{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\t
\n", "\t\tこの企画は、雑誌や教科書にでているグラフをSageで再現し、\n", "\t\tグラフの意味を理解すると共にSageの使い方をマスターすることを目的としています。\n", "\t
\n", "\t\n", "\t\t今回は、道具としてのベイズ統計\n", "\t\tのp196の学生のテスト結果を階層ベイズ法を使って表現した図を題材にします。\n", "\t
\n", "\t\n",
"\t\t
\n",
"\t
\n", "\t\t最初に必要なライブラリーやパッケージをロードしておきます。\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# RとPandasのデータフレームを相互に変換する関数を読み込む\n", "# Rの必要なライブラリ\n", "r('library(ggplot2)')\n", "r('library(jsonlite)')\n", "\n", "# python用のパッケージ\n", "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt \n", "import seaborn as sns\n", "%matplotlib inline\n", "\n", "# jupyter用のdisplayメソッド\n", "from IPython.display import display, Latex, HTML, Math, JSON\n", "# sageユーティリティ\n", "load('script/sage_util.py')\n", "# Rユーティリティ\n", "load('script/RUtil.py')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\t学生のテスト結果は、10点満点中、Xのような得点になっています。\n", "\t
\n", "\t\n", "\t\tこれまで、度数分布図はRを使っていましたが、点数毎のカウント数を保持する辞書型変数を\n", "\t\tplot関数に渡すと度数分布が表示されることが分かりました。\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[1] 20" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X = [1, 0, 10, 4, 10, 10, 10, 6, 4, 10, 1, 9, 0, 5, 10, 7, 1, 9, 2, 8]\n", "N = len(X)\n", "r(X).name('X')\n", "r(N).name('N')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\t度数を計算する関数_mkHistを以下のように定義します。\n", "\t\t処理は、データの値毎にカウント数をアップしているだけです。\n", "\t\tポイントとしては、hist.setdefaultを使って要素が未定義\n", "\t\tの場合に、0をデフォルト値としているところです。\n", "\t
\n", "\t\n", "\t\t作成した度数分布図をhist_plt変数に保持しておきます。\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# 度数分布の作成\n", "def _mkHist(data):\n", " hist = {}\n", " for k in data:\n", " hist.setdefault(k,0)\n", " hist[k] += 1\n", " return hist" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Xの度数分布を表示\n", "hist_plt = list_plot(_mkHist(X), zorder=2)\n", "hist_plt.show(figsize=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\t階層ベイズのギブス・サンプリングを行うプログラムJAGSをRから使うためのライブラリ\n", "\t\tを呼び込みます。\n", "\t
\n", "\t\n", "\t\trjagsについては、singular piont氏の「\n", "\t\tJAGSを使ってギブスサンプリングを試してみた \n", "\t\t」を参考にしました。\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ " [1] \"rjags\" \"coda\" \"jsonlite\" \"ggplot2\" \"stats\" \"graphics\" \"grDevices\" \"utils\" \n", " [9] \"datasets\" \"methods\" \"base\" " ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#r(\"install.packages('coda')\")\n", "#r(\"install.packages('rjags', version='3.15', dependencies=TRUE)\")\n", "r('library(rjags)')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "\n", "\t\n", "\t\t学生の持つ問題解決能力をq(皆同じ値と仮定)とすると、i番目の学生が10点満点中k点を取る確率$p_i$は以下のようになります。\n", "$$\n", "\t\tp_i = {}_{10} C_k q^k (1 - q)^{10 - k}\n", "$$\t\t\n", "\t
\n", "\n", "\n", "\t\n", "\t\tjagsのモデルファイルは、とても簡単です。\n", "\t
\n", "\t\n", "\t\ti番目の学生得点は、dbin(q, 10)に比例し、\n", "$$\n", "\t\tx_i \\sim dbin(q, 10)\n", "$$\t\n", "\t\t問題解決能力をqは、一様分布dunif(0, 1)に比例すると仮定します。\n", "$$\n", "\t\tq \\sim dunif(0, 1)\n", "$$\t\t\t\n", "\t
\n", "\t\n", "\t\tこれをJAGSのモデルで記述すると、以下のようになります。(とてもストレートで読みやすいと思いませんか)\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Overwriting data/ex_5.jags\n" ] } ], "source": [ "%%writefile data/ex_5.jags\n", "model {\n", " for (i in 1:N) {\n", " x[i] ~ dbin(q, 10) \n", " }\n", " q ~ dunif(0,1)\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\t上記のモデルを使ってjagsのモデルオブジェクトを生成します。\n", "\t
\n", "\t\n", "\t\tdataとして、学生の得点Xとサンプル数Nを渡します。\n", "\t
\n", "\t\n", "\t\tn.chainsで4つのチェインを指定し、n.adapt=1000で稼働検査期間(buring in period)を1000と指定します。\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# mcmcモデルの作成\n", "junk = r('mcmc.model <- jags.model(\"data/ex_5.jags\", data=list(\"x\"=X,\"N\"=N), n.chains=4, n.adapt=1000)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\tサンプリングには、jagsをそのまま使うのではなく、codaを使ってサンプリングを行います。\n", "\t\tこれによって、サンプリング後の収束判定や変数の分布図のプロット等がとても簡単になります。\n", "\t
