u4e8b\u524d\u60c5\u5831\u3092\u53d6\u308a\u5165\u308c\u305f\u3044\u3068\u3059\u308b\u3002\u30d9\u30fc\u30bf\u5206\u5e03\u306f\u78ba\u7387\u306e\u4e8b\u524d\u5206\u5e03\u3068\u3057\u3066\u3088\u304f\u7528\u3044\u3089\u308c\u308b\u3002\u3053\u3053\u3067\u306f\u3001\u5e73\u5747\u304c0.2\u3068\u306a\u308b\u3088\u3046\u306a\u30d9\u30fc\u30bf\u5206\u5e03 $\\text{Beta}(\\alpha, \\beta) $ \u3092\u4eee\u5b9a\u3057\u3088\u3046\u3002\u4f8b\u3048\u3070\u3001$\\alpha=2, \\beta=8$ \u3068\u3059\u308b\u3068\u5e73\u5747\u306f $\\frac{\\alpha}{\\alpha+\\beta} = \\frac{2}{2+8}=0.2$ \u3068\u306a\u308b\u3002<\/li>\n\n\n\n<li>\u5c24\u5ea6\u95a2\u6570\u306e\u5b9a\u7fa9:10\u4eba\u4e2d4\u4eba\u304c\u52b9\u679c\u3092\u793a\u3057\u305f\u3068\u3044\u3046\u30c7\u30fc\u30bf\u306f\u3001\u4e8c\u9805\u5206\u5e03\u306b\u5f93\u3046\u3068\u8003\u3048\u3089\u308c\u308b\u3002$P(\\text{data}\u2223p)=\\text{Binomial}(10,4,p)$<\/li>\n\n\n\n<li>\u4e8b\u5f8c\u5206\u5e03\u306e\u8a08\u7b97:\u30d9\u30fc\u30bf\u5206\u5e03\u3068\u4e8c\u9805\u5206\u5e03\u306e\u7d44\u307f\u5408\u308f\u305b\u306f\u3001\u4e8b\u5f8c\u5206\u5e03\u3082\u30d9\u30fc\u30bf\u5206\u5e03\u306b\u306a\u308b\u3068\u3044\u3046\u4fbf\u5229\u306a\u6027\u8cea\uff08\u5171\u5f79\u4e8b\u524d\u5206\u5e03\uff09\u304c\u3042\u308b\u3002\u4e8b\u5f8c\u5206\u5e03\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306f\u3001$\\alpha_\\text{posterior}=\\alpha_\\text{prior}+\\text{\u6210\u529f\u6570}\u3001\\beta_\\text{posterior}=\\beta_\\text{prior}+\\text{\u5931\u6557\u6570} $\u3068\u306a\u308b\u3002\u4eca\u56de\u306e\u30b1\u30fc\u30b9\u3067\u306f\u3001\u6210\u529f\u6570=4\u3001\u5931\u6557\u6570=10-4=6 \u306a\u306e\u3067\u3001$\\alpha_\\text{posterior}=2+4=6, \\beta_\\text{posterior}=8+6=14$\u3057\u305f\u304c\u3063\u3066\u3001\u4e8b\u5f8c\u5206\u5e03\u306f $\\text{Beta}(6,14)$ \u3068\u306a\u308a\u3001\u305d\u306e\u5e73\u5747\u306f\u3001$6\/(6+14) = 6\/20 = 3\/10 = 0.3$ \u3068\u306a\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u7c21\u5358\u306aR\u8a08\u7b97\u4f8b<\/h3>\n\n\n\n<p>R\u3092\u4f7f\u3063\u3066\u3001\u3053\u308c\u3089\u306e\u5206\u5e03\u3092\u8996\u899a\u5316\u3057\u3001\u4e8b\u5f8c\u5206\u5e03\u304b\u3089\u63a8\u5b9a\u5024\u3092\u5f97\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n<p><strong>R \u30b9\u30af\u30ea\u30d7\u30c8\u4f8b\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u4e8b\u524d\u5206\u5e03\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\nalpha_prior &lt;- 2\nbeta_prior &lt;- 8\n\n# \u89b3\u6e2c\u30c7\u30fc\u30bf\nsuccesses &lt;- 4 # \u52b9\u679c\u304c\u3042\u3063\u305f\u60a3\u8005\u6570\ntrials &lt;- 10 # \u6295\u4e0e\u3057\u305f\u60a3\u8005\u6570\nfailures &lt;- trials - successes # \u52b9\u679c\u304c\u306a\u304b\u3063\u305f\u60a3\u8005\u6570\n\n# \u4e8b\u5f8c\u5206\u5e03\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\nalpha_posterior &lt;- alpha_prior + successes\nbeta_posterior &lt;- beta_prior + failures\n\n# p\u306e\u53d6\u308a\u3046\u308b\u7bc4\u56f2\np_values &lt;- seq(0, 1, length.out = 1000)\n\n# \u4e8b\u524d\u5206\u5e03\u306e\u78ba\u7387\u5bc6\u5ea6\nprior_density &lt;- dbeta(p_values, alpha_prior, beta_prior)\n\n# \u4e8b\u5f8c\u5206\u5e03\u306e\u78ba\u7387\u5bc6\u5ea6\nposterior_density &lt;- dbeta(p_values, alpha_posterior, beta_posterior)\n\n# \u30d7\u30ed\u30c3\u30c8\npar(mar = c(5, 5, 4, 2), cex.main = 1.5, cex.lab = 1.5, cex.axis = 1.5)\nplot(p_values, prior_density,\n    type = \"l\", col = \"blue\", lwd = 2,\n    main = \"\u4e8b\u524d\u5206\u5e03\u3068\u4e8b\u5f8c\u5206\u5e03\u306e\u6bd4\u8f03\",\n    xlab = \"\u65b0\u85ac\u306e\u52b9\u679c\u304c\u3042\u308b\u78ba\u7387 (p)\", ylab = \"\u78ba\u7387\u5bc6\u5ea6\",\n    ylim = c(0, max(prior_density, posterior_density) * 1.1)\n)\nlines(p_values, posterior_density, col = \"red\", lwd = 2)\nlegend(\"topright\", legend = c(\"Prior\", \"Posterior\"), col = c(\"blue\", \"red\"), lwd = 2, cex = 1.5)\n\n# \u4e8b\u5f8c\u5206\u5e03\u306e\u5e73\u5747\u306895%\u4fe1\u7528\u533a\u9593\nposterior_mean &lt;- alpha_posterior \/ (alpha_posterior + beta_posterior)\ncredible_interval &lt;- qbeta(c(0.025, 0.975), alpha_posterior, beta_posterior)\n\nprint(paste(\"\u4e8b\u5f8c\u5206\u5e03\u306e\u5e73\u5747:\", round(posterior_mean, 3)))\nprint(paste(\"95%\u4fe1\u7528\u533a\u9593:\", round(credible_interval&#91;1], 3), \"-\", round(credible_interval&#91;2], 3)))\n<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>\u5b9f\u884c\u7d50\u679c\uff1a<\/strong><\/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-4-683x1024.png\" alt=\"\" class=\"wp-image-4230\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/image-4-683x1024.png 683w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/image-4-200x300.png 200w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/image-4-768x1152.png 768w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/image-4.png 800w\" sizes=\"(max-width: 683px) 100vw, 683px\" \/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>> print(paste(\"\u4e8b\u5f8c\u5206\u5e03\u306e\u5e73\u5747:\", round(posterior_mean, 3)))\n&#91;1] \"\u4e8b\u5f8c\u5206\u5e03\u306e\u5e73\u5747: 0.3\"\n> print(paste(\"95%\u4fe1\u7528\u533a\u9593:\", round(credible_interval&#91;1], 3), \"-\", round(credible_interval&#91;2], 3)))\n&#91;1] \"95%\u4fe1\u7528\u533a\u9593: 0.126 - 0.512\"<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">\u7d50\u679c\u89e3\u91c8<\/h3>\n\n\n\n<p>\u4e0a\u8a18\u306eR\u30b3\u30fc\u30c9\u3092\u5b9f\u884c\u3059\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306a\u7d50\u679c\u304c\u5f97\u3089\u308c\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4e8b\u524d\u5206\u5e03\uff08\u9752\u7dda\uff09\u306f\u3001\u65b0\u85ac\u306e\u52b9\u679c\u304c20%\u3042\u305f\u308a\u306b\u4e2d\u5fc3\u304c\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u308b\u3002\u3053\u308c\u306f\u3001\u30c7\u30fc\u30bf\u3092\u898b\u308b\u524d\u306e\u79c1\u305f\u3061