{"id":488,"date":"2024-04-26T16:17:51","date_gmt":"2024-04-26T07:17:51","guid":{"rendered":"https:\/\/chocottopro.com\/?p=488"},"modified":"2024-04-26T16:17:51","modified_gmt":"2024-04-26T07:17:51","slug":"pymc3%e3%82%92%e4%bd%bf%e3%81%a3%e3%81%9f%e3%83%99%e3%82%a4%e3%82%ba%e6%8e%a8%e8%ab%96%e3%81%ae%e3%83%a1%e3%83%aa%e3%83%83%e3%83%88%e3%81%a8%e3%80%81%e5%85%b7%e4%bd%93%e7%9a%84%e3%81%aa%e6%b4%bb","status":"publish","type":"post","link":"https:\/\/chocottopro.com\/?p=488","title":{"rendered":"PyMC3\u3092\u4f7f\u3063\u305f\u30d9\u30a4\u30ba\u63a8\u8ad6\u306e\u30e1\u30ea\u30c3\u30c8\u3068\u3001\u5177\u4f53\u7684\u306a\u6d3b\u7528\u4e8b\u4f8b5\u9078"},"content":{"rendered":"\n<p>PyMC3\u306f\u3001Python\u3067\u30d9\u30a4\u30ba\u63a8\u8ad6\u3092\u5b9f\u8df5\u3059\u308b\u305f\u3081\u306e\u5f37\u529b\u306a\u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u3059\u3002\u672c\u8a18\u4e8b\u3067\u306f\u3001PyMC3\u3092\u4f7f\u3063\u305f\u30d9\u30a4\u30ba\u30e2\u30c7\u30ea\u30f3\u30b0\u306e\u57fa\u790e\u304b\u3089\u3001\u5b9f\u8df5\u7684\u306a\u6d3b\u7528\u4e8b\u4f8b\u307e\u3067\u3001\u5e45\u5e83\u304f\u89e3\u8aac\u3057\u307e\u3059\u3002\u521d\u5fc3\u8005\u304b\u3089\u4e0a\u7d1a\u8005\u307e\u3067\u3001PyMC3\u3067\u30d9\u30a4\u30ba\u63a8\u8ad6\u3092\u3082\u3063\u3068\u8eab\u8fd1\u306b\u611f\u3058\u3066\u3044\u305f\u3060\u304f\u305f\u3081\u306e\u60c5\u5831\u304c\u6e80\u8f09\u3067\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-sgb-block-simple sgb-box-simple sgb-box-simple--title-normal sgb-box-simple--with-border\"><div style=\"background-color:var(--wp--preset--color--sango-main);color:#FFF\" class=\"sgb-box-simple__title\">\u3053\u306e\u8a18\u4e8b\u3092\u8aad\u3093\u3060\u3089\u308f\u304b\u308b\u3053\u3068<\/div><div class=\"sgb-box-simple__body\" style=\"border-color:var(--wp--preset--color--sango-main);background-color:#FFF\">\n<ul class=\"wp-block-list\">\n<li>PyMC3\u306e\u57fa\u672c\u7684\u306a\u4f7f\u3044\u65b9\u3068\u3001\u30d9\u30a4\u30ba\u63a8\u8ad6\u306e\u6982\u8981<\/li>\n\n\n\n<li> \u30de\u30fc\u30b1\u30c6\u30a3\u30f3\u30b0\u3001\u91d1\u878d\u3001\u88fd\u9020\u696d\u306a\u3069\u69d8\u3005\u306a\u5206\u91ce\u3067\u306ePyMC3\u6d3b\u7528\u4e8b\u4f8b<\/li>\n\n\n\n<li> PyMC3\u3092\u4f7f\u3044\u3053\u306a\u3059\u305f\u3081\u306eTips\u3068\u3001\u30d9\u30a4\u30ba\u63a8\u8ad6\u306e\u5b66\u7fd2\u30ea\u30bd\u30fc\u30b9<\/li>\n\n\n\n<li> PyMC3\u3092\u5b66\u3076\u610f\u7fa9\u3068\u3001\u30c7\u30fc\u30bf\u30b5\u30a4\u30a8\u30f3\u30c6\u30a3\u30b9\u30c8\u3068\u3057\u3066\u306e\u30b9\u30ad\u30eb\u30a2\u30c3\u30d7<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"toc\"><br \/>\n<b>Warning<\/b>:  Undefined array key \"is_admin\" in <b>\/home\/c7479301\/public_html\/chocottopro.com\/wp-content\/themes\/sango-theme\/library\/gutenberg\/dist\/classes\/Toc.php<\/b> on line <b>116<\/b><br \/>\n<br \/>\n<b>Warning<\/b>:  Undefined array key \"is_category_top\" in <b>\/home\/c7479301\/public_html\/chocottopro.com\/wp-content\/themes\/sango-theme\/library\/gutenberg\/dist\/classes\/Toc.php<\/b> on line <b>121<\/b><br \/>\n<br \/>\n<b>Warning<\/b>:  Undefined array key \"is_top\" in <b>\/home\/c7479301\/public_html\/chocottopro.com\/wp-content\/themes\/sango-theme\/library\/gutenberg\/dist\/classes\/Toc.php<\/b> on line <b>128<\/b><br \/>\n    <div id=\"toc_container\" class=\"sgb-toc--bullets js-smooth-scroll\" data-dialog-title=\"Table of Contents\">\n      <p class=\"toc_title\">\u76ee\u6b21 <\/p>\n      <ul class=\"toc_list\">  <li class=\"first\">    <a href=\"#i-0\">PyMC3\u3068\u306f?\u78ba\u7387\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3067\u30d9\u30a4\u30ba\u63a8\u8ad6\u3092\u5b9f\u73fe\u3059\u308bPython\u30e9\u30a4\u30d6\u30e9\u30ea<\/a>    <ul class=\"menu_level_1\">      <li class=\"first\">        <a href=\"#i-1\">\u30d9\u30a4\u30ba\u63a8\u8ad6\u306e\u6982\u8981\u3068PyMC3\u3092\u4f7f\u3046\u30e1\u30ea\u30c3\u30c8<\/a>      <\/li>      <li class=\"last\">        <a href=\"#i-2\">PyMC3\u306e\u57fa\u672c\u7684\u306a\u4f7f\u3044\u65b9\u3068\u6587\u6cd5<\/a>      <\/li>    <\/ul>  <\/li>  <li>    <a href=\"#i-3\">PyMC3\u3092\u4f7f\u3063\u305f\u30d9\u30a4\u30ba\u63a8\u8ad6\u306e\u5177\u4f53\u7684\u306a\u6d3b\u7528\u4e8b\u4f8b<\/a>    <ul class=\"menu_level_1\">      <li class=\"first\">        <a href=\"#i-4\">\u6d3b\u7528\u4e8b\u4f8b1: \u30de\u30fc\u30b1\u30c6\u30a3\u30f3\u30b0\u306b\u304a\u3051\u308b\u9867\u5ba2\u30bb\u30b0\u30e1\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3<\/a>      <\/li>      <li>        <a href=\"#i-5\">\u6d3b\u7528\u4e8b\u4f8b2: \u91d1\u878d\u5de5\u5b66\u3067\u306e\u30ea\u30b9\u30af\u8a55\u4fa1\u30e2\u30c7\u30ea\u30f3\u30b0<\/a>      <\/li>      <li>        <a href=\"#i-6\">\u6d3b\u7528\u4e8b\u4f8b3: \u88fd\u9020\u696d\u3067\u306e\u54c1\u8cea\u7ba1\u7406\u3068\u7570\u5e38\u691c\u77e5<\/a>      <\/li>      <li>        <a href=\"#i-7\">\u6d3b\u7528\u4e8b\u4f8b4: \u533b\u7642\u30fb\u5275\u85ac\u5206\u91ce\u3067\u306e\u30d1\u30fc\u30bd\u30ca\u30e9\u30a4\u30ba\u30c9\u6cbb\u7642\u306e\u5b9f\u73fe<\/a>      <\/li>      <li class=\"last\">        <a href=\"#i-8\">\u6d3b\u7528\u4e8b\u4f8b5: \u74b0\u5883\u79d1\u5b66\u306b\u304a\u3051\u308b\u751f\u614b\u7cfb\u30e2\u30c7\u30ea\u30f3\u30b0\u3068\u4e88\u6e2c<\/a>      <\/li>    <\/ul>  <\/li>  <li class=\"last\">    <a href=\"#i-9\">\u307e\u3068\u3081 \u2013 PyMC3\u3067\u30d9\u30a4\u30ba\u63a8\u8ad6\u3092\u3082\u3063\u3068\u8eab\u8fd1\u306b<\/a>    <ul class=\"menu_level_1\">      <li class=\"first\">        <a href=\"#i-10\">PyMC3\u3092\u4f7f\u3044\u3053\u306a\u3059\u305f\u3081\u306eTips<\/a>      <\/li>      <li class=\"last\">        <a href=\"#i-11\">\u30d9\u30a4\u30ba\u63a8\u8ad6\u306e\u3055\u3089\u306a\u308b\u7406\u89e3\u3092\u6df1\u3081\u308b\u305f\u3081\u306e\u53c2\u8003\u8cc7\u6599<\/a>      <\/li>    <\/ul>  <\/li><\/ul>\n      \n    <\/div><\/div><h2 class=\"wp-block-heading\" id=\"i-0\">PyMC3\u3068\u306f?\u78ba\u7387\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3067\u30d9\u30a4\u30ba\u63a8\u8ad6\u3092\u5b9f\u73fe\u3059\u308bPython\u30e9\u30a4\u30d6\u30e9\u30ea<\/h2>\n\n\n\n<p>PyMC3\u306f\u3001Python\u3067Flexible\u306a\u30d9\u30a4\u30ba\u30e2\u30c7\u30ea\u30f3\u30b0\u3092\u5b9f\u73fe\u3059\u308b\u305f\u3081\u306e\u5f37\u529b\u306a\u30aa\u30fc\u30d7\u30f3\u30bd\u30fc\u30b9\u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u3059\u3002\u78ba\u7387\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306e\u8003\u3048\u65b9\u306b\u57fa\u3065\u3044\u3066\u304a\u308a\u3001\u8907\u96d1\u306a\u30e2\u30c7\u30eb\u306e\u69cb\u9020\u3092Python\u30b3\u30fc\u30c9\u3067\u660e\u793a\u7684\u306b\u8a18\u8ff0\u3067\u304d\u308b\u306e\u304c\u7279\u5fb4\u3067\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-1\">\u30d9\u30a4\u30ba\u63a8\u8ad6\u306e\u6982\u8981\u3068PyMC3\u3092\u4f7f\u3046\u30e1\u30ea\u30c3\u30c8<\/h3>\n\n\n\n<p>\u30d9\u30a4\u30ba\u63a8\u8ad6\u306f\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u4e8b\u524d\u5206\u5e03\u3068\u5c24\u5ea6\u95a2\u6570\u304b\u3089\u4e8b\u5f8c\u5206\u5e03\u3092\u5c0e\u51fa\u3059\u308b\u7d71\u8a08\u7684\u30a2\u30d7\u30ed\u30fc\u30c1\u3067\u3059\u3002\u4e8b\u524d\u5206\u5e03\u306f\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u306b\u95a2\u3059\u308b\u4e3b\u89b3\u7684\u306a\u4fe1\u5ff5\u3092\u78ba\u7387\u5206\u5e03\u3067\u8868\u73fe\u3057\u305f\u3082\u306e\u3067\u3001\u5c24\u5ea6\u95a2\u6570\u306f\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u306e\u30c7\u30fc\u30bf\u306e\u751f\u6210\u78ba\u7387\u3092\u8868\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u3092\u7d44\u307f\u5408\u308f\u305b\u308b\u3053\u3068\u3067\u3001\u30c7\u30fc\u30bf\u3092\u89b3\u6e2c\u3057\u305f\u5f8c\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u78ba\u7387\u5206\u5e03\u3067\u3042\u308b\u4e8b\u5f8c\u5206\u5e03\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30d9\u30a4\u30ba\u63a8\u8ad6\u306e\u5927\u304d\u306a\u5229\u70b9\u306f\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u4e0d\u78ba\u5b9f\u6027\u3092\u5b9a\u91cf\u7684\u306b\u8a55\u4fa1\u3067\u304d\u308b\u70b9\u3067\u3059\u3002\u307e\u305f\u3001\u5c11\u6570\u306e\u30c7\u30fc\u30bf\u304b\u3089\u3067\u3082\u63a8\u8ad6\u304c\u53ef\u80fd\u3067\u3001\u4e8b\u524d\u77e5\u8b58\u3092\u6d3b\u7528\u3057\u3066\u30e2\u30c7\u30ea\u30f3\u30b0\u3067\u304d\u308b\u305f\u3081\u3001\u8907\u96d1\u306a\u554f\u984c\u306b\u67d4\u8edf\u306b\u5bfe\u5fdc\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