\n", "\t\n", "\t\tcoda.samplesの引数で、サンプリングする変数名qとサンプリング数1000を指定します。\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# サンプリング(途中経過が出力されるので、junkで吸収)\n", "junk = r('mcmc.sample <- coda.samples(mcmc.model, c(\"q\"), 1000)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\tsummary関数を使ってサンプリング結果を出力します。\n", "\t
\n", "\t\n", "\t\tqの平均値が0.5837391、qの標準偏差が0.0349724と求まっています。\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "\n", "Iterations = 1:1000\n", "Thinning interval = 1 \n", "Number of chains = 4 \n", "Sample size per chain = 1000 \n", "\n", "1. Empirical mean and standard deviation for each variable,\n", " plus standard error of the mean:\n", "\n", " Mean SD Naive SE Time-series SE \n", " 0.5838555 0.0347887 0.0005501 0.0005257 \n", "\n", "2. Quantiles for each variable:\n", "\n", " 2.5% 25% 50% 75% 97.5% \n", "0.5145 0.5607 0.5837 0.6070 0.6533 \n" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 出力結果\n", "r('summary(mcmc.sample)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\t変数の収束を数値で判断する場合には、codaのgelman.plot等を使いますが、\n", "\t\tここでは、plot関数でqのサンプルリング状況とqの密度分布を表示してその収束\n", "\t\t具合を表示します。(pdfからpngへの変換に時間がかかるためグラフの例はこれだけにします)\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Fr6ptKvPDqejtUMtgu7OCu6t0qzIdM8O18WdU9OksvaoXXRt6uVHXE3S4/kNU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qlUJz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\n", "text/plain": [ "\n", "\t\tjagsの計算結果をsageに戻すには、sageobj関数を使用してsummary結果を\n", "\t\tsageに渡します。\n", "\t
\n", "\t\n", "\t\tsummaryをsageobjに変換した結果を見やすくしたもの以下に示します。\n", "\t
\n", "\t\n", "\t\tDATAの中のstatistics辞書に含まれるDATAが結果であることが分かりました。\n", "\t\tこれを使ってqの統計情報をq_statに代入しています。\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# 統計情報をSageに戻る方法\n", "summary = sageobj(r('summary(mcmc.sample)'))" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "{'DATA': {'end': 1000,\n", " 'nchain': 4,\n", " 'quantiles': {'DATA': [0.514490020509135,\n", " 0.560679874496162,\n", " 0.583723358170264,\n", " 0.606952806527294,\n", " 0.653261601057],\n", " '_Names': ['2.5%', '25%', '50%', '75%', '97.5%']},\n", " 'start': 1,\n", " 'statistics': {'DATA': [0.58385552580395,\n", " 0.034788658624687,\n", " 0.000550056989980358,\n", " 0.000525669302561606],\n", " '_Names': ['Mean', 'SD', 'Naive SE', 'Time-series SE']},\n", " 'thin': 1},\n", " '_Names': ['statistics', 'quantiles', 'start', 'end', 'thin', 'nchain'],\n", " '_r_class': 'summary.mcmc'}" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "summary" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[0.58385552580395,\n", " 0.034788658624687,\n", " 0.000550056989980358,\n", " 0.000525669302561606]" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# summaryからqに関する統計情報を抽出\n", "q_stat = summary['DATA']['statistics']['DATA']; q_stat" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\tjagsを使ったギブス・サンプリングで求まったqを使って学生の得点確率pの確率分布を表示してみます。\n", "\t
\n", "\t\n", "\t\t_pで二項分布を定義し、0から10までの得点の確率分布(赤の線)を以下に示します。\n", "\t
\n", "\t\n", "\t\t学生の問題解決能力をqを一定としたために、分布が学生の得点分布をうまく表現できていません。\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# 二項分布を定義\n", "def _p(q, x):\n", " return binomial(10, x)*q^x*(1-q)^(10-x)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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RcYhKlWPss/Dcepv/0JHTKTqOUCwEykN9+CB0q5bB/uxz8Na5WXQcotKn0SBj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\nKxxpkpKScPLkSaSmpqJBgwa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"text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# pの確率分布をプロット\n", "q = q_stat[0]\n", "p_plt = list_plot([_p(q, x)*N for x in (0..10)], plotjoined=True, rgbcolor=\"red\")\n", "(hist_plt + p_plt).show(figsize=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\tそこで、個人の学習能力にばらつきがあると仮定したモデルを作成します。\n", "\t