\u306e\u521d\u671f\u306e\u4fe1\u5ff5\u3060\u3002<\/li>\n\n\n\n<li>\u4e8b\u5f8c\u5206\u5e03\uff08\u8d64\u7dda\uff09\u306f\u3001\u30c7\u30fc\u30bf\uff0810\u4eba\u4e2d4\u4eba\u306b\u52b9\u679c\uff09\u3092\u8003\u616e\u3057\u305f\u5f8c\u306e\u65b0\u85ac\u306e\u52b9\u679c\u306e\u78ba\u7387\u5206\u5e03\u3067\u3042\u308b\u3002\u3053\u306e\u5206\u5e03\u306f\u4e8b\u524d\u5206\u5e03\u3088\u308a\u3082\u53f3\u306b\u30b7\u30d5\u30c8\u3057\u3001\u3088\u308a\u72ed\u304f\u306a\u3063\u3066\u3044\u308b\u306f\u305a\u3060\u3002\u3053\u308c\u306f\u3001\u65b0\u3057\u3044\u30c7\u30fc\u30bf\u306b\u3088\u3063\u3066\u300c\u52b9\u679c\u304c\u3042\u308b\u78ba\u7387 p\u300d\u306b\u95a2\u3059\u308b\u79c1\u305f\u3061\u306e\u4fe1\u5ff5\u304c\u66f4\u65b0\u3055\u308c\u3001\u4e0d\u78ba\u5b9f\u6027\u304c\u6e1b\u5c11\u3057\u305f\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3002<\/li>\n\n\n\n<li><strong>\u4e8b\u5f8c\u5206\u5e03\u306e\u5e73\u5747<\/strong>\u306f\u3001\u65b0\u85ac\u306e\u52b9\u679c\u306e\u6700\u3082\u78ba\u304b\u3089\u3057\u3044\u5024\u3092\u793a\u3059\u3002\u4e0a\u8a18\u306e\u4f8b\u3067\u306f\u30010.3\uff0830%\uff09\u306b\u306a\u308b\u3060\u308d\u3046\u3002<\/li>\n\n\n\n<li><strong>95%\u4fe1\u7528\u533a\u9593<\/strong>\u306f\u3001\u65b0\u85ac\u306e\u52b9\u679c\u306e\u771f\u306e\u5024\u304c95%\u306e\u78ba\u7387\u3067\u3053\u306e\u7bc4\u56f2\u5185\u306b\u3042\u308b\u3068\u79c1\u305f\u3061\u304c\u4fe1\u3058\u308b\u533a\u9593\u3067\u3042\u308b\u3002\u4f8b\u3048\u3070\u3001[0.126, 0.512] \u306e\u3088\u3046\u306a\u7d50\u679c\u304c\u5f97\u3089\u308c\u308c\u3070\u3001\u300c\u65b0\u85ac\u306e\u52b9\u679c\u304c\u3042\u308b\u78ba\u7387\u306f95%\u306e\u78ba\u7387\u306712.6%\u304b\u308951.2%\u306e\u9593\u306b\u3042\u308b\u300d\u3068\u89e3\u91c8\u3067\u304d\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u3053\u306e\u7d50\u679c\u304b\u3089\u3001\u300c\u65b0\u85ac\u306e\u52b9\u679c\u304c\u6a19\u6e96\u6cbb\u7642\u306e20%\u3088\u308a\u3082\u9ad8\u3044\u53ef\u80fd\u6027\u300d\u306b\u3064\u3044\u3066\u3001\u78ba\u7387\u7684\u306a\u8a55\u4fa1\u3092\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u4e8b\u5f8c\u5206\u5e03\u304c20%\u3088\u308a\u3082\u9ad8\u3044\u5024\u306b\u3069\u308c\u304f\u3089\u3044\u306e\u78ba\u7387\u3092\u5272\u308a\u5f53\u3066\u3066\u3044\u308b\u304b\u3092\u76f4\u63a5\u78ba\u8a8d\u3067\u304d\u308b\u306e\u304c\u3001\u30d9\u30a4\u30ba\u7d71\u8a08\u306e\u5f37\u529b\u306a\u70b9\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u307e\u3068\u3081<\/h2>\n\n\n\n<p>\u30d9\u30a4\u30ba\u306e\u7406\u8ad6\u306f\u3001<strong>\u65b0\u3057\u3044\u60c5\u5831\u306b\u57fa\u3065\u3044\u3066\u4fe1\u5ff5\u3092\u5408\u7406\u7684\u306b\u66f4\u65b0\u3059\u308b\u305f\u3081\u306e\u6570\u5b66\u7684\u306a\u6307\u91dd<\/strong>\u3092\u63d0\u4f9b\u3059\u308b\u3002\u305d\u3057\u3066\u3001\u30d9\u30a4\u30ba\u7d71\u8a08\u306f\u3001\u3053\u306e\u7406\u8ad6\u3092<strong>\u30c7\u30fc\u30bf\u304b\u3089\u672a\u77e5\u306e\u4e8b\u67