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"source": [
"# 第11回 ベイズ統計学\n"
],
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"[](https://colab.research.google.com/github/slt666666/biostatistics_text_wed/blob/main/source/_static/colab_notebook/chapter11.ipynb)\n",
"\n",
"※Web上ではテーブルや記号など一部LaTeXが反映されず見にくくなってしまっていますが、Google Colabだとちゃんと見えます。"
],
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"cell_type": "markdown",
"source": [
"## はじめに\n",
"\n",
"ここまで扱ってきた統計手法は「得られたデータが母集団からどのくらいの頻度（確率）で発生するのか」という考えが軸になっていました。このような統計学を頻度論と呼びます。\n",
"\n",
"頻度論では、分布の平均値などのパラメータが定数で、得られたデータが変数（確率変数）となっていました。「平均$\\mu=170$の正規分布から得られた身長$185$はどのくらいの確率で生じるか」という形です。\n",
"\n",
"一方、**ベイズ統計学**では、「手元にあるデータはどのようなパラメータに基づく母集団から得られるだろうか」という考え方をします。\n",
"\n",
"「身長を調べたら$174, 165, 183...$が得られたが、これはどの様なパラメータの母集団から得られる確率が高いか」という形です。母平均などのパラメータが変数（確率変数）で、データが定数と考えられます。\n",
"\n",
"今回はこのベイズ統計学について基本的な所を学びます。"
],
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"source": [
"## 条件付き確率とベイズの定理\n",
"\n",
"まずベイズ統計学において重要な定理である、**ベイズの定理**と、ベイズの定理を説明するのに必要な**条件付き確率**について説明します。\n",
"\n",
"ある試行において、事象Aが起こったという条件下で事象Bが起きる確率のことを、事象Aの条件下で事象Bが起きる条件付き確率$P(B|A)$と言います。\n",
"\n",
"条件付き確率の例として、\n",
"\n",
"たとえば、6本のうち2本があたりのくじがあるとします。Aさんが1本のくじをひき、あたりを引いたときに、Bさんもあたりくじをひく確率は条件付き確率と言えます。\n",
"\n",
"まず、何の条件も無しにBさんがあたりを引く確率は$P(B) = \\dfrac{2}{6}$です。\n",
"\n",
"Aさんが1本あたりを引いたという条件下では、Bさんがあたりを引く確率は、残る5本のうちあたりは1本なので、$P(B|A)=\\dfrac{1}{5}$となります。\n",
"\n",
"Aさんがあたりをひいたという条件によってBさんがあたりを引く確率が変化しました。この様な場合、条件付き確率で考える必要があります。\n",
"\n",
"条件付き確率については、下式が成り立つことが知られています。\n",
"\n",
"$P(B|A)P(A)= P(A \\cap B)$\n",
"\n",
"$P(A|B)P(B)= P(A \\cap B)$"
],
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{
"cell_type": "markdown",
"source": [
"### ベイズの定理\n",
"\n",
"ベイズの定理は、条件付き確率に関する等式を指し、\n",
"\n",
"$P(A|B) = \\dfrac{P(B|A)P(A)}{P(B)}$\n",
"\n",
"で表されます。\n",
"\n",
"この定理を用いると、$P(B|A)$を用いて、$P(A|B)$を求める事が出来ます。\n",
"\n",
"先ほどのくじ引きの例で言うと、\n",
"\n",
"$P(A|B)$ ... 二人目(B)があたりだったとき、一人目があたりの確率\n",
"\n",
"$P(B|A)$ ... 一人目(A)があたりだったとき、二人目があたりの確率\n",
"\n",
"となるので、求めるのが簡単そうな$P(B|A)$を用いて、難しそうな$P(A|B)$を求める事が出来ます。\n",
"\n",
"よく例として用いられるのは病気の診断です。\n",
"\n",
"$A$ ... 病気に実際になっている事象\n",
"\n",
"$B$ ... 検査で陽性になる事象\n",
"\n",
"があったとします。同じように考えると、\n",
"\n",
"$P(A|B)$ ... 検査が陽性だったとき、実際に病気である確率\n",
"\n",
"$P(B|A)$ ... 病気の時に、検査が陽性になる確率\n",
"\n",
"となるので、患者の知りたい$P(A|B)$を、検査薬の精度である$P(B|A)$から求める事が出来ます。"
],
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"source": [
"### モンティ・ホール問題\n",
"\n",
"有名な例として、モンティ・ホール問題があります。\n",
"\n",
"```\n",
"3つのドアABCがあって、1つのドアは当たり、2つのドアははずれ。\n",
"\n",
"1つのドアを選択した後、司会が残り2つのドアのうちはずれのドアを開けて見せてくれます。\n",
"\n",
"ここで、最初に選んだドアを変更してもよいと言われます。\n",
"\n",
"あたりをひくためにはドアを変更するべきか？変更しないべきか？\n",
"```\n",
"\n",
"という問題です。\n",
"\n",
"例として、最初にドアAを選んだところ、司会がドアBを開けて外れだと見せてくれた状況を考えてみます。\n",
"\n",
"この条件下で最初に選んだドアAがあたりである確率$P(A|B)$をまず求めてみます。\n",
"\n",
"ベイズの定理$P(A|B) = \\dfrac{P(B|A)P(A)}{P(B)}$を用いて考えると、\n",
"\n",
"前提条件無しにAを選んであたりの確率が$P(A) = \\dfrac{1}{3}$\n",
"\n",
"残り2つのドアから(あたりはずれ関係なしに)司会がBをあける確率$P(B) = \\dfrac{1}{2}$\n",
"\n",
"Aがあたりのとき、司会がBをあける確率$P(B|A)=\\dfrac{1}{2}$\n",
"\n",
"となるので、司会がBをあけた時、Aがあたりの確率は$P(A|B) = \\dfrac{P(B|A)P(A)}{P(B)} = \\dfrac{\\dfrac{1}{2} \\times \\dfrac{1}{3}}{\\dfrac{1}{2}}=\\dfrac{1}{3}$となります。\n",
"\n",
"次に、最初にAを選んで、司会がBのドアを開いたとき、Cがあたりの確率$P(C|B)$は、\n",
"\n",
"同じようにベイズの定理より、$P(C|B)=\\dfrac{P(B|C)P(C)}{P(B)}$と計算できます。\n",
"\n",
"前提条件無しにCを選んで当たりの確率は$P(C)=\\dfrac{1}{3}$\n",
"\n",
"残り2つのドアから(あたりはずれ関係なしに)司会がBをあける確率は$P(B) = \\dfrac{1}{2}$\n",
"\n",
"Cがあたりの条件の下、司会がBをあける確率は$P(B|C)=1$\n",
"\n",
"となるので、$P(C|B)=\\dfrac{P(B|C)P(C)}{P(B)} = \\dfrac{1 \\times \\dfrac{1}{3}}{\\dfrac{1}{2}}=\\dfrac{2}{3}$です。\n",
"\n",
"よって、一見直感に反する気がしますが、もともと選んでいた扉から変更した方があたりの確率が2倍高くなることがわかります。"
],
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"source": [
"検査で陽性になった時に実際に病気である確率も計算してみましょう。\n",
"\n",
"世界中で0.1%の人が病気にかかっているとします。$P(A) = 0.001$\n",
"\n",
"検査結果が陽性である確率は3%です$P(B) = 0.03$\n",
"\n",
"また、病気の患者が検査を受けると陽性の結果となる確率が99％とします。$P(B|A) = 0.99$\n",
"\n",
"この時、検査で陽性になった時に実際に病気の確率は、ベイズの定理より…\n",
"\n",
"$P(A|B) = \\dfrac{P(B|A)P(A)}{P(B)}$\n",
"\n"
],
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"source": [
"# ベイズの定理を用いて、検査で陽性になった時に実際に病気である確率を求める。\n",
"\n",
"0.99 * 0.001 / 0.03"
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"source": [
"ということで、99%正しい検査で陽性となっても、実際に病気である確率はかなり低くなります。\n",
"\n",
"ただ、病気である確率は何も検査をしないと0.1％だったのが、検査によって陽性反応が出たという条件の下だと、病気である確率が3.2％に上がる、つまり32倍上がっていると考えることもできます。\n",
"\n",
"
\n",
"\n",
"このように、\n",
"\n",
"開けたドアがあたりである確率や、病気である確率などを「別のドアははずれだった」や「検査結果が陽性だった」などの観測データを基に更新する事が出来ます。\n",
"\n",
"もともとの確率を**事前確率**、得られたデータを基にベイズの定理によって更新された後の確率を**事後確率**と呼びます。\n",
"\n",
"今回は確率を値として求めていましたが、この後扱うベイズ統計学では確率分布を主に扱っていきます。\n",
"\n",
"つまり、データが得られる前にパラメータ(母平均など)が従うと想定する分布、**事前確率分布**(**事前分布**と呼ぶことが多い)を、データが得られた後に更新して**事後確率分布**(**事後分布**と呼ぶことが多い)を求める形になります。"
],
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"cell_type": "markdown",
"source": [
"## ベイズ統計の流れ\n",
"\n",
"例えば、植物の葉の長さ$X$を5標本測定した結果、\n",
"\n",
"$x_1=2.4, x_2=3.2, x_3=2.2, x_4=4.6, x_5=3.3$\n",
"\n",
"というデータが得られたとします。\n",
"\n",
"植物の葉の長さ$X$は正規分布$X\\sim N(\\theta, 1)$に従っているとすると、この$\\theta$を求めたい状況です。\n",
"\n",
"今回はこの$\\theta$の分布を求めていきます。\n",
"\n",
"まず事前分布として$\\theta \\sim N(0, 10000)$に従うと仮定します。分散がとても大きいので、$\\theta$は大きい場合もあるし小さい場合もある、つまりあんまりよくわかってない状況です。この分布が**事前分布**になります。\n",
"\n",
"さて、先ほど葉の長さ$X$は正規分布$N(\\theta, 1) = \\dfrac{1}{\\sqrt{2\\pi}}exp(-\\dfrac{(x-\\theta)^2}{2})$に従うので\n",
"\n",
"$x_1=2.4, x_2=3.2, x_3=2.2, x_4=4.6, x_5=3.3$というデータが得られる確率は\n",
"\n",
"$\\prod_{5}^{i=1}\\dfrac{1}{\\sqrt{2\\pi}}exp(-\\dfrac{(x_i-\\theta)^2}{2})$\n",
"\n",
"$= \\dfrac{1}{\\sqrt{2\\pi}}exp(-\\dfrac{(2.4-\\theta)^2}{2}) \\times \\dfrac{1}{\\sqrt{2\\pi}}exp(-\\dfrac{(3.2-\\theta)^2}{2}) \\times \\cdots \\times \\dfrac{1}{\\sqrt{2\\pi}}exp(-\\dfrac{(3.3-\\theta)^2}{2})$\n",
"\n",
"で計算できます。\n",
"\n",
"このデータが得られる事象を$D$とすると、$\\theta$の下$D$が得られる確率の関数は、\n",
"\n",
"$f(D|\\theta) = \\prod_{5}^{i=1}\\dfrac{1}{\\sqrt{2\\pi}}exp(-\\dfrac{(x_i-\\theta)^2}{2})$\n",
"\n",
"と表せます。\n",
"\n",
"次に、パラメータ$\\theta$の事前分布$N(0, 10000)$の確率密度関数$f(\\theta)$は\n",
"\n",
"$f(\\theta) = \\dfrac{1}{\\sqrt{20000\\pi}}exp(-\\dfrac{\\theta^2}{20000})$\n",
"\n",
"と表せます。\n",
"\n",
"データが得られたときに、$\\theta$がどうなるか$f(\\theta|D)$を知りたいので、\n",
"\n",
"これらをベイズの定理$P(A|B) = \\dfrac{P(B|A)P(A)}{P(B)}$に基づいて考えると、\n",
"\n",
"$f(\\theta|D) = \\dfrac{f(D|\\theta)f(\\theta)}{f(D)}$\n",
"\n",
"となります。\n",
"\n",
"ただ、実際に計算をする際には、$f(D)$を求めることは非常に難しく、\n",
"\n",
"また、後ほど説明する$f(D)$を直接$求めなくても良い仕組みがあったりするので、下記の様に表される場合が多いです。\n",
"\n",
"$f(\\theta|D) \\propto f(D|\\theta)f(\\theta)$\n",
"\n",
"$= \\bigg\\lbrack\\prod_{5}^{i=1}\\dfrac{1}{\\sqrt{2\\pi}}exp(-\\dfrac{(x_i-\\theta)^2}{2})\\bigg\\rbrack \\cdot \\bigg\\lbrack\\dfrac{1}{\\sqrt{20000\\pi}}exp(-\\dfrac{\\theta^2}{20000})\\bigg\\rbrack$\n",
"\n",
"$\\propto$は比例を意味します。\n",
"\n",
"この様な計算で事後分布を得る事が出来ます。\n",
"\n",
"これは正規分布の期待値$\\theta$だけでなく、回帰式$収穫量=\\beta_0+肥料\\times\\beta_1$のパラメーター$\\beta_0, \\beta_1$等においても同様に事後分布が求められます。\n",
"\n",
"データに基づいて、肥料の効果がどの様な分布に従うか(事後分布)が得られます。\n",
"\n",
"![\"title\"](\"https://github.com/slt666666/biostatistics_text_wed/blob/main/source/_static/images/chapter11/beta1.png?raw=true\")
\n",
"\n",
"これまで扱ってきた線形回帰の肥料の効果$\\beta_1 = 20$です！という形では無く、\n",
"\n",
"事後分布という形で得られるので、肥料の効果$\\beta_1$は95%の確率で$18.5 \\leqq \\beta_1 \\leqq 20.6$に入る。みたいな情報が手に入ります。\n",
"\n"
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"source": [
"### 計算が難しすぎる問題\n",
"\n",
"と、事後分布から上手く計算出来ればよいのですが、\n",
"\n",
"例えば先ほど得られた$\\theta$の事後分布は、\n",
"\n",
"$f(\\theta|D) \\propto f(D|\\theta)f(\\theta)$\n",
"\n",
"$= \\bigg\\lbrack\\prod_{5}^{i=1}\\dfrac{1}{\\sqrt{2\\pi}}exp(-\\dfrac{(x_i-\\theta)^2}{2})\\bigg\\rbrack \\cdot \\bigg\\lbrack\\dfrac{1}{\\sqrt{20000\\pi}}exp(-\\dfrac{\\theta^2}{20000})\\bigg\\rbrack$\n",
"\n",
"と表されていました。\n",
"\n",
"この事後分布から$\\theta$が$a \\leqq \\theta \\leqq b$となる確率を求めるには、\n",
"\n",
"$P(a \\leqq \\theta \\leqq b) = \\int_{a}^{b}f(\\theta|D)d\\theta$\n",
"\n",
"という積分計算をする必要があります。しかし、この積分計算は難しすぎて出来ません。\n",
"\n",
"そのため、この事後分布から平均値$\\theta$は$90\\%$の確率で$2.5 \\leqq \\theta \\leqq 3.5$とか、肥料の効果$\\beta_1$は$95\\%$の確率で$18.5 \\leqq \\beta_1 \\leqq 20.6$に入る。みたいな情報は簡単には手に入らず、あまり役に立ちません。\n",
"\n",
"そこで、事後分布が複雑すぎて積分が出来ないという問題を解決するために、MCMCという技術を使用します。"
],
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"source": [
"## MCMCの基本\n",
"\n",
"MCMC(Markov Chain Monte Carlo)とは**マルコフ連鎖モンテカルロ法**の略で、乱数を生成する手法の１つになります。\n",
"\n",
"特にこのMCMCは**事後分布に従う乱数**を生成する事が出来る手法になります。\n",
"\n",
"直接積分を行って、$P(a \\leqq \\theta \\leqq b) = \\int_{a}^{b}f(\\theta|D)d\\theta$ などを求めるのは難しいので、\n",
"\n",
"事後分布$f(\\theta|D)$に従う乱数を大量に生成することで、実際どのくらいの値が$95\\%$で生じるのか等を評価する事が出来ます。\n",
"\n",
"MCMCは**マルコフ連鎖**と**モンテカルロ法**を組み合わせた手法になります。簡単にそれぞれについて触れておきます。\n"
],
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"source": [
"### モンテカルロ法\n",
"\n",
"モンテカルロ法は乱数を用いて近似計算を行う手法です。\n",
"\n",
"円周率を近似計算する方法として有名です。\n",
"\n",
"下図のように、辺の長さが2である正方形の中に半径1の円があると考えます。\n",
"\n",
"![\"title\"](\"https://github.com/slt666666/biostatistics_text_wed/blob/main/source/_static/images/chapter11/circle1.png?raw=true\")
\n",
"\n",
"この正方形の中にランダムに点を打っていきます。\n",
"\n",
"すると、円の領域に入る点の個数は、領域の面積に比例すると考えられます。\n",
"\n",
"つまり、$N$点ランダムに打つと、$X$点が円内に入ったとすると、\n",
"\n",