\n", "\t\n", "\t\t学生iの問題解決能力を$q_i$とし、$q_i$が以下の学習曲線で変化すると仮定します。\n", "\t
\n", "\t\n", "\t\tこの学習曲線をロジットモデルと呼び、以下の式で表されます。\n", "$$\n", "\t\tlog\\frac{q_i}{1 - q_i} = \\beta + \\gamma_i\n", "$$\t\t\n", "\t
\n", "\t\n", "\t\t学生の問題解決能力は、クラスの全体の平均的な理解度合い$\\beta$とそれからのずれ\n", "\t\t$\\gamma_i$(これを個人の理解度と呼ぶことにしましょう)\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 個人差を考慮した階層ベイズモデル\n", "# 学習曲線(成長曲線と本では紹介)\n", "var('x')\n", "plot(1/(1 + e^(-x)), [x, -4, 4]).show(figsize=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\t個人の理解度正規分布を持つと仮定し、この事前分布$\\pi(\\gamma_i | \\sigma)$を以下のように定義します。\n", "$$\n", "\t\t\\pi(\\gamma_i | \\sigma) \\sim \\mathcal{N}(\\gamma_i, \\sigma)\n", "$$\t\t\n", "\t
\n", "\t\n", "\t\tまた、$\\beta$も正規分布を持つと仮定し、$\\sigma$は逆ガンマ分布従うと仮定します。\t\t\n", "\t
\n", "\t\n", "\t\t残念ながらjagsには逆ガンマ分布が提供されていないため、$\\tau$のガンマ分布を使って\n", "\t\tモデルを作成します。\n", "$$\n", "\t\t\\tau = \\frac{1}{\\sigma^2}\n", "$$\t\n", "\t
\n", "\t\n", "\t\t$\\tau$の初期分布として、$\\gamma(x, 0.1, 0.1)$を使います。\n", "\t\tこれは、かなり一定値に近い分布となります。\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# σ^2には限りなく一定に近いγ(x, 0.1, 0.1)を使用\n", "Ga(x, a, lam) = x^(a-1)*e^(-lam*x)*lam^a/gamma(a)\n", "plot(lambda x: Ga(x, 0.1, 0.1), [x, 0, 1]).show(figsize=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\t個人の学習能力を考慮した階層ベイズモデルをjagsの形式で以下に定義します。\n", "\t
\n", "\t\n", "\t\tx_hat, x_mean, x_sdは、平均の収束度合いを計算するためにチェック用に定義しています。\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Overwriting data/ex_6.jags\n" ] } ], "source": [ "%%writefile data/ex_6.jags\n", "model {\n", " for (i in 1:N) {\n", " x[i] ~ dbin(q[i], 10)\n", " logit(q[i]) <- beta + gam[i]\n", " gam[i] ~ dnorm(0, tau)\n", " # add for check\n", " x_hat[i] ~ dbin(q[i], 10)\n", " }\n", " beta ~ dnorm(0, 0.0001)\n", " tau ~ dgamma(0.1, 0.1)\n", " # add for check\n", " x_mean <- mean(x_hat)\n", " x_sd <- sd(x_hat)\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\t先ほどと同様にjagsモデルを作成し、サンプリングを実行します。\n", "\t
\n", "\t\n", "\t\tサンプリングで取り出すのは、x_mean, x_sd, q, beta, tauとします。\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# mcmcモデルの作成\n", "junk = r('mcmc.model <- jags.model(\"data/ex_6.jags\", data=list(\"x\"=X,\"N\"=N), n.chains=4, n.adapt=1000)')" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# サンプリング(途中経過が出力されるので、junkで吸収)\n", "junk = r('mcmc.sample <- coda.samples(mcmc.model, c(\"x_mean\", \"x_sd\", \"q\", \"beta\",\"tau\"), 4000)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\t計算結果は、先ほどとは異なり、24x4のマトリックスとして返されます。\n", "\t
\n", "\t\n", "\t\tそれをsageのbeta, q, tau, x_mean, x_sdにセットしています。\n", "\t
\n", "\t\n", "\t\tx_meanが5.84929375、x_sdが3.79893738478という値は、\n", "\t\t実データの平均5.9と標準偏差3.80とよく一致しています。\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# 出力結果()\n", "# r('summary(mcmc.sample)')" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "24 x 4 dense matrix over Real Double Field (use the '.str()' method to see the entries)" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# summaryからx_mean, x_sd, tau, betaを取り出す\n", "summary = sageobj(r('summary(mcmc.sample)'))\n", "stat = summary['DATA']['statistics']; stat" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5.8496625 3.90080927524 0.911430402062 0.0996895973171\n", "[0.131847137525641, 0.0460888891423977, 