>PyMC3\u306f\u3001\u3053\u306e\u3088\u3046\u306a\u30d9\u30a4\u30ba\u63a8\u8ad6\u306e\u8003\u3048\u65b9\u3092Python\u3067\u76f4\u611f\u7684\u306b\u5b9f\u88c5\u3067\u304d\u308b\u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u3059\u3002\u30e2\u30c7\u30eb\u306e\u69cb\u9020\u3092\u5ba3\u8a00\u7684\u306b\u8a18\u8ff0\u3067\u304d\u3001\u4e8b\u5f8c\u5206\u5e03\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3082\u7c21\u5358\u306b\u884c\u3048\u307e\u3059\u3002NumPy\u3084Theano\u306a\u3069\u306e\u884c\u5217\u8a08\u7b97\u30e9\u30a4\u30d6\u30e9\u30ea\u3068\u89aa\u548c\u6027\u304c\u9ad8\u304f\u3001\u5927\u898f\u6a21\u306a\u30e2\u30c7\u30eb\u306b\u3082\u30b9\u30b1\u30fc\u30eb\u3067\u304d\u308b\u306e\u304c\u7279\u9577\u3067\u3059\u3002<\/p>\n\n\n\n<p>Stan\u3084TensorFlow Probability\u306a\u3069\u4ed6\u306e\u30d9\u30a4\u30ba\u63a8\u8ad6\u30e9\u30a4\u30d6\u30e9\u30ea\u3068\u6bd4\u3079\u308b\u3068\u3001PyMC3\u306f\u3088\u308a\u30b7\u30f3\u30d7\u30eb\u3067\u67d4\u8edf\u306a\u30e2\u30c7\u30eb\u8a18\u8ff0\u304c\u53ef\u80fd\u3067\u3059\u3002Python\u3068\u306e\u89aa\u548c\u6027\u304c\u9ad8\u3044\u305f\u3081\u7fd2\u5f97\u304c\u5bb9\u6613\u3067\u3001\u8c4a\u5bcc\u306a\u30c9\u30ad\u30e5\u30e1\u30f3\u30c8\u3068\u30b3\u30df\u30e5\u30cb\u30c6\u30a3\u306e\u30b5\u30dd\u30fc\u30c8\u3082\u9b45\u529b\u306e\u4e00\u3064\u3068\u8a00\u3048\u308b\u3067\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-2\">PyMC3\u306e\u57fa\u672c\u7684\u306a\u4f7f\u3044\u65b9\u3068\u6587\u6cd5<\/h3>\n\n\n\n<p>PyMC3\u3092\u4f7f\u3063\u305f\u30d9\u30a4\u30ba\u30e2\u30c7\u30ea\u30f3\u30b0\u306e\u57fa\u672c\u7684\u306a\u30b9\u30c6\u30c3\u30d7\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u30e2\u30c7\u30eb\u306e\u5b9a\u7fa9<\/li>\n\n\n\n<li>\u4e8b\u524d\u5206\u5e03\u306e\u8a2d\u5b9a<\/li>\n\n\n\n<li>\u5c24\u5ea6\u95a2\u6570\u306e\u5b9a\u7fa9<\/li>\n\n\n\n<li>MCMC\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306e\u5b9f\u884c<\/li>\n\n\n\n<li>\u7d50\u679c\u306e\u53ef\u8996\u5316\u3068\u89e3\u91c8<\/li>\n<\/ol>\n\n\n\n<p>\u30e2\u30c7\u30eb\u306e\u5b9a\u7fa9\u306b\u306f<code>pm.Model()<\/code>\u3092\u4f7f\u3044\u3001\u4e8b\u524d\u5206\u5e03\u306e\u8a2d\u5b9a\u306b\u306f<code>pm.Normal()<\/code>\u306a\u3069\u306e\u78ba\u7387\u5206\u5e03\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3092\u7528\u3044\u307e\u3059\u3002\u5c24\u5ea6\u95a2\u6570\u3082\u540c\u69d8\u306b\u78ba\u7387\u5206\u5e03\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3067\u5b9a\u7fa9\u3057\u3001<code>pm.sample()<\/code>\u3067\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0b\u306f\u3001\u30b5\u30a4\u30b3\u30ed\u306e\u76ee\u306e\u89b3\u6e2c\u30c7\u30fc\u30bf\u304b\u3089\u3001\u30b5\u30a4\u30b3\u30ed\u306e\u771f\u306e\u78ba\u7387\u5206\u5e03\u3092\u63a8\u5b9a\u3059\u308b\u4f8b\u3067\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">import pymc3 as pm\nimport numpy as np\n\n# \u30c7\u30fc\u30bf\u306e\u6e96\u5099\nobserved_data = np.random.randint(1, 7, size=100)  # \u30b5\u30a4\u30b3\u30ed\u3092100\u56de\u632f\u3063\u305f\u7d50\u679c\u3092\u4eee\u5b9a\n\nwith pm.Model() as model:\n    # \u4e8b\u524d\u5206\u5e03\u306e\u8a2d\u5b9a\n    prior_mean = pm.Normal('prior_mean', mu=3.5, sd=2.5)\n    prior_std = pm.HalfNormal('prior_std', sd=2.5)\n\n    # \u5c24\u5ea6\u95a2\u6570\u306e\u5b9a\u7fa9    \n    likelihood = pm.Normal('obs', mu=prior_mean, sd=prior_std, observed=observed_data)\n\n    # \u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306e\u5b9f\u884c\n    trace = pm.sample(1000, tune=1000, cores=1, random_seed=123)\n\n# \u7d50\u679c\u306e\u8981\u7d04\npm.summary(trace)<\/pre>\n\n\n\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u4e8b\u524d\u5206\u5e03\u3068\u3057\u3066\u30b5\u30a4\u30b3\u30ed\u306e\u76ee\u306e\u5e73\u5747\u306b<code>Normal(3.5, 2.5)<\/code>\u3001\u6a19\u6e96\u504f\u5dee\u306b<code>HalfNormal(2.5)<\/code>\u3092\u8a2d\u5b9a\u3057\u3066\u3044\u307e\u3059\u3002\u5c24\u5ea6\u95a2\u6570\u306b\u306f\u6b63\u898f\u5206\u5e03\u3092\u4f7f\u3044\u3001\u4e8b\u524d\u5206\u5e03\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u5e73\u5747\u3068\u6a19\u6e96\u504f\u5dee\u306b\u6301\u3064\u3053\u3068\u3067\u968e\u5c64\u30d9\u30a4\u30ba\u30e2\u30c7\u30eb\u3092\u8868\u73fe\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p><code>pm.sample()<\/code>\u3067\u306f\u3001\u30c1\u30e5\u30fc\u30cb\u30f3\u30b0\u30921000\u56de\u3001\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u30921000\u56de\u884c\u3063\u3066\u3044\u307e\u3059\u3002<code>cores=1<\/code>\u3067\u4e26\u5217\u5316\u3092\u7121\u52b9\u306b\u3001<code>random_seed=123<\/code>\u3067\u4e71\u6570\u30b7\u30fc\u30c9\u3092\u56fa\u5b9a\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p><code>pm.summary()<\/code>\u3092\u4f7f\u3048\u3070\u3001\u4e8b\u5f8c\u5206\u5e03\u306e\u8981\u7d04\u7d71\u8a08\u91cf\u3092\u7c21\u5358\u306b\u8868\u793a\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0a\u306e\u3088\u3046\u306b\u3001PyMC3\u3092\u4f7f\u3048\u3070\u30d9\u30a4\u30ba\u30e2\u30c7\u30ea\u30f3\u30b0\u306b\u5fc5\u8981\u306a\u4e00\u9023\u306e\u624b\u9806\u3092Python\u30b3\u30fc\u30c9\u3068\u3057\u3066\u660e\u5feb\u306b\u8a18\u8ff0\u3067\u304d\u307e\u3059\u3002\u78ba\u7387\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306e\u67d4\u8edf\u6027\u3092\u6d3b\u304b\u3057\u3066\u3001\u30c7\u30fc\u30bf\u306e\u80cc\u5f8c\u306b\u3042\u308b\u8907\u96d1\u306a\u69cb\u9020\u3092\u63a8\u8ad6\u3067\u304d\u308b\u306e\u304c\u5927\u304d\u306a\u9b45\u529b\u3068\u8a00\u3048\u308b\u3067\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"i-3\">PyMC3\u3092\u4f7f\u3063\u305f\u30d9\u30a4\u30ba\u63a8\u8ad6\u306e\u5177\u4f53\u7684\u306a\u6d3b\u7528\u4e8b\u4f8b<\/h2>\n\n\n\n<p>PyMC3\u306f\u3001\u30de\u30fc\u30b1\u30c6\u30a3\u30f3\u30b0\u3001\u91d1\u878d\u3001\u88fd\u9020\u3001\u533b\u7642\u3001\u74b0\u5883\u306a\u3069\u3001\u69d8\u3005\u306a\u5206\u91ce\u3067\u30d9\u30a4\u30ba\u63a8\u8ad6\u3092\u5b9f\u8df5\u3059\u308b\u305f\u3081\u306b\u6d3b\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u3053\u3067\u306f\u3001PyMC3\u306e\u5177\u4f53\u7684\u306a\u9069\u7528\u4e8b\u4f8b\u30925\u3064\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-4\">\u6d3b\u7528\u4e8b\u4f8b1: \u30de\u30fc\u30b1\u30c6\u30a3\u30f3\u30b0\u306b\u304a\u3051\u308b\u9867\u5ba2\u30bb\u30b0\u30e1\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3<\/h3>\n\n\n\n<p>EC\u30b5\u30a4\u30c8\u306e\u8cfc\u8cb7\u5c65\u6b74\u30c7\u30fc\u30bf\u304b\u3089\u9867\u5ba2\u30bb\u30b0\u30e1\u30f3\u30c8\u3092\u62bd\u51fa\u3057\u3001\u30de\u30fc\u30b1\u30c6\u30a3\u30f3\u30b0\u65bd\u7b56\u306e\u6700\u9069\u5316\u3092\u56f3\u308b\u969b\u306b\u3001PyMC3\u304c\u6d3b\u7528\u3067\u304d\u307e\u3059\u3002\u30d9\u30a4\u30b8\u30a2\u30f3\u975e\u8ca0\u5024\u884c\u5217\u56e0\u5b50\u5206\u89e3\uff08BNMF\uff09\u3092\u7528\u3044\u308b\u3053\u3068\u3067\u3001\u9867\u5ba2-\u5546\u54c1\u306e\u8cfc\u8cb7\u884c\u5217\u304b\u3089\u6f5c\u5728\u7684\u306a\u9867\u5ba2\u30bb\u30b0\u30e1\u30f3\u30c8\u3068\u5546\u54c1\u306e\u7279\u5fb4\u3092\u63a8\u5b9a\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0b\u306f\u3001PyMC3\u3067BNMF\u3092\u5b9f\u88c5\u3057\u305f\u30b5\u30f3\u30d7\u30eb\u30b3\u30fc\u30c9\u3067\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">import pymc3 as pm\nimport numpy as np\n\n# \u8cfc\u8cb7\u884c\u5217\u306e\u6e96\u5099\uff08\u30e6\u30fc\u30b6\u30fc\u6570\u00d7\u5546\u54c1\u6570\uff09\npurchase_matrix = np.random.randint(0, 2, size=(100, 50))\n\nwith pm.Model() as model:\n    # \u6f5c\u5728\u5909\u6570\u306e\u6b21\u5143\u6570\n    K = 5\n\n    # \u9867\u5ba2\u306e\u6f5c\u5728\u5909\u6570\n    U = pm.Normal('U', mu=0, sd=1, shape=(100, K))\n\n    # \u5546\u54c1\u306e\u6f5c\u5728\u5909\u6570\n    V = pm.Normal('V', mu=0, sd=1, shape=(K, 50))\n\n    # \u89b3\u6e2c\u30e2\u30c7\u30eb\n    obs = pm.Bernoulli('obs', logit_p=pm.math.dot(U, V), observed=purchase_matrix)\n\n    # \u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\n    trace = pm.sample(1000, tune=1000, cores=1, random_seed=123)\n\n# \u4e8b\u5f8c\u5206\u5e03\u306e\u8981\u7d04\npm.summary(trace)<\/pre>\n\n\n\n<p>\u4e8b\u5f8c\u5206\u5e03\u304b\u3089\u5f97\u3089\u308c\u305f\u9867\u5ba2\u30bb\u30b0\u30e1\u30f3\u30c8\u3092\u57fa\u306b\u3001\u30bb\u30b0\u30e1\u30f3\u30c8\u5225\u306e\u6700\u9069\u306a\u5546\u54c1\u30ec\u30b3\u30e1\u30f3\u30c7\u30fc\u30b7\u30e7\u30f3\u3084\u8ca9\u4fc3\u65bd\u7b56\u3092\u8a2d\u8a08\u3067\u304d\u307e\u3059\u3002PyMC3\u3092\u6d3b\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u30c7\u30fc\u30bf\u306b\u57fa\u3065\u3044\u305f\u52b9\u679c\u7684\u306a\u30de\u30fc\u30b1\u30c6\u30a3\u30f3\u30b0\u6226\u7565\u306e\u7acb\u6848\u304c\u53ef\u80fd\u306b\u306a\u308b\u3067\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-5\">\u6d3b\u7528\u4e8b\u4f8b2: \u91d1\u878d\u5de5\u5b66\u3067\u306e\u30ea\u30b9\u30af\u8a55\u4fa1\u30e2\u30c7\u30ea\u30f3\u30b0<\/h3>\n\n\n\n<p>\u682a\u4fa1\u306e\u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3\u3092\u9069\u5207\u306b\u30e2\u30c7\u30eb\u5316\u3057\u3001\u30d0\u30ea\u30e5\u30fc\u30fb\u30a2\u30c3\u30c8\u30fb\u30ea\u30b9\u30af\uff08VaR\uff09\u306a\u3069\u306e\u30ea\u30b9\u30af\u6307\u6a19\u3092\u9ad8\u5ea6\u5316\u3059\u308b\u969b\u306b\u3082\u3001PyMC3\u304c\u529b\u3092\u767a\u63ee\u3057\u307e\u3059\u3002\u30d9\u30a4\u30b8\u30a2\u30f3\u30fb\u30b9\u30c8\u30ad\u30e3\u30b9\u30c6\u30a3\u30c3\u30af\u30fb\u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3\u30fb\u30e2\u30c7\u30eb\u3092\u7528\u3044\u308c\u3070\u3001\u682a\u4fa1\u30ea\u30bf\u30fc\u30f3\u306e\u6642\u7cfb\u5217\u30c7\u30fc\u30bf\u304b\u3089\u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3\u306e\u6642\u9593\u5909\u5316\u3092\u67d4\u8edf\u306b\u63a8\u5b9a\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0b\u306f\u3001PyMC3\u3067\u30b9\u30c8\u30ad\u30e3\u30b9\u30c6\u30a3\u30c3\u30af\u30fb\u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3\u30fb\u30e2\u30c7\u30eb\u3092\u5b9f\u88c5\u3057\u305f\u30b5\u30f3\u30d7\u30eb\u30b3\u30fc\u30c9\u3067\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">import pymc3 as pm\nimport numpy as np\n\n# \u30ea\u30bf\u30fc\u30f3\u306e\u6642\u7cfb\u5217\u30c7\u30fc\u30bf\u306e\u6e96\u5099\nreturns = np.random.normal(0, 1, size=1000)\n\nwith pm.Model() as model:\n    # \u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3\u306e\u521d\u671f\u5024\n    sigma0 = pm.HalfNormal('sigma0', sd=1)\n\n    # \u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3\u306e\u6642\u9593\u5909\u5316\n    sigma = pm.GaussianRandomWalk('sigma', sigma0, shape=1000)\n\n    # \u89b3\u6e2c\u30e2\u30c7\u30eb\n    obs = pm.Normal('obs', mu=0, sd=pm.math.exp(sigma\/2), observed=returns)\n\n    # \u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\n    trace = pm.sample(1000, tune=1000, target_accept=0.9, random_seed=123)\n\n# \u4e8b\u5f8c\u5206\u5e03\u306e\u8981\u7d04    \npm.summary(trace)<\/pre>\n\n\n\n<p>\u30dc\u30e9\u30c6\u30a3\u30ea\u30c6\u30a3\u306e\u4e0d\u78ba\u5b9f\u6027\u3092\u8003\u616e\u3057\u305f\u30ea\u30b9\u30af\u8a55\u4fa1\u304c\u53ef\u80fd\u3068\u306a\u308a\u3001\u3088\u308a\u9811\u5065\u306a\u30ea\u30b9\u30af\u7ba1\u7406\u4f53\u5236\u306e\u69cb\u7bc9\u306b\u5bc4\u4e0e\u3057\u307e\u3059\u3002\u91d1\u878d\u5de5\u5b66\u306e\u69d8\u3005\u306a\u5834\u9762\u3067\u3001PyMC3\u3092\u6d3b\u7528\u3057\u305f\u30d9\u30a4\u30ba\u30e2\u30c7\u30ea\u30f3\u30b0\u304c\u6709\u52b9\u306b\u50cd\u304f\u306f\u305a\u3067\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-6\">\u6d3b\u7528\u4e8b\u4f8b3: \u88fd\u9020\u696d\u3067\u306e\u54c1\u8cea\u7ba1\u7406\u3068\u7570\u5e38\u691c\u77e5<\/h3>\n\n\n\n<p>\u534a\u5c0e\u4f53\u306e\u88fd\u9020\u5de5\u7a0b\u306b\u304a\u3051\u308b\u7570\u5e38\u3092\u30ea\u30a2\u30eb\u30bf\u30a4\u30e0\u306b\u691c\u77e5\u3057\u3001\u6b69\u7559\u307e\u308a\u3092\u6539\u5584\u3057\u305f\u3044\u5834\u5408\u3082\u3001PyMC3\u304c\u6d3b\u7528\u3067\u304d\u307e\u3059\u3002\u30d9\u30a4\u30b8\u30a2\u30f3\u5909\u5316\u70b9\u691c\u77e5\u30e2\u30c7\u30eb\u3092\u7528\u3044\u308b\u3053\u3068\u3067\u3001\u88fd\u9020\u88c5\u7f6e\u306e\u30bb\u30f3\u30b5\u30fc\u30c7\u30fc\u30bf\u304b\u3089\u7570\u5e38\u767a\u751f\u7b87\u6240\u3092\u63a8\u5b9a\u53ef\u80fd\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0b\u306f\u3001PyMC3\u3067\u5909\u5316\u70b9\u691c\u77e5\u30e2\u30c7\u30eb\u3092\u5b9f\u88c5\u3057\u305f\u30b5\u30f3\u30d7\u30eb\u30b3\u30fc\u30c9\u3067\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">import pymc3 as pm\nimport numpy as np\n\n# \u30bb\u30f3\u30b5\u30fc\u30c7\u30fc\u30bf\u306e\u6e96\u5099\nsensor_data = np.random.normal(0, 1, size=1000)\nsensor_data[500:] += 2  # \u30b9\u30c6\u30c3\u30d7\u72b6\u306e\u7570\u5e38\u3092\u4eee\u5b9a\n\nwith pm.Model() as model:\n    # \u5404\u6642\u70b9\u3067\u306e\u5e73\u5747\u5024\n    mu = pm.Normal('mu', mu=0, sd=1, shape=1000)\n\n    # \u5404\u6642\u70b9\u3067\u306e\u7570\u5e38\u5224\u5b9a\n    cp = pm.Bernoulli('cp', p=0.01, shape=1000)\n\n    # \u7570\u5e38\u306e\u5927\u304d\u3055\n    delta = pm.Normal('delta', mu=0, sd=1)\n\n    # \u89b3\u6e2c\u30e2\u30c7\u30eb\n    obs = pm.Normal('obs', mu=mu + cp*delta, sd=1, observed=sensor_data)\n\n    # \u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\n    trace = pm.sample(1000, tune=1000, cores=1, random_seed=123)\n\n# \u4e8b\u5f8c\u5206\u5e03\u306e\u8981\u7d04    \npm.summary(trace)<\/pre>\n\n\n\n<p>\u65e9\u671f\u306e\u7570\u5e38\u691c\u77e5\u306b\u3088\u308a\u4e0d\u826f\u54c1\u306e\u767a\u751f\u3092\u6291\u5236\u3067\u304d\u3001\u88fd\u9020\u5de5\u7a0b\u306e\u6b69\u7559\u307e\u308a\u5411\u4e0a\u3068\u54c1\u8cea\u7ba1\u7406\u30b3\u30b9\u30c8\u306e\u524a\u6e1b\u3092\u5b9f\u73fe\u3057\u307e\u3059\u3002PyMC3\u3092\u6d3b\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u88fd\u9020\u696d\u306e\u54c1\u8cea\u7ba1\u7406\u3092\u30c7\u30fc\u30bf\u30c9\u30ea\u30d6\u30f3\u306b\u9ad8\u5ea6\u5316\u3067\u304d\u308b\u3067\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-7\">\u6d3b\u7528\u4e8b\u4f8b4: \u533b\u7642\u30fb\u5275\u85ac\u5206\u91ce\u3067\u306e\u30d1\u30fc\u30bd\u30ca\u30e9\u30a4\u30ba\u30c9\u6cbb\u7642\u306e\u5b9f\u73fe<\/h3>\n\n\n\n<p>\u60a3\u8005\u3054\u3068\u306e\u7279\u6027\u3092\u8003\u616e\u3057\u305f\u6700\u9069\u306a\u6295\u85ac\u91cf\u3092\u4e88\u6e2c\u3059\u308b\u969b\u306b\u3082\u3001PyMC3\u304c\u6d3b\u7528\u3067\u304d\u307e\u3059\u3002\u30d9\u30a4\u30b8\u30a2\u30f3\u30fb\u30cf\u30a4\u30d6\u30ea\u30c3\u30c9\u30fb\u30e2\u30c7\u30eb\u3092\u7528\u3044\u308c\u3070\u3001\u670d\u85ac\u5f8c\u306e\u8840\u4e2d\u85ac\u7269\u6fc3\u5ea6\u30c7\u30fc\u30bf\u304b\u3089\u85ac\u7269\u52d5\u614b\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u500b\u4eba\u5dee\u3092\u63a8\u5b9a\u53ef\u80fd\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0b\u306f\u3001PyMC3\u3067\u85ac\u7269\u52d5\u614b\u30e2\u30c7\u30eb\u3092\u5b9f\u88c5\u3057\u305f\u30b5\u30f3\u30d7\u30eb\u30b3\u30fc\u30c9\u3067\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">import pymc3 as pm\nimport numpy as np\nimport theano.tensor as tt\n\n# \u8840\u4e2d\u85ac\u7269\u6fc3\u5ea6\u30c7\u30fc\u30bf\u306e\u6e96\u5099\uff08\u60a3\u8005\u6570\u00d7\u6642\u70b9\u6570\uff09\nconcentration_data = np.random.normal(0, 1, size=(100, 10))\n\nwith pm.Model() as model:\n    # \u500b\u4eba\u3054\u3068\u306e\u85ac\u7269\u52d5\u614b\u30d1\u30e9\u30e1\u30fc\u30bf\n    CL = pm.Lognormal('CL', mu=0, sd=1, shape=100)  # \u30af\u30ea\u30a2\u30e9\u30f3\u30b9\n    V = pm.Lognormal('V', mu=0, sd=1, shape=100)   # \u5206\u5e03\u5bb9\u7a4d\n\n    # \u6bcd\u96c6\u56e3\u30d1\u30e9\u30e1\u30fc\u30bf\n    mu_CL = pm.Normal('mu_CL', mu=0, sd=1)\n    mu_V = pm.Normal('mu_V', mu=0, sd=1)\n    sd_CL = pm.HalfNormal('sd_CL', sd=1)\n    sd_V = pm.HalfNormal('sd_V', sd=1)\n\n    # \u500b\u4eba\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u6bcd\u96c6\u56e3\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u95a2\u4fc2\n    CL_obs = pm.Lognormal('CL_obs', mu=mu_CL, sd=sd_CL, observed=CL)\n    V_obs = pm.Lognormal('V_obs', mu=mu_V, sd=sd_V, observed=V)\n\n    # \u85ac\u7269\u52d5\u614b\u30e2\u30c7\u30eb\n    def pk_model(CL, V, t):\n        # 1\u30b3\u30f3\u30d1\u30fc\u30c8\u30e1\u30f3\u30c8\u30e2\u30c7\u30eb\u3092\u4eee\u5b9a\n        ka = 1.0  # \u5438\u53ce\u901f\u5ea6\u5b9a\u6570\n        D = 1.0   # \u6295\u4e0e\u91cf\n        k = CL \/ V\n        C = D*ka \/ (V * (ka - k)) * (tt.exp(-k*t) - tt.exp(-ka*t))\n        return C\n\n    # \u89b3\u6e2c\u30e2\u30c7\u30eb\n    C_pred = pk_model(CL, V, np.arange(10))\n    obs = pm.Normal('obs', mu=C_pred, sd=0.1, observed=concentration_data)\n\n    # \u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\n    trace = pm.sample(1000, tune=1000, target_accept=0.9, random_seed=123)\n\n# \u4e8b\u5f8c\u5206\u5e03\u306e\u8981\u7d04\npm.summary(trace)<\/pre>\n\n\n\n<p>\u60a3\u8005\u3054\u3068\u306b\u6700\u9069\u306a\u6295\u85ac\u30ec\u30b8\u30e1\u30f3\u3092\u4e88\u6e2c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u3001\u526f\u4f5c\u7528\u306e\u4f4e\u6e1b\u3068\u6cbb\u7642\u52b9\u679c\u306e\u6700\u5927\u5316\u3092\u4e21\u7acb\u3067\u304d\u307e\u3059\u3002PyMC3\u3092\u6d3b\u7528\u3057\u305f\u30d9\u30a4\u30ba\u63a8\u8ad6\u306f\u3001\u30d1\u30fc\u30bd\u30ca\u30e9\u30a4\u30ba\u30c9\u533b\u7642\u306e\u767a\u5c55\u306b\u5927\u304d\u304f\u5bc4\u4e0e\u3059\u308b\u306f\u305a\u3067\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-8\">\u6d3b\u7528\u4e8b\u4f8b5: \u74b0\u5883\u79d1\u5b66\u306b\u304a\u3051\u308b\u751f\u614b\u7cfb\u30e2\u30c7\u30ea\u30f3\u30b0\u3068\u4e88\u6e2c<\/h3>\n\n\n\n<p>\u6e56\u6cbc\u306e\u5bcc\u6804\u990a\u5316\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3057\u3001\u6c34\u8cea\u6539\u5584\u7b56\u306e\u52b9\u679c\u3092\u4e88\u6e2c\u3059\u308b\u969b\u306b\u3082\u3001PyMC3\u304c\u6d3b\u7528\u3067\u304d\u307e\u3059\u3002\u30d9\u30a4\u30b8\u30a2\u30f3\u30fb\u30e1\u30ab\u30cb\u30b9\u30c6\u30a3\u30c3\u30af\u30fb\u30e2\u30c7\u30eb\u3092\u7528\u3044\u308c\u3070\u3001\u6c34\u8cea\u30c7\u30fc\u30bf\u304b\u3089\u5bcc\u6804\u990a\u5316\u306e\u539f\u56e0\u3068\u306a\u308b\u7269\u8cea\u30d5\u30ed\u30fc\u3092\u63a8\u5b9a\u53ef\u80fd\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0b\u306f\u3001PyMC3\u3067\u5bcc\u6804\u990a\u5316\u30e2\u30c7\u30eb\u3092\u5b9f\u88c5\u3057\u305f\u30b5\u30f3\u30d7\u30eb\u30b3\u30fc\u30c9\u3067\u3059\u3002<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">import pymc3 as pm\nimport numpy as np\nimport theano.tensor as tt\n\n# \u6c34\u8cea\u30c7\u30fc\u30bf\u306e\u6e96\u5099\uff08\u6642\u7cfb\u5217\u306e\u5168\u30ea\u30f3\u6fc3\u5ea6\uff09\ntp_data = np.random.normal(0.1, 0.02, size=100)\n\nwith pm.Model() as model:\n    # \u5bcc\u6804\u990a\u5316\u306e\u539f\u56e0\u3068\u306a\u308b\u7269\u8cea\u30d5\u30ed\u30fc\n    loading = pm.Normal('loading', mu=1, sd=0.2)      # \u6d41\u5165\u8ca0\u8377\u91cf\n    sediment_release = pm.Normal('sediment_release', mu=0.1, sd=0.02)  # \u5e95\u6ce5\u304b\u3089\u306e\u6eb6\u51fa\n\n    # \u6e56\u6cbc\u306e\u7269\u8cea\u53ce\u652f\u30e2\u30c7\u30eb \n    def lake_model(loading, sediment_release, t):\n        V = 1e6  # \u6e56\u6cbc\u306e\u4f53\u7a4d\n        Q = 1e5  # \u6d41\u51fa\u91cf\n        k = 0.1  # \u6c88\u6bbf\u9664\u53bb\u901f\u5ea6\u5b9a\u6570\n        dCdt = (loading + sediment_release - Q*C - k*V*C) \/ V\n        return dCdt\n\n    # \u89b3\u6e2c\u30e2\u30c7\u30eb\n    C0 = pm.Normal('C0', mu=0.1, sd=0.02)  # \u521d\u671f\u6fc3\u5ea6\n    C = tt.concatenate([[C0], tt.scan(fn=lake_model, sequences=[loading, sediment_release, np.arange(99)], outputs_info=[C0])[0]])\n\n    obs = pm.Normal('obs', mu=C, sd=0.01, observed=tp_data)\n\n    # \u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\n    trace = pm.sample(1000, tune=1000, target_accept=0.9, random_seed=123)\n\n# \u4e8b\u5f8c\u5206\u5e03\u306e\u8981\u7d04\npm.summary(trace)<\/pre>\n\n\n\n<p>\u5bcc\u6804\u990a\u5316\u30e1\u30ab\u30cb\u30ba\u30e0\u306e\u5b9a\u91cf\u7684\u306a\u7406\u89e3\u304c\u6df1\u307e\u308a\u3001\u52b9\u679c\u7684\u306a\u6c34\u8cea\u6539\u5584\u7b56\u306e\u7acb\u6848\u3068\u5408\u610f\u5f62\u6210\u306b\u5f79\u7acb\u3066\u3089\u308c\u307e\u3059\u3002PyMC3\u3092\u6d3b\u7528\u3057\u305f\u30d9\u30a4\u30ba\u30e2\u30c7\u30ea\u30f3\u30b0\u306f\u3001\u74b0\u5883\u554f\u984c\u306e\u89e3\u6c7a\u306b\u5927\u304d\u304f\u8ca2\u732e\u3059\u308b\u3067\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0a\u306e\u4e8b\u4f8b\u304b\u3089\u3001PyMC3\u3092\u7528\u3044\u305f\u30d9\u30a4\u30ba\u30e2\u30c7\u30ea\u30f3\u30b0\u304c\u3001\u69d8\u3005\u306a\u9818\u57df\u306e\u610f\u601d\u6c7a\u5b9a\u3084\u4e88\u6e2c\u30bf\u30b9\u30af\u306b\u6709\u7528\u3067\u3042\u308b\u3053\u3068\u304c\u304a\u308f\u304b\u308a\u3044\u305f\u3060\u3051\u305f\u3068\u601d\u3044\u307e\u3059\u3002\u30d9\u30a4\u30ba\u63a8\u8ad6\u306e\u67d4\u8edf\u6027\u3092\u6d3b\u304b\u3057\u3066\u8907\u96d1\u306a\u30c7\u30fc\u30bf\u306e\u80cc\u5f8c\u306b\u3042\u308b\u30e1\u30ab\u30cb\u30ba\u30e0\u3092\u63a8\u5b9a\u3057\u3001\u4e0d\u78ba\u5b9f\u6027\u3092\u8003\u616e\u306b\u5165\u308c\u306a\u304c\u3089\u610f\u601d\u6c7a\u5b9a\u306e\u8cea\u3092\u9ad8\u3081\u3089\u308c\u308b\u306e\u304c\u3001PyMC3\u306e\u5927\u304d\u306a\u5f37\u307f\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u4eca\u56de\u7d39\u4ecb\u3057\u305f\u4e8b\u4f8b\u306f\u6c37\u5c71\u306e\u4e00\u89d2\u306b\u904e\u304e\u307e\u305b\u3093\u3002\u305c\u3072\u7686\u3055\u3093\u3082\u3001\u81ea\u8eab\u306e\u696d\u52d9\u3084\u7814\u7a76\u3078\u306ePyMC3\u306e\u6d3b\u7528\u65b9\u6cd5\u3092\u8003\u3048\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002PyMC3\u3092\u4f7f\u3044\u3053\u306a\u3059\u3053\u3068\u3067\u3001\u30c7\u30fc\u30bf\u306b\u57fa\u3065\u304f\u5408\u7406\u7684\u610f\u601d\u6c7a\u5b9a\u306e\u5b9f\u8df5\u8005\u3068\u306a\u308c\u308b\u306f\u305a\u3067\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"i-9\">\u307e\u3068\u3081 \u2013 PyMC3\u3067\u30d9\u30a4\u30ba\u63a8\u8ad6\u3092\u3082\u3063\u3068\u8eab\u8fd1\u306b<\/h2>\n\n\n\n<p>PyMC3\u306f\u3001\u30d9\u30a4\u30ba\u63a8\u8ad6\u3092\u5b9f\u8df5\u3059\u308b\u305f\u3081\u306e\u5f37\u529b\u304b\u3064\u67d4\u8edf\u306a\u30c4\u30fc\u30eb\u3067\u3059\u3002\u672c\u8a18\u4e8b\u3067\u306f\u3001PyMC3\u306e\u57fa\u672c\u7684\u306a\u4f7f\u3044\u65b9\u304b\u3089\u3001\u5b9f\u969b\u306e\u30c7\u30fc\u30bf\u89e3\u6790\u3078\u306e\u5fdc\u7528\u307e\u3067\u3001\u5e45\u5e83\u3044\u30c8\u30d4\u30c3\u30af\u3092\u53d6\u308a\u4e0a\u3052\u3066\u304d\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-10\">PyMC3\u3092\u4f7f\u3044\u3053\u306a\u3059\u305f\u3081\u306eTips<\/h3>\n\n\n\n<p>PyMC3\u3092\u6d3b\u7528\u3057\u3066\u30d9\u30a4\u30ba\u30e2\u30c7\u30ea\u30f3\u30b0\u3092\u884c\u3046\u4e0a\u3067\u3001\u4ee5\u4e0b\u306e\u70b9\u306b\u7559\u610f\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u4e8b\u524d\u5206\u5e03\u306f\u614e\u91cd\u306b\u9078\u3076\u3002\u7121\u60c5\u5831\u4e8b\u524d\u5206\u5e03\u3092\u5b89\u6613\u306b\u4f7f\u308f\u306a\u3044\u3002<\/li>\n\n\n\n<li>\u968e\u5c64\u30d9\u30a4\u30ba\u30e2\u30c7\u30eb\u3092\u6d3b\u7528\u3057\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u9593\u306e\u95a2\u4fc2\u6027\u3092\u8868\u73fe\u3059\u308b\u3002<\/li>\n\n\n\n<li>MCMC\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306e\u53ce\u675f\u3092\u5165\u5ff5\u306b\u30c1\u30a7\u30c3\u30af\u3059\u308b\u3002<\/li>\n\n\n\n<li>\u30e2\u30c7\u30eb\u6bd4\u8f03\u306b\u306f\u3001WAIC\u3001LOOIC\u3001WBIC\u306a\u3069\u3092\u6d3b\u7528\u3059\u308b\u3002<\/li>\n\n\n\n<li>\u4e8b\u5f8c\u5206\u5e03\u306f\u3001\u8981\u7d04\u7d71\u8a08\u91cf\u3068\u30d3\u30b8\u30e5\u30a2\u30e9\u30a4\u30bc\u30fc\u30b7\u30e7\u30f3\u306e\u4e21\u9762\u304b\u3089\u89e3\u91c8\u3059\u308b\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u3053\u308c\u3089\u3092\u5b9f\u8df5\u3059\u308b\u3053\u3068\u3067\u3001PyMC3\u3092\u4f7f\u3063\u305f\u30d9\u30a4\u30ba\u63a8\u8ad6\u306e\u7cbe\u5ea6\u3068\u4fe1\u983c\u6027\u3092\u9ad8\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u306f\u305a\u3067\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"i-11\">\u30d9\u30a4\u30ba\u63a8\u8ad6\u306e\u3055\u3089\u306a\u308b\u7406\u89e3\u3092\u6df1\u3081\u308b\u305f\u3081\u306e\u53c2\u8003\u8cc7\u6599<\/h3>\n\n\n\n<p>\u30d9\u30a4\u30ba\u63a8\u8ad6\u306e\u7406\u8ad6\u3068\u5b9f\u8df5\u3092\u30de\u30b9\u30bf\u30fc\u3059\u308b\u306b\u306f\u3001\u826f\u8cea\u306a\u5b66\u7fd2\u30ea\u30bd\u30fc\u30b9\u304c\u6b20\u304b\u305b\u307e\u305b\u3093\u3002\u30aa\u30b9\u30b9\u30e1\u306e\u66f8\u7c4d\u3084\u30aa\u30f3\u30e9\u30a4\u30f3\u8b1b\u5ea7\u3092\u305c\u3072\u30c1\u30a7\u30c3\u30af\u3057\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u66f8\u7c4d\n<ul class=\"wp-block-list\">\n<li>\u201cBayesian Analysis with Python\u201d by Osvaldo Martin<\/li>\n\n\n\n<li>\u201cBayesian Methods for Hackers\u201d by Cameron Davidson-Pilon<\/li>\n\n\n\n<li>\u201cStatistical Rethinking\u201d by Richard McElreath<\/li>\n\n\n\n<li>\u201cDoing Bayesian Data Analysis\u201d by John Kruschke<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u30aa\u30f3\u30e9\u30a4\u30f3\u8b1b\u5ea7\n<ul class=\"wp-block-list\">\n<li>\u201cBayesian Statistics: From Concept to Data Analysis\u201d (Coursera)<\/li>\n\n\n\n<li>\u201cBayesian Machine Learning in Python: A\/B Testing\u201d 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