"$\\dfrac{X}{N}\\sim\\dfrac{\\pi\\times1^2}{2\\times2}=\\dfrac{\\pi}{4}$\n",
"\n",
"となるので、大数の法則から、打つ点の数$N$が増えるにつれて、$\\dfrac{\\pi}{4}$へ収束していくと考えられます。\n",
"\n",
"下図の様に、モンテカルロ法により、ランダムに点を大量に打った結果から、$3.14...$に近い円周率が得られます。\n",
"\n",
"![\"title\"](\"https://github.com/slt666666/biostatistics_text_wed/blob/main/source/_static/images/chapter11/circle2.png?raw=true\")
\n",
"\n",
"この様に、直接計算するのではなく、乱数に基づいて複雑な問題の近似的な解や確率的な結果を導き出す手法がモンテカルロ法になります。\n",
"\n",
"これは、例えば事後分布$f(\\theta|D)$の期待値を計算で求めるには、$\\int_{-\\infty}^{\\infty}f(\\theta|D)\\cdot \\theta d\\theta$を計算する必要がありますが、\n",
"\n",
"事後分布に従う乱数を1000個くらい生成してその平均値を取れば、かなり事後分布$f(\\theta|D)$の期待値に近い値を得ることが出来る、という風に活用できます。"
],
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"cell_type": "markdown",
"source": [
"### マルコフ連鎖\n",
"\n",
"マルコフ連鎖は、「現在の状態だけが未来の状態を決める」というルールを持つ確率モデルを意味します。\n",
"\n",
"式で表すと、ある時刻$t+1$の時の状態$X_{t+1}$は、その直前の時刻$t$の状態$X_t$によってのみ決まる、ということになるので\n",
"\n",
"$P(X_{t+1}|X_t,...,X_1) = P(X_{t+1}|X_t)$\n",
"\n",
"と表す事が出来ます。\n",
"\n",
"具体的な例をあげると、明日の天気が今日の天気に基づいて決まるとします。\n",
"\n",
"この時、明日の天気の確率は例えば下図の様な推移確率で表せます。\n",
"\n",
"![\"title\"](\"https://github.com/slt666666/biostatistics_text_wed/blob/main/source/_static/images/chapter11/tenki.png?raw=true\")
\n",
"\n",
"マルコフ連鎖の有用な特徴として、十分に長い時間が経ったとき、確率分布は初期状態に依存せず、ある特定の分布に収束します。\n",
"\n",
"今回の天気のケースだと、天気の確率は晴れ25%曇り52%雨23%へと収束していきます。\n",
"\n",
"![\"title\"](\"https://github.com/slt666666/biostatistics_text_wed/blob/main/source/_static/images/chapter11/tenki2.png?raw=true\")
\n",
"\n",
"この収束した確率分布を**定常分布**と呼んだりします。\n",
"\n",
"事後分布がこの定常分布になる様に推移確率を構築して利用できれば、事後分布に従う乱数が上手く生成できそうです。"
],
"metadata": {
"id": "hAiJDvNKTjXU"
}
},
{
"cell_type": "markdown",
"source": [
"### MCMCの例え\n",
"\n",
"このモンテカルロ法とマルコフ連鎖を組み合わせたものがMCMCになるわけですが、「宝探し」に例えてみます。\n",
"\n",
"まず、求めたい目的の分布（**事後分布**）を宝の地図の「本当の宝が埋まっている場所の確率分布」とします。\n",
"\n",
"これは直接求めるのが計算的に難しいので、乱数を使用します。\n",
"\n",
"まず、地図上の場所をランダムに掘ってみて、あたりが出た点の情報から目的の分布を求めるのが、**モンテカルロ法**になります、ただこれだけだと効率が悪いです。\n",
"\n",
"そこで、「今いる場所」から「次に行く場所」を、宝が埋まっている確率が高い場所へ誘導するルールである、**マルコフ連鎖**を活用してより効率よくランダムな場所を選んでいきます。\n",
"\n",
"つまり、MCMCは「現在の場所」の良し悪しで「次に行く場所」を決めるルールを使って、何度も移動を繰り返す（マルコフ連鎖）ことで、宝のありそうな場所（高確率な場所）ばかり掘ることに収束していき、結果的に宝の地図（目的の分布）の形がわかる、という手法になります。"
],
"metadata": {
"id": "EFrJhOn0i3e2"
}
},
{
"cell_type": "markdown",
"source": [
"## メトロポリス法\n",
"\n",
"このMCMC法にはいくつか手法が存在しており、メトロポリス・ヘイスティングス法、ギブスサンプリング、ハミルトニアンモンテカルロ法 (HMC) などがあります。\n",
"\n",
"ここでは**メトロポリス法**について簡単に触れておきます。\n",
"\n",
"メトロポリス法では、ある確率密度関数$f(x)$に対し、下記の流れで$f(x)$に従う乱数を生成します。\n",
"\n",
"1. 初期値$\\theta_t$を決める\n",
"2. 次の候補値$\\theta_{a}$をランダムに決める。\n",
"3. $f(\\theta_t) < f(\\theta_{a})$の場合は、その点に移動する$\\theta_{t+1} = \\theta_a$\n",
"\n",
"3. $f(\\theta_t) > f(\\theta_{a})$の場合は、確率$r=\\dfrac{f(\\theta_{a})}{f(\\theta_{t})}$で$\\theta_{t+1} = \\theta_a$へ移動し、それ以外の場合移動しない($\\theta_{t+1} = \\theta_t$)\n",
"4. 2 - 4を繰り返す。\n",
"\n",
"イメージとしては下図のようになります。\n",
"\n",
"![\"title\"](\"https://github.com/slt666666/biostatistics_text_wed/blob/main/source/_static/images/chapter11/metro.png?raw=true\")
\n",
"\n",
"何度もこの移動を繰り返すことで、確率密度関数$f(x)$の中で、確率的に起きやすい部分の乱数を生成する形になります。\n",
"\n",
"この様に大量の乱数を生成することで、目的とする事後分布の形や期待値などの値を推定する事が出来ます。\n",
"\n",
"![\"title\"](\"https://github.com/slt666666/biostatistics_text_wed/blob/main/source/_static/images/chapter11/metro2.png?raw=true\")
\n",
"\n",
"実際に期待値を求めたりする際には、生成した乱数を活用する際に、\n",
"\n",
"* どれだけの乱数を生成するのか(**繰り返し数**と呼ぶ)\n",
"\n",
"* 最初の初期値に引っ張られている部分(**バーンイン期間**と呼ぶ)を切り捨てる\n",
"\n",
"* 連続した乱数($\\theta_t, \\theta_{t+1}$)は相関が強い場合があるので**間引く**必要がある\n",
"\n",
"* 初期値を変えて乱数生成を何セット(**チェーン**と呼ぶ)も行い収束を評価する\n",
"\n",
"といったことを意識する必要があります。\n"
],
"metadata": {
"id": "tR-D54HeI_pC"
}
},
{
"cell_type": "markdown",
"source": [
"## RによるMCMCの実行\n",
"\n",
"ここまで見てきたように、MCMCを実施するのは非常に複雑な処理を行う必要がありますが、\n",
"\n",
"Rではベイズ推定を高速で行うことができる`Stan`というプログラムを使用するためのパッケージ`rstan`が利用できます。\n",
"\n",
"`rstan`をインストールすることで、MCMCを簡単に実施する事が出来ます。\n",
"\n",
"`rstan`はGoogle Colabにはもともとインストールされていないので、新たにインストールする必要があります。\n",
"\n",
"```\n",
"# rstanのインストール\n",
"install.packages(\"rstan\")\n",
"```"
],
"metadata": {
"id": "HsuwaCVAn5eC"
}
},
{
"cell_type": "code",
"source": [
"# rstanをインストールする\n",
"install.packages(\"rstan\")"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "3PvuWnujbT8Q",
"outputId": "00830c59-bf18-483d-b5ab-a45eb3c6ccaa"
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stderr",
"text": [
"Installing package into ‘/usr/local/lib/R/site-library’\n",
"(as ‘lib’ is unspecified)\n",
"\n",
"also installing the dependencies ‘numDeriv’, ‘abind’, ‘tensorA’, ‘distributional’, ‘checkmate’, ‘matrixStats’, ‘posterior’, ‘StanHeaders’, ‘inline’, ‘gridExtra’, ‘RcppParallel’, ‘loo’, ‘QuickJSR’, ‘RcppEigen’, ‘BH’\n",