0.966227574796758, 0.410937138520737, 0.965358858506929, 0.965203322553168, 0.965358462473892, 0.605169408206735, 0.41447668617391, 0.965078601878168, 0.130231103796037, 0.884874646490626, 0.0466880809742211, 0.507878709050931, 0.966355936883709, 0.698121225811493, 0.130500176198087, 0.886112404377343, 0.223037946063444, 0.792454698689964]\n" ] } ], "source": [ "# 結果を変数にセット\n", "vals = stat.column(0).list()\n", "beta = vals[0]\n", "q = vals[1:21]\n", "tau = vals[21]\n", "x_mean = vals[22]\n", "x_sd = vals[23]\n", "print x_mean, x_sd, beta, tau\n", "print q" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\t個人の理解度$\\gamma$を持つ学生が得点xを取る確率は、以下のようになります。\n", "$$\n", "\t\tf(\\beta, \\sigma, \\gamma | x) = {}_{10} C_x q^x (1 - q)^{10-x} \\frac{1}{\\sqrt{2 \\pi}\\sigma} e^{- \\frac{\\gamma^2}{2 \\sigma^2}}\n", "$$\t\n", "\t
\n", "\t\n", "\t\tこれを$\\gamma$で積分したものが、学生が得点xを取る確率になります。\n", "$$\n", "\t\tf(\\beta, \\sigma | x) = \\int f(\\beta, \\sigma, \\gamma | x) d \\gamma\n", "$$\t\n", "\t
\n", "\t\n", "\t\tsage$f(\\beta, \\sigma, \\gamma | x)$を関数_r(x, b, r, sig)に定義します。\n", "\t
\n", "\t\n", "\t\tまた、x=0~10までの各分布を以下にプロットします。プロットの結果から分布の積分を求めるには、\n", "\t\t-20から20の範囲で数値積分すれば良いことが読み取れます。\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# f(beta, sig, r | x)の定義\n", "sig = sqrt(1/tau)\n", "def _r(x, b, r, sig):\n", " q = 1/(1+e^(-b-r))\n", " return binomial(10, x)*q^x*(1-q)^(10-x)*1/(sqrt(2*pi)*sig)*e^(-r^2/(2*sig*sig))" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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//l8RW7ZovP120/YfpKaqFBYqDB9eURUzM1X69Cnr4CdP1jFNWLrUu81++kkh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\noOuweLHo/VNTNfr3LzNTtWg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RWNib48dXen1/ly4WISHiOqtz+kZEVH0vilJmbtq5U6uV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\nUOJ51fj7bw4zZpjdqjYGqKzE+fN8qrsCgO4K/P0l+Ps7fzsEAVi+XIU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"text/plain": [ "Graphics object consisting of 11 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# f(beta, sig, r | x)のプロット\n", "plts = Graphics()\n", "for x in (0..10):\n", " plts += plot(lambda r : _r(x, beta, r, sig), [r, -10, 10])\n", "plts.show(figsize=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\tSageの最大の武器はその数式処理能力です、ここでは数値積分関数(numerical_integral)を\n", "\t\t使って$f(\\beta, \\sigma, \\gamma | x)$を数値積分します。\t\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# γの周辺確率を求める\n", "# f(beta, sig | x) = integral f(beta, sig, r | x) dr\n", "def _rInt(x, b, sig):\n", " (s, e) = numerical_integral(lambda r : _r(x, beta, r, sig), -20, 20)\n", " return s" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\t\n", "\t\tようやく求める図をプロットするのに必要な道具が揃いました。\n", "\t
\n", "\t\n", "\t\t数値積分は、_rInt関数で行い、xが0から10までの$f(\\beta, \\sigma, \\gamma | x)$の\n", "\t\t値をプロットし、度数分布図と重ねて表示したのが、以下の図です。\n", "\t
\n", "\t\n", "\t\tこのようにSageとjagsの組み合わせによって通常の処理形では難しい階層ベイズ推定を\n", "\t\t使ったモデルの解析がとても簡単にできることがご理解頂けと思います。\n", "\t
\n", "\t\n", "\t\tこれを機会に是非Sageとjagsを使ってみてください。\n", "\t
\n", "" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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NGDHCSk9Pt44++ugWH7asS2iKiAigcxmJiEgDBYKIiAAKBBERaaBA\nEBERQIEgIiINFAgiIgIoEEREpIECQUREAAWCiIg0UCCIiAigQBARkQYKBBERAeD/AYREGjQtqT4j\nAAAAAElFTkSuQmCC\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r_plt = list_plot([_rInt(x, beta, sig)*N for x in (0..10)], plotjoined=True, rgbcolor=\"red\")\n", "(hist_plt + r_plt).show(figsize=4)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 7.2", "language": "", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }