{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Sageでグラフを再現してみよう:データ解析のための統計モデリング入門第9章\n", "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、 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", "\n", "前回に続き、\n", "[データ解析のための統計モデリング入門](http://www.amazon.co.jp/dp/400006973X/)\n", "(以下、久保本と書きます)の第9章の例題をSageを使って再現してみます。\n", "\n", "今回の目標は、図9.6です。\n", "\n", "![図9.6](images/Fig9.6.png)\n", "\n", "数式処理システムSageのノートブックは、計算結果を表示するだけではなく、実際に動かすことができるの大きな特徴です。\n", "この機会にSageを分析に活用してみてはいかがでしょうか。\n", " \n", "## 前準備 \n", "今回使用するpyjagsがSageの環境では動作しないため、kernelはPython 2を使用します。\n", "\n", "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。sage_util.py, RUtil.pyはloadの代わりにexecを使用して読み込みます。" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%HTML\n", "" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# 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", "# statsmodelsを使ってglmを計算します\n", "import statsmodels.formula.api as smf\n", "import statsmodels.api as sm\n", "from scipy.stats.stats import pearsonr\n", "# jags用パッケージ\n", "import pyjags\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", "exec(open('script/sage_util.py').read())\n", "# Rユーティリティ\n", "exec(open('script/RUtil.py').read())\n", "# 乱数のシードをセット\n", "np.random.seed(101)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 例題のデータ\n", "今回の例題は、サポートページにR形式のd.RDataで提供されているため、RからJSON形式に変換してpythonで使用しています。" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# 9章のデータをRからJSON形式に変換\n", "d = pd.read_json('''\n", "[{\"x\":3,\"y\":5},{\"x\":3.2105,\"y\":3},{\"x\":3.4211,\"y\":6},{\"x\":3.6316,\"y\":7},{\"x\":3.8421,\"y\":7},\n", " {\"x\":4.0526,\"y\":5},{\"x\":4.2632,\"y\":9},{\"x\":4.4737,\"y\":9},{\"x\":4.6842,\"y\":7},{\"x\":4.8947,\"y\":10},\n", " {\"x\":5.1053,\"y\":12},{\"x\":5.3158,\"y\":8},{\"x\":5.5263,\"y\":7},{\"x\":5.7368,\"y\":4},{\"x\":5.9474,\"y\":4},\n", " {\"x\":6.1579,\"y\":11},{\"x\":6.3684,\"y\":9},{\"x\":6.5789,\"y\":9},{\"x\":6.7895,\"y\":8},{\"x\":7,\"y\":6}]\n", "''')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### データ処理のルーティーン\n", "データを読み込んだら、以下のルーティーンを実行します。\n", "- describeでデータの統計情報を把握する\n", "- 可視化してデータの特徴をつかむ\n", "\n", "今回のデータは、3章のデータと同様で、架空の植物$i$の種子数を$y_i$とサイズ$x_i$からなる20個のデータです。" ] }, { "cell_type": "code", "execution_count": 86, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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xyyhat
count20.00000020.00000020.000000
mean5.0000007.3000007.300000
std1.2454862.4083190.756972
min3.0000003.0000006.147684
25%3.9999755.7500006.682186
50%5.0000007.0000007.263051
75%6.0000259.0000007.894257
max7.00000012.0000008.580117
\n", "
" ], "text/plain": [ " x y yhat\n", "count 20.000000 20.000000 20.000000\n", "mean 5.000000 7.300000 7.300000\n", "std 1.245486 2.408319 0.756972\n", "min 3.000000 3.000000 6.147684\n", "25% 3.999975 5.750000 6.682186\n", "50% 5.000000 7.000000 7.263051\n", "75% 6.000025 9.000000 7.894257\n", "max 7.000000 12.000000 8.580117" ] }, "execution_count": 86, "metadata": {}, "output_type": "execute_result" } ], "source": [ "d.describe()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "プロット図からx, yともに整数の離散値であり、xとyの関係は以下の様になっています。線形回帰の結果も合わせて表示しています。" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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KXzmMPgT8nrX2BvDPgZ80xpxOuE1yyGhKSRGRBKjnKyKSAIWviEgC\nFL4iIglQ+IqIJEDhKyKSAIWviEgCFL4iIglQ+IqIJOD/A3UoQXQT+iIGAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# seabornの線形回帰機能を使って、入力データのプロット(lmplot)\n", "sns.lmplot(x='x', y='y', data=d)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2.6節の「確率分布の選び方」から、離散値のyの平均と分散を求めてみます。