"\n",
"\n"
]
}
]
},
{
"cell_type": "markdown",
"source": [
"今回はある植物の葉の長さが正規分布$N(\\mu, \\sigma^2)$に従っているとして、\n",
"\n",
"この平均値$\\mu$と標準偏差$\\sigma$についてMCMCを用いたベイズ推定を実施してみます。\n",
"\n",
"実際に30個体の植物の葉の長さを調査した結果が下の様に得られたときに、この平均値$\\mu$や標準偏差$\\sigma$が従う事後分布がどの様な分布となるのか求めます。"
],
"metadata": {
"id": "2cajM_8YcwDU"
}
},
{
"cell_type": "code",
"source": [
"# 得られた30個体の葉の長さのデータを読み込む\n",
"data <- read.csv(\"https://raw.githubusercontent.com/slt666666/biostatistics_text_wed/refs/heads/main/source/_static/data/chapter11_leaf_length.csv\")\n",
"# データの一部を表示\n",
"head(data)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 303
},
"id": "s1aKRV252i-m",
"outputId": "745a5260-9eaa-41db-d683-0101f1e7e69b"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/html": [
"\n",
"A data.frame: 6 × 1\n",
"\n",
"\t | leaf_length |
|---|
\n",
"\t | <dbl> |
|---|
\n",
"\n",
"\n",
"\t| 1 | 3.41 |
|---|
\n",
"\t| 2 | 3.70 |
|---|
\n",
"\t| 3 | 3.95 |
|---|
\n",
"\t| 4 | 5.29 |
|---|
\n",
"\t| 5 | 2.80 |
|---|
\n",
"\t| 6 | 3.72 |
|---|
\n",
"\n",
"
\n"
],
"text/markdown": "\nA data.frame: 6 × 1\n\n| | leaf_length <dbl> |\n|---|---|\n| 1 | 3.41 |\n| 2 | 3.70 |\n| 3 | 3.95 |\n| 4 | 5.29 |\n| 5 | 2.80 |\n| 6 | 3.72 |\n\n",
"text/latex": "A data.frame: 6 × 1\n\\begin{tabular}{r|l}\n & leaf\\_length\\\\\n & \\\\\n\\hline\n\t1 & 3.41\\\\\n\t2 & 3.70\\\\\n\t3 & 3.95\\\\\n\t4 & 5.29\\\\\n\t5 & 2.80\\\\\n\t6 & 3.72\\\\\n\\end{tabular}\n",
"text/plain": [
" leaf_length\n",
"1 3.41 \n",
"2 3.70 \n",
"3 3.95 \n",
"4 5.29 \n",
"5 2.80 \n",
"6 3.72 "
]
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"Stanを動かすためには、事前分布等の情報を記述したStanファイル`xxx.stan`を用意する必要があります。\n",
"\n",
"今回は下の内容を書き込んだ`chapter11_mcmc.stan`というファイルを使用します。\n",
"\n",
"```\n",
"# データの説明\n",
"data {\n",
" int N;\n",
" vector[N] leaf_length;\n",
"}\n",
"\n",
"# 事後分布を得たいパラメータの説明(今回は平均値と標準偏差)\n",
"parameters {\n",
" real mu;\n",
" real sigma;\n",
"}\n",
"\n",
"# 事前分布の設定\n",
"model {\n",
" for (i in 1:N) {\n",
" leaf_length[i] ~ normal(mu, sigma);\n",
" }\n",
"}\n",
"```"
],
"metadata": {
"id": "Yz9-jI3dmYoP"
}
},
{
"cell_type": "code",
"source": [
"# Stan用の設定ファイルをダウンロード\n",
"system(\"wget https://raw.githubusercontent.com/slt666666/biostatistics_text_wed/refs/heads/main/source/_static/data/chapter11_mcmc.stan\")"
],
"metadata": {
"id": "Z6Ao4SdkZxKu"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"では実際に`Stan`を動かしていきます。\n",
"\n",
"まずは`rstan`パッケージを読み込みます。"
],
"metadata": {
"id": "ipSINAJgnT_p"
}
},
{
"cell_type": "code",
"source": [
"# rstanパッケージの読み込み\n",
"library(rstan)\n",
"\n",
"# 計算の高速化設定\n",
"rstan_options(auto_write = TRUE)\n",
"options(mc.cores = parallel::detectCores())"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "JR3fg-7pgxKA",
"outputId": "da7da5e2-c492-40d0-8510-75da6eab9416"
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stderr",
"text": [
"Loading required package: StanHeaders\n",
"\n",
"\n",
"rstan version 2.32.7 (Stan version 2.32.2)\n",
"\n",
"\n",
"For execution on a local, multicore CPU with excess RAM we recommend calling\n",
"options(mc.cores = parallel::detectCores()).\n",
"To avoid recompilation of unchanged Stan programs, we recommend calling\n",
"rstan_options(auto_write = TRUE)\n",
"For within-chain threading using `reduce_sum()` or `map_rect()` Stan functions,\n",
"change `threads_per_chain` option:\n",
"rstan_options(threads_per_chain = 1)\n",
"\n",
"\n"
]
}
]
},
{
"cell_type": "markdown",
"source": [
"続いて、観測データをStanで動かす用に少し整えます。"
],
"metadata": {
"id": "tZrzioezxD9G"
}
},
{
"cell_type": "code",
"source": [
"# 観測データをrstan用にまとめる\n",
"sample_size <- nrow(data)\n",
"data_list <- list(leaf_length = data$leaf_length, N = sample_size)\n",
"data_list"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 132
},
"id": "RWnLrVrEhWzC",
"outputId": "8b67bc01-84ef-4d55-8bd0-d938aa1d9f47"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/html": [
"\n",
"\t- $leaf_length
\n",
"\t\t- \n",
"
- 3.41
- 3.7
- 3.95
- 5.29
- 2.8
- 3.72
- 2.03
- 2.9
- 3.83
- 3
- 3.97
- 2.34
- 1.24
- 3.78
- 3.33
- 2.42
- 2.3
- 2.3
- 4.97
- 3.68
- 4.34
- 4.02
- 2.53
- 1.68
- 1.85
- 2.44
- 1.91
- 2.24
- 3.57
- 1.37
\n",
" \n",
"\t- $N
\n",
"\t\t- 30
\n",
"
\n"
],
"text/markdown": "$leaf_length\n: 1. 3.41\n2. 3.7\n3. 3.95\n4. 5.29\n5. 2.8\n6. 3.72\n7. 2.03\n8. 2.9\n9. 3.83\n10. 3\n11. 3.97\n12. 2.34\n13. 1.24\n14. 3.78\n15. 3.33\n16. 2.42\n17. 2.3\n18. 2.3\n19. 4.97\n20. 3.68\n21. 4.34\n22. 4.02\n23. 2.53\n24. 1.68\n25. 1.85\n26. 2.44\n27. 1.91\n28. 2.24\n29. 3.57\n30. 1.37\n\n\n\n$N\n: 30\n\n\n",