c4\u3092\u63a8\u8ad6\u3059\u308b<\/strong>\u3068\u3044\u3046\u7d71\u8a08\u7684\u306a\u554f\u984c\u306b\u5fdc\u7528\u3057\u305f\u3082\u306e\u3060\u3002\u4e8b\u524d\u60c5\u5831\u3092\u6d3b\u7528\u3057\u3001\u4e0d\u78ba\u5b9f\u6027\u3092\u78ba\u7387\u5206\u5e03\u3068\u3057\u3066\u660e\u793a\u7684\u306b\u8868\u73fe\u3067\u304d\u308b\u30d9\u30a4\u30ba\u7d71\u8a08\u306f\u3001\u30c7\u30fc\u30bf\u304c\u5c11\u306a\u3044\u72b6\u6cc1\u3084\u8907\u96d1\u306a\u554f\u984c\u3092\u6271\u3046\u969b\u306b\u7279\u306b\u5f37\u529b\u306a\u30c4\u30fc\u30eb\u3068\u306a\u308b\u3002<\/p>\n\n\n\n<p>\u5f93\u6765\u306e\u7d71\u8a08\u5b66\u3068\u306f\u7570\u306a\u308b\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u63d0\u4f9b\u3059\u308b\u3053\u3068\u3067\u3001\u30d9\u30a4\u30ba\u7d71\u8a08\u306f\u79c1\u305f\u3061\u306e\u30c7\u30fc\u30bf\u5206\u6790\u3068\u610f\u601d\u6c7a\u5b9a\u306e\u65b9\u6cd5\u306b\u65b0\u305f\u306a\u8996\u70b9\u3092\u3082\u305f\u3089\u3057\u3066\u3044\u308b\u3002\u4e0d\u78ba\u5b9f\u306a\u4e16\u754c\u3067\u3088\u308a\u826f\u3044\u610f\u601d\u6c7a\u5b9a\u3092\u884c\u3046\u305f\u3081\u306b\u3001\u30d9\u30a4\u30ba\u7d71\u8a08\u306f\u4eca\u5f8c\u307e\u3059\u307e\u3059\u91cd\u8981\u306a\u5f79\u5272\u3092\u62c5\u3063\u3066\u3044\u304f\u3053\u3068\u3060\u308d\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u79c1\u305f\u3061\u304c\u751f\u304d\u308b\u4e16\u754c\u306f\u4e0d\u78ba\u5b9f\u6027\u306b\u6e80\u3061\u3066\u3044\u308b\u3002\u660e\u65e5\u306e\u5929\u6c17\u3001\u65b0\u3057\u3044\u6cbb\u7642\u6cd5\u306e\u52b9\u679c\u3001\u30de\u30fc\u30b1\u30c6\u30a3\u30f3\u30b0\u30ad\u30e3\u30f3\u30da\u30fc\u30f3\u306e\u6210\u529f\u7387\u306a\u3069\u3001\u672a\u6765\u306e\u51fa\u6765\u4e8b\u3092\u5b8c\u5168\u306b\u4e88\u6e2c\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3002\u3057\u304b\u3057\u3001\u3053\u306e\u4e0d\u78ba\u5b9f\u6027\u3092\u6570\u5b66\u7684\u306b\u6349\u3048\u3001\u5408\u7406\u7684\u306a\u610f\u601d\u6c7a\u5b9a\u3092\u652f\u63f4\u3059\u308b [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":4230,"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":[45],"tags":[],"class_list":["post-4220","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-45"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/image-4.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4220","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=4220"}],"version-history":[{"count":9,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4220\/revisions"}],"predecessor-version":[{"id":4232,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4220\/revisions\/4232"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media\/4230"}],"wp:attachment":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media?parent=4220"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/categories?post=4220"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/tags?post=4220"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}