"text/latex": "\\begin{description}\n\\item[\\$leaf\\_length] \\begin{enumerate*}\n\\item 3.41\n\\item 3.7\n\\item 3.95\n\\item 5.29\n\\item 2.8\n\\item 3.72\n\\item 2.03\n\\item 2.9\n\\item 3.83\n\\item 3\n\\item 3.97\n\\item 2.34\n\\item 1.24\n\\item 3.78\n\\item 3.33\n\\item 2.42\n\\item 2.3\n\\item 2.3\n\\item 4.97\n\\item 3.68\n\\item 4.34\n\\item 4.02\n\\item 2.53\n\\item 1.68\n\\item 1.85\n\\item 2.44\n\\item 1.91\n\\item 2.24\n\\item 3.57\n\\item 1.37\n\\end{enumerate*}\n\n\\item[\\$N] 30\n\\end{description}\n",
"text/plain": [
"$leaf_length\n",
" [1] 3.41 3.70 3.95 5.29 2.80 3.72 2.03 2.90 3.83 3.00 3.97 2.34 1.24 3.78 3.33\n",
"[16] 2.42 2.30 2.30 4.97 3.68 4.34 4.02 2.53 1.68 1.85 2.44 1.91 2.24 3.57 1.37\n",
"\n",
"$N\n",
"[1] 30\n"
]
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"`stan`関数で、観測データに基づきMCMCを実施します。\n",
"\n",
"先ほど少し触れた、乱数をどれだけ生成するか(`iter`)や、何セット生成するか(`chains`)、初期値に引っ張られている最初の部分をどれだけ捨てるか(`warmup`)等を設定可能です。"
],
"metadata": {
"id": "RmR42HbqxWV2"
}
},
{
"cell_type": "code",
"source": [
"# 事後分布に従う乱数を設定した条件で生成する\n",
"mcmc_result <- stan(\n",
" file = \"chapter11_mcmc.stan\",\n",
" data = data_list,\n",
" seed = 1,\n",
" chains = 4,\n",
" iter = 500,\n",
" warmup = 100,\n",
" thin = 1\n",
")"
],
"metadata": {
"id": "urP9AeJjhoDu",
"colab": {
"base_uri": "https://localhost:8080/"
},
"outputId": "081def53-6c76-4d95-f1e3-1b944482e76b"
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"on: 400 / 500 [ 80%] (Sampling)\n",
"Chain 2: Iteration: 450 / 500 [ 90%] (Sampling)\n",
"Chain 2: Iteration: 500 / 500 [100%] (Sampling)\n",
"Chain 2: \n",
"Chain 2: Elapsed Time: 0.008 seconds (Warm-up)\n",
"Chain 2: 0.02 seconds (Sampling)\n",
"Chain 2: 0.028 seconds (Total)\n",
"Chain 2: \n"
]
}
]
},
{
"cell_type": "markdown",
"source": [
"`traceplot`関数でMCMCによって生成された、$\\mu$と$\\sigma$それぞれの事後分布に従う乱数のプロットが確認できます。"
],
"metadata": {
"id": "D3C0oJ8Jxw7F"
}
},
{
"cell_type": "code",
"source": [
"# 各パラメータ毎の、事後分布に従う乱数のプロットを描写\n",
"traceplot(mcmc_result, inc_warmup = TRUE)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 437
},
"id": "y9L8hnGPirO3",
"outputId": "f9894bc9-8f1f-4dc1-8ba9-5ce4df215424"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"plot without title"
],
"image/png": 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QwhA6TiL4d9UxpVp720djcuf32Pr9418MRtyXO369Fd7btrAnBwz0he8bT1sUu7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LHti4Z+av79r1B//lcnS7gHwY8m06vdLf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\nEgx2AAAAkmCwAwAAkMS/ACq+7YXfpDWeAAAAAElFTkSuQmCC"
},
"metadata": {
"image/png": {
"width": 420,
"height": 420
}
}
}
]
},
{
"cell_type": "markdown",
"source": [
"実際に生成された乱数は`extract`関数で取り出す事が出来ます。\n",
"\n",
"生成された$\\mu$の事後分布に従う乱数を確認してみると、"
],
"metadata": {
"id": "c0BJct8K1C9i"
}
},
{
"cell_type": "code",
"source": [
"# 乱数の一覧を表示(今回はμについてのみ)\n",
"mcmc_sample <- rstan::extract(mcmc_result, permuted = FALSE)\n",
"mu_mcmc <- mcmc_sample[, , \"mu\"]\n",
"mu_mcmc"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"id": "flsWCisZix-d",
"outputId": "243fd354-4110-4ba3-e1c7-d0e20fa7c989"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/html": [
"\n",
"A matrix: 400 × 4 of type dbl\n",
"\n",
"\t| chain:1 | chain:2 | chain:3 | chain:4 |
|---|
\n",
"\n",
"\n",
"\t| 3.167323 | 3.107269 | 3.137632 | 2.945441 |
\n",
"\t| 3.158748 | 2.954508 | 2.945913 | 3.153128 |
\n",
"\t| 3.012268 | 2.898971 | 3.252446 | 3.387234 |
\n",
"\t| 2.921264 | 2.901714 | 3.327342 | 3.197402 |
\n",
"\t| 2.987323 | 3.036068 | 3.135673 | 2.911286 |
\n",
"\t| 3.132632 | 2.986705 | 3.053652 | 3.033662 |
\n",
"\t| 3.088383 | 2.958998 | 2.585260 | 3.201880 |
\n",
"\t| 2.959421 | 3.073231 | 2.999887 | 2.521098 |
\n",
"\t| 3.042668 | 2.964002 | 3.318621 | 3.033941 |
\n",
"\t| 3.267857 | 2.937091 | 3.429638 | 3.226385 |
\n",
"\t| 2.991114 | 3.058901 | 3.107264 | 3.112874 |
\n",
"\t| 2.898987 | 2.964952 | 3.391698 | 3.060725 |
\n",
"\t| 3.078447 | 3.249246 | 2.969146 | 3.112372 |
\n",
"\t| 2.881136 | 3.117366 | 2.995423 | 3.143285 |
\n",
"\t| 3.168513 | 3.163378 | 3.047915 | 3.294352 |
\n",
"\t| 2.929619 | 3.006824 | 3.256087 | 3.026518 |
\n",
"\t| 3.162431 | 3.235590 | 2.793152 | 3.008537 |
\n",
"\t| 2.921232 | 2.750609 | 2.922763 | 3.008537 |
\n",
"\t| 3.336976 | 2.794308 | 2.843784 | 2.791023 |
\n",
"\t| 3.301000 | 2.713182 | 2.762237 | 3.235705 |
\n",
"\t| 3.434762 | 2.791725 | 3.501821 | 2.868957 |
\n",
"\t| 3.551916 | 2.630766 | 3.344492 | 3.281196 |
\n",
"\t| 2.956426 | 2.622577 | 3.151397 | 3.578281 |
\n",
"\t| 3.047474 | 2.608363 | 3.028146 | 3.321705 |
\n",
"\t| 3.008846 | 2.996881 | 3.163145 | 3.082944 |
\n",
"\t| 3.049499 | 3.095770 | 2.803022 | 3.249558 |
\n",
"\t| 3.121102 | 2.679215 | 3.056800 | 3.040097 |
\n",
"\t| 3.172086 | 2.842131 | 3.189916 | 3.386811 |
\n",
"\t| 2.804062 | 3.103470 | 2.925003 | 3.306485 |
\n",
"\t| 3.082550 | 3.070847 | 3.056858 | 2.883389 |
\n",
"\t| ⋮ | ⋮ | ⋮ | ⋮ |
\n",
"\t| 3.203721 | 3.247525 | 2.992605 | 3.216896 |
\n",
"\t| 3.577929 | 3.577007 | 2.916364 | 2.626270 |
\n",
"\t| 3.204219 | 2.687873 | 3.081554 | 3.263883 |
\n",
"\t| 2.777291 | 2.798245 | 2.962036 | 3.150704 |
\n",
"\t| 2.886785 | 2.806866 | 3.091254 | 3.272017 |
\n",
"\t| 3.107557 | 2.874603 | 2.983559 | 3.255215 |
\n",
"\t| 2.870461 | 2.901519 | 3.104152 | 3.114434 |
\n",
"\t| 3.108692 | 2.841913 | 2.965541 | 3.139302 |
\n",
"\t| 3.160798 | 2.883811 | 3.048992 | 2.960382 |
\n",
"\t| 3.233902 | 3.005365 | 3.005222 | 2.912974 |
\n",
"\t| 2.769425 | 3.249851 | 2.990102 | 2.856859 |
\n",
"\t| 2.768880 | 3.149935 | 2.907080 | 2.889390 |
\n",
"\t| 3.232266 | 3.214242 | 2.999129 | 2.691058 |
\n",
"\t| 3.005913 | 2.960399 | 3.051999 | 3.193684 |
\n",
"\t| 2.970707 | 2.997429 | 2.971520 | 3.224793 |
\n",
"\t| 2.916883 | 2.932452 | 2.947030 | 3.287863 |
\n",
"\t| 2.913657 | 3.188352 | 2.774632 | 2.850115 |
\n",
"\t| 2.677152 | 3.052175 | 3.306482 | 2.854481 |
\n",
"\t| 3.253922 | 2.781623 | 3.315664 | 3.017958 |
\n",
"\t| 3.113329 | 2.867124 | 3.283247 | 3.190078 |
\n",
"\t| 3.104619 | 3.008510 | 2.808756 | 3.244952 |
\n",
"\t| 2.998002 | 2.963301 | 2.707647 | 2.916113 |
\n",
"\t| 3.037929 | 2.963301 | 2.794969 | 3.016596 |
\n",
"\t| 2.941871 | 3.106839 | 2.794969 | 2.975226 |
\n",
"\t| 3.009796 | 3.389576 | 3.389445 | 2.662658 |
\n",
"\t| 3.061508 | 3.103502 | 3.145590 | 2.532223 |
\n",
"\t| 3.122780 | 2.786339 | 3.021533 | 2.588823 |
\n",
"\t| 3.019956 | 2.983126 | 2.990337 | 3.488857 |
\n",
"\t| 3.229480 | 2.938959 | 3.017920 | 3.335616 |
\n",
"\t| 2.986012 | 3.100848 | 3.367453 | 3.037148 |
\n",
"\n",
"
\n"
],
"text/markdown": "\nA matrix: 400 × 4 of type dbl\n\n| chain:1 | chain:2 | chain:3 | chain:4 |\n|---|---|---|---|\n| 3.167323 | 3.107269 | 3.137632 | 2.945441 |\n| 3.158748 | 2.954508 | 2.945913 | 3.153128 |\n| 3.012268 | 2.898971 | 3.252446 | 3.387234 |\n| 2.921264 | 2.901714 | 3.327342 | 3.197402 |\n| 2.987323 | 3.036068 | 3.135673 | 2.911286 |\n| 3.132632 | 2.986705 | 3.053652 | 3.033662 |\n| 3.088383 | 2.958998 | 2.585260 | 3.201880 |\n| 2.959421 | 3.073231 | 2.999887 | 2.521098 |\n| 3.042668 | 2.964002 | 3.318621 | 3.033941 |\n| 3.267857 | 2.937091 | 3.429638 | 3.226385 |\n| 2.991114 | 3.058901 | 3.107264 | 3.112874 |\n| 2.898987 | 2.964952 | 3.391698 | 3.060725 |\n| 3.078447 | 3.249246 | 2.969146 | 3.112372 |\n| 2.881136 | 3.117366 | 2.995423 | 3.143285 |\n| 3.168513 | 3.163378 | 3.047915 | 3.294352 |\n| 2.929619 | 3.006824 | 3.256087 | 3.026518 |\n| 3.162431 | 3.235590 | 2.793152 | 3.008537 |\n| 2.921232 | 2.750609 | 2.922763 | 3.008537 |\n| 3.336976 | 2.794308 | 2.843784 | 2.791023 |\n| 3.301000 | 2.713182 | 2.762237 | 3.235705 |\n| 3.434762 | 2.791725 | 3.501821 | 2.868957 |\n| 3.551916 | 2.630766 | 3.344492 | 3.281196 |\n| 2.956426 | 2.622577 | 3.151397 | 3.578281 |\n| 3.047474 | 2.608363 | 3.028146 | 3.321705 |\n| 3.008846 | 2.996881 | 3.163145 | 3.082944 |\n| 3.049499 | 3.095770 | 2.803022 | 3.249558 |\n| 3.121102 | 2.679215 | 3.056800 | 3.040097 |\n| 3.172086 | 2.842131 | 3.189916 | 3.386811 |\n| 2.804062 | 3.103470 | 2.925003 | 3.306485 |\n| 3.082550 | 3.070847 | 3.056858 | 2.883389 |\n| ⋮ | ⋮ | ⋮ | ⋮ |\n| 3.203721 | 3.247525 | 2.992605 | 3.216896 |\n| 3.577929 | 3.577007 | 2.916364 | 2.626270 |\n| 3.204219 | 2.687873 | 3.081554 | 3.263883 |\n| 2.777291 | 2.798245 | 2.962036 | 3.150704 |\n| 2.886785 | 2.806866 | 3.091254 | 3.272017 |\n| 3.107557 | 2.874603 | 2.983559 | 3.255215 |\n| 2.870461 | 2.901519 | 3.104152 | 3.114434 |\n| 3.108692 | 2.841913 | 2.965541 | 3.139302 |\n| 3.160798 | 2.883811 | 3.048992 | 2.960382 |\n| 3.233902 | 3.005365 | 3.005222 | 2.912974 |\n| 2.769425 | 3.249851 | 2.990102 | 2.856859 |\n| 2.768880 | 3.149935 | 2.907080 | 2.889390 |\n| 3.232266 | 3.214242 | 2.999129 | 2.691058 |\n| 3.005913 | 2.960399 | 3.051999 | 3.193684 |\n| 2.970707 | 2.997429 | 2.971520 | 3.224793 |\n| 2.916883 | 2.932452 | 2.947030 | 3.287863 |\n| 2.913657 | 3.188352 | 2.774632 | 2.850115 |\n| 2.677152 | 3.052175 | 3.306482 | 2.854481 |\n| 3.253922 | 2.781623 | 3.315664 | 3.017958 |\n| 3.113329 | 2.867124 | 3.283247 | 3.190078 |\n| 3.104619 | 3.008510 | 2.808756 | 3.244952 |\n| 2.998002 | 2.963301 | 2.707647 | 2.916113 |\n| 3.037929 | 2.963301 | 2.794969 | 3.016596 |\n| 2.941871 | 3.106839 | 2.794969 | 2.975226 |\n| 3.009796 | 3.389576 | 3.389445 | 2.662658 |\n| 3.061508 | 3.103502 | 3.145590 | 2.532223 |\n| 3.122780 | 2.786339 | 3.021533 | 2.588823 |\n| 3.019956 | 2.983126 | 2.990337 | 3.488857 |\n| 3.229480 | 2.938959 | 3.017920 | 3.335616 |\n| 2.986012 | 3.100848 | 3.367453 | 3.037148 |\n\n",
"text/latex": "A matrix: 400 × 4 of type dbl\n\\begin{tabular}{llll}\n chain:1 & chain:2 & chain:3 & chain:4\\\\\n\\hline\n\t 3.167323 & 3.107269 & 3.137632 & 2.945441\\\\\n\t 3.158748 & 2.954508 & 2.945913 & 3.153128\\\\\n\t 3.012268 & 2.898971 & 3.252446 & 3.387234\\\\\n\t 2.921264 & 2.901714 & 3.327342 & 3.197402\\\\\n\t 2.987323 & 3.036068 & 3.135673 & 2.911286\\\\\n\t 3.132632 & 2.986705 & 3.053652 & 3.033662\\\\\n\t 3.088383 & 2.958998 & 2.585260 & 3.201880\\\\\n\t 2.959421 & 3.073231 & 2.999887 & 2.521098\\\\\n\t 3.042668 & 2.964002 & 3.318621 & 3.033941\\\\\n\t 3.267857 & 2.937091 & 3.429638 & 3.226385\\\\\n\t 2.991114 & 3.058901 & 3.107264 & 3.112874\\\\\n\t 2.898987 & 2.964952 & 3.391698 & 3.060725\\\\\n\t 3.078447 & 3.249246 & 2.969146 & 3.112372\\\\\n\t 2.881136 & 3.117366 & 2.995423 & 3.143285\\\\\n\t 3.168513 & 3.163378 & 3.047915 & 3.294352\\\\\n\t 2.929619 & 3.006824 & 3.256087 & 3.026518\\\\\n\t 3.162431 & 3.235590 & 2.793152 & 3.008537\\\\\n\t 2.921232 & 2.750609 & 2.922763 & 3.008537\\\\\n\t 3.336976 & 2.794308 & 2.843784 & 2.791023\\\\\n\t 3.301000 & 2.713182 & 2.762237 & 3.235705\\\\\n\t 3.434762 & 2.791725 & 3.501821 & 2.868957\\\\\n\t 3.551916 & 2.630766 & 3.344492 & 3.281196\\\\\n\t 2.956426 & 2.622577 & 3.151397 & 3.578281\\\\\n\t 3.047474 & 2.608363 & 3.028146 & 3.321705\\\\\n\t 3.008846 & 2.996881 & 3.163145 & 3.082944\\\\\n\t 3.049499 & 3.095770 & 2.803022 & 3.249558\\\\\n\t 3.121102 & 2.679215 & 3.056800 & 3.040097\\\\\n\t 3.172086 & 2.842131 & 3.189916 & 3.386811\\\\\n\t 2.804062 & 3.103470 & 2.925003 & 3.306485\\\\\n\t 3.082550 & 3.070847 & 3.056858 & 2.883389\\\\\n\t ⋮ & ⋮ & ⋮ & ⋮\\\\\n\t 3.203721 & 3.247525 & 2.992605 & 3.216896\\\\\n\t 3.577929 & 3.577007 & 2.916364 & 2.626270\\\\\n\t 3.204219 & 2.687873 & 3.081554 & 3.263883\\\\\n\t 2.777291 & 2.798245 & 2.962036 & 3.150704\\\\\n\t 2.886785 & 2.806866 & 3.091254 & 3.272017\\\\\n\t 3.107557 & 2.874603 & 2.983559 & 3.255215\\\\\n\t 2.870461 & 2.901519 & 3.104152 & 3.114434\\\\\n\t 3.108692 & 2.841913 & 2.965541 & 3.139302\\\\\n\t 3.160798 & 2.883811 & 3.048992 & 2.960382\\\\\n\t 3.233902 & 3.005365 & 3.005222 & 2.912974\\\\\n\t 2.769425 & 3.249851 & 2.990102 & 2.856859\\\\\n\t 2.768880 & 3.149935 & 2.907080 & 2.889390\\\\\n\t 3.232266 & 3.214242 & 2.999129 & 2.691058\\\\\n\t 3.005913 & 2.960399 & 3.051999 & 3.193684\\\\\n\t 2.970707 & 2.997429 & 2.971520 & 3.224793\\\\\n\t 2.916883 & 2.932452 & 2.947030 & 3.287863\\\\\n\t 2.913657 & 3.188352 & 2.774632 & 2.850115\\\\\n\t 2.677152 & 3.052175 & 3.306482 & 2.854481\\\\\n\t 3.253922 & 2.781623 & 3.315664 & 3.017958\\\\\n\t 3.113329 & 2.867124 & 3.283247 & 3.190078\\\\\n\t 3.104619 & 3.008510 & 2.808756 & 3.244952\\\\\n\t 2.998002 & 2.963301 & 2.707647 & 2.916113\\\\\n\t 3.037929 & 2.963301 & 2.794969 & 3.016596\\\\\n\t 2.941871 & 3.106839 & 2.794969 & 2.975226\\\\\n\t 3.009796 & 3.389576 & 3.389445 & 2.662658\\\\\n\t 3.061508 & 3.103502 & 3.145590 & 2.532223\\\\\n\t 3.122780 & 2.786339 & 3.021533 & 2.588823\\\\\n\t 3.019956 & 2.983126 & 2.990337 & 3.488857\\\\\n\t 3.229480 & 2.938959 & 3.017920 & 3.335616\\\\\n\t 2.986012 & 3.100848 & 3.367453 & 3.037148\\\\\n\\end{tabular}\n",
"text/plain": [
" chain:1 chain:2 chain:3 chain:4 \n",
" [1,] 3.167323 3.107269 3.137632 2.945441\n",
" [2,] 3.158748 2.954508 2.945913 3.153128\n",
" [3,] 3.012268 2.898971 3.252446 3.387234\n",
" [4,] 2.921264 2.901714 3.327342 3.197402\n",
" [5,] 2.987323 3.036068 3.135673 2.911286\n",
" [6,] 3.132632 2.986705 3.053652 3.033662\n",
" [7,] 3.088383 2.958998 2.585260 3.201880\n",
" [8,] 2.959421 3.073231 2.999887 2.521098\n",
" [9,] 3.042668 2.964002 3.318621 3.033941\n",
"[10,] 3.267857 2.937091 3.429638 3.226385\n",
"[11,] 2.991114 3.058901 3.107264 3.112874\n",
"[12,] 2.898987 2.964952 3.391698 3.060725\n",
"[13,] 3.078447 3.249246 2.969146 3.112372\n",
"[14,] 2.881136 3.117366 2.995423 3.143285\n",
"[15,] 3.168513 3.163378 3.047915 3.294352\n",
"[16,] 2.929619 3.006824 3.256087 3.026518\n",
"[17,] 3.162431 3.235590 2.793152 3.008537\n",
"[18,] 2.921232 2.750609 2.922763 3.008537\n",
"[19,] 3.336976 2.794308 2.843784 2.791023\n",
"[20,] 3.301000 2.713182 2.762237 3.235705\n",
"[21,] 3.434762 2.791725 3.501821 2.868957\n",
"[22,] 3.551916 2.630766 3.344492 3.281196\n",
"[23,] 2.956426 2.622577 3.151397 3.578281\n",
"[24,] 3.047474 2.608363 3.028146 3.321705\n",
"[25,] 3.008846 2.996881 3.163145 3.082944\n",
"[26,] 3.049499 3.095770 2.803022 3.249558\n",
"[27,] 3.121102 2.679215 3.056800 3.040097\n",
"[28,] 3.172086 2.842131 3.189916 3.386811\n",
"[29,] 2.804062 3.103470 2.925003 3.306485\n",
"[30,] 3.082550 3.070847 3.056858 2.883389\n",
"[31,] ⋮ ⋮ ⋮ ⋮ \n",
"[32,] 3.203721 3.247525 2.992605 3.216896\n",
"[33,] 3.577929 3.577007 2.916364 2.626270\n",
"[34,] 3.204219 2.687873 3.081554 3.263883\n",
"[35,] 2.777291 2.798245 2.962036 3.150704\n",
"[36,] 2.886785 2.806866 3.091254 3.272017\n",
"[37,] 3.107557 2.874603 2.983559 3.255215\n",
"[38,] 2.870461 2.901519 3.104152 3.114434\n",
"[39,] 3.108692 2.841913 2.965541 3.139302\n",
"[40,] 3.160798 2.883811 3.048992 2.960382\n",
"[41,] 3.233902 3.005365 3.005222 2.912974\n",
"[42,] 2.769425 3.249851 2.990102 2.856859\n",
"[43,] 2.768880 3.149935 2.907080 2.889390\n",
"[44,] 3.232266 3.214242 2.999129 2.691058\n",
"[45,] 3.005913 2.960399 3.051999 3.193684\n",
"[46,] 2.970707 2.997429 2.971520 3.224793\n",
"[47,] 2.916883 2.932452 2.947030 3.287863\n",
"[48,] 2.913657 3.188352 2.774632 2.850115\n",
"[49,] 2.677152 3.052175 3.306482 2.854481\n",
"[50,] 3.253922 2.781623 3.315664 3.017958\n",
"[51,] 3.113329 2.867124 3.283247 3.190078\n",
"[52,] 3.104619 3.008510 2.808756 3.244952\n",
"[53,] 2.998002 2.963301 2.707647 2.916113\n",
"[54,] 3.037929 2.963301 2.794969 3.016596\n",
"[55,] 2.941871 3.106839 2.794969 2.975226\n",
"[56,] 3.009796 3.389576 3.389445 2.662658\n",
"[57,] 3.061508 3.103502 3.145590 2.532223\n",
"[58,] 3.122780 2.786339 3.021533 2.588823\n",
"[59,] 3.019956 2.983126 2.990337 3.488857\n",
"[60,] 3.229480 2.938959 3.017920 3.335616\n",
"[61,] 2.986012 3.100848 3.367453 3.037148"
]
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"この乱数をグラフ化すると、事後分布の形が分かります。"
],
"metadata": {
"id": "1kihnd1r1XOT"
}
},
{
"cell_type": "code",
"source": [
"# 生成した乱数から事後分布の形を図示(今回はμについてのみ)\n",
"library(ggplot2)\n",
"\n",
"mu_df <- data.frame(mu_mcmc = mu_mcmc)\n",
"\n",
"g <- ggplot(data=mu_df, aes(x=mu_mcmc))\n",
"g <- g + geom_histogram()\n",
"g"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 493
},
"id": "znRB1jCajbbr",
"outputId": "ac3d1b7d-1cc0-4dc2-f44c-d86a30419346"
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stderr",
"text": [
"Warning message in `[<-.data.frame`(`*tmp*`, , x_vars, value = list(x = c(3.16732265137227, :\n",
"“replacement element 1 has 1600 rows to replace 400 rows”\n",
"\u001b[1m\u001b[22m`stat_bin()` using `bins = 30`. Pick better value `binwidth`.\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"plot without title"
],
"image/png": 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IRESC4ISYOQRAipSPapCYmQXBCSBiGJ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\nAUICDPw/AThq6Lpw6IAAAAAASUVORK5CYII="
},
"metadata": {
"image/png": {
"width": 420,
"height": 420
}
}
}
]
},
{
"cell_type": "markdown",
"source": [
"また、`print`関数を使用することで、生成した乱数に基づいたパーセント点を表示する事が出来ます。\n",
"\n"
],
"metadata": {
"id": "xwIX-2tB1e4m"
}
},
{
"cell_type": "code",
"source": [
"# 生成した乱数から事後分布のP(a≤μ≤b)などを求める\n",
"print(\n",
" mcmc_result,\n",
" probs = c(0.025, 0.5, 0.975)\n",
")"
],
"metadata": {
"id": "2Cpc9s1DiDCN",
"colab": {
"base_uri": "https://localhost:8080/"
},
"outputId": "7a768e46-125e-4756-d1c0-a50d849c9d53"
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Inference for Stan model: anon_model.\n",
"4 chains, each with iter=500; warmup=100; thin=1; \n",
"post-warmup draws per chain=400, total post-warmup draws=1600.\n",
"\n",
" mean se_mean sd 2.5% 50% 97.5% n_eff Rhat\n",
"mu 3.03 0.01 0.20 2.63 3.02 3.43 875 1\n",
"sigma 1.08 0.00 0.15 0.84 1.07 1.41 1553 1\n",
"lp__ -16.49 0.04 1.02 -19.28 -16.20 -15.50 769 1\n",
"\n",
"Samples were drawn using NUTS(diag_e) at Mon Jan 5 05:42:46 2026.\n",
"For each parameter, n_eff is a crude measure of effective sample size,\n",
"and Rhat is the potential scale reduction factor on split chains (at \n",
"convergence, Rhat=1).\n"
]
}
]
},
{
"cell_type": "markdown",
"source": [
"この結果から、$\\mu$の事後分布から$P(a \\leqq \\mu \\leqq b)=0.95$となる値が分かります。"
],
"metadata": {
"id": "lmHW5-tE1ytW"
}
},
{
"cell_type": "markdown",
"source": [
"この様な形で、事前分布を仮定し、得られたデータに基づいて事後分布を得ることで、統計モデルのパラメータ等を推定する方法がベイズ統計の考え方になります。\n",
"\n",
"細かい手法や計算等は今は理解しなくて良いですが、こういったアプローチの統計学があるということを覚えておくと良いかと思います。\n",
"\n",
"また`Stan`についても殆ど説明はしませんでしたが、使いこなせると様々な統計モデルを自在に構築する事が出来るようになります。"
],
"metadata": {
"id": "-C51o1QN-Qdn"
}
}
]
}