この結果、平均と分散がほぼ等しいので、ポアソン分布を仮定します。" ] }, { "cell_type": "code", "execution_count": 88, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "7.3 5.8\n" ] } ], "source": [ "# yの値は0以上の離散値で、yの平均と分散がほぼ等しい\n", "print d.y.mean(), d.y.var()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "平均λ=7.3のポアソン分布の確率密度のプロットとyの確率密度のプロットを重ね合わせてみます。確率密がほぼ一致することが分かります。" ] }, { "cell_type": "code", "execution_count": 83, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# d.yの確率密度分布(青)と平均7.3のポアソン分布(赤)を重ねてみる\n", "ax = sns.distplot(d.y)\n", "# 平均λ= 7.3のポアソン分布からサンプルを3000個生成して、その確率密度分布をプロット\n", "sns.distplot(np.random.poisson(lam=7.3, size=3000), hist=False, color='red', ax=ax)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## GLMでポアソン分布のパラメータ推定\n", "3章と同様に、GLMを使ってポアソン分布のパラメータを求めてみます。" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# statsmodelsを使ってglmを計算します\n", "import statsmodels.formula.api as smf\n", "import statsmodels.api as sm\n", "from scipy.stats.stats import pearsonr" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "以下の解析から、ポアソン分布の平均$\\lambda=exp(1.57 + 0.08x)$が得られます。" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "Intercept 1.566046\n", "x 0.083343\n", "dtype: float64" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fit = smf.glm('y ~ x', data=d, family=sm.families.Poisson(link=sm.families.links.log)).fit()\n", "fit.params" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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mkkQqRqEgUp5uYJxw9T2RTUOhILJB0ZVy/5Zwve4ZM/vTmEsSqRiFgsjG3Qh8\n0Tn3BOFyrO81s5NirkmkInTpbBER8bSnICIinkJBREQ8hYKIiHgKBRER8RQKIiLiKRRERMRTKIiI\niKdQEBER7/8DQnnrd3tCiPUAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# λの予測値nuをyhatにセット\n", "d['yhat'] = fit.predict()\n", "ax = d.plot(x='x', y='yhat')\n", "d.plot(kind='scatter', x='x', y='y', ax=ax)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## GLMのベイズモデル化\n", "ベイズモデルの事後分布は、(尤度)x(事前分布)に比例することから、以下の関係が成り立ちます。\n", "$$\n", "p(\\beta_1, \\beta_2 | Y) \\propto p(Y | \\beta_1, \\beta_2)\\, p(\\beta_1)\\, p(\\beta_2)\n", "$$\n", "\n", "ここで、$p(\\beta_1, \\beta_2 | Y)$は、Yが与えられたときの$\\{ \\beta_1, \\beta_2 \\}$の同時分布です。\n", "\n", "### 無情報事前分布\n", "$p(\\beta_1), p(\\beta_2)$は、$\\beta_1, \\beta_2$の事前分布ですが、どのような分布をとるかが指定されていない、部情報事前分布と呼ばれるものです。ここではできるだけ均質な分布とするために、N(0, 100)のひらべったい正規分布とします。" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 平均0、標準偏差1 N(0, 1)と平均0、標準偏差100 N(0, 100)のヒストグラムを比較\n", "np.random.seed(101)\n", "N_1 = [np.random.normal(0, 1) for i in range(1000)]\n", "N_100 = [np.random.normal(0, 100) for i in range(1000)]\n", "ax = sns.distplot(N_1)\n", "sns.distplot(N_100, ax=ax).set(xlim=(-10, 10))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## jagsを使ったベイズ統計モデルの事後分布の推定\n", "久保本では、WinBUGSを使っていますが、MacOSXやLinuxではWinBUGSと定義ファイルが同じ、jagsを使用します。\n", "\n", "以下に、平均λが$\\beta_1 + \\beta_2 x$のポアソン分布を持つモデルを定義します。\n", "\n", "model{}で囲まれている部分がモデル定義部で、この中にforループ、確率的な関係を表す~と左辺を右辺に代入する<-の演算子を使ってモデルを構築します。\n", "\n", "本来なら、\n", "
\n",
    "log(lambda[i]) <- beta1 + beta2 * X[i] \n",
    "
\n", "とするところを、\n", "
\n",
    "log(lambda[i]) <- beta1 + beta2 * (X[i] - MeanX)\n",
    "
\n", "としているのは、処理の高速化のためだそうです。実際オリジナルの式だと収束にとても時間がかかりました。\n", "\n", "dpoisは、ポアソン分布を、dnormは正規分布を表し、dnormの第2引数にはtau=分散を指定します。従ってbeta1, beta2には、分散100の正規分布N(0, 100)からサンプリングされます。" ] }, { "cell_type": "code", "execution_count": 91, "metadata": { "collapsed": true }, "outputs": [], "source": [ "N = len(d.x)\n", "code = '''\n", "model {\n", " for (i in 1:N) {\n", " Y[i] ~ dpois(lambda[i])\n", " log(lambda[i]) <- beta1 + beta2 * (X[i] - MeanX)\n", " }\n", " beta1 ~ dnorm(0, 1.0E-4)\n", " beta2 ~ dnorm(0, 1.0E-4)\n", "}\n", "'''" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "pyjags.Modelへの引数は、以下の通りです。\n", "- code: モデルを指定\n", "- data: モデルで使用されるデータを dict形式で指定\n", "- chains: 平行してサンプリングを行う個数を指定" ] }, { "cell_type": "code", "execution_count": 92, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "adapting: iterations 3000 of 3000, elapsed 0:00:00, remaining 0:00:00\n" ] } ], "source": [ "model = pyjags.Model(code, data=dict(X=d.x, Y=d.y, N=N, MeanX= d.x.mean()), chains=3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "model.sampleを使って、変数beta1, beta2についてサンプリングします。" ] }, { "cell_type": "code", "execution_count": 93, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sampling: iterations 1500 of 1500, elapsed 0:00:00, remaining 0:00:00\n" ] } ], "source": [ "samples = model.sample(500, vars=['beta1', 'beta2'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "samplesに返された値はdict型で、'beta1', 'beta2'でそれぞれのサンプリングを取り出します。\n", "\n", "個々のサンプルは、1xサンプリング数xchainsの配列となっています。" ] }, { "cell_type": "code", "execution_count": 96, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(1, 500, 3)" ] }, "execution_count": 96, "metadata": {}, "output_type": "execute_result" } ], "source": [ "samples['beta1'].shape" ] }, { "cell_type": "code", "execution_count": 97, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "beta1 mean = 1.98, 95% credible interval [1.84 2.11]\n", "beta2 mean = 0.09, 95% credible interval [-0.03 0.19]\n" ] } ], "source": [ "def summary(samples, varname, p=95):\n", " values = samples[varname]\n", " ci = np.percentile(values, [100-p, p])\n", " print('{:<6} mean = {:>5.2f}, {}% credible interval [{:>4.2f} {:>4.2f}]'.format(\n", " varname, np.mean(values), p, *ci))\n", "\n", "for varname in ['beta1', 'beta2']:\n", " summary(samples, varname)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 結果の可視化\n", "R用のrjagsでは、サンプリングの精度を表す$\\hat{R}$等が求められますが、pyjagsにはそれらの計算機能がありません。\n", "その代わりサンプリング結果を可視化して判断することにします。\n", "\n", "chainsのch1, ch2, ch3がほぼ同じような分布をしており、収束していると考えられます。\n", "\n", "確率分布も1.98を中心としたきれいな分布になっています。" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# beta1の可視化\n", "df_b1 = pd.DataFrame(samples['beta1'][0], columns=['ch1', 'ch2', 'ch3'])" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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fYe3aXqzf+yCu2nEt7j/6IP717a0dsW0Z8mq1eg6EhHKO53lzFt0+NDyF7lK+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\n4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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df_b1.plot()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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r9/H81Za7VJuA313W7SQTGcLhGA/f0sHzbw3xFy8pbtvWhN/jXPZnNoKVn7uw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\ngAshhEX9f3NWOUDi+KcYAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sns.distplot(df_b1.values.flatten())\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "同様にbeta2の結果もプロットしてみます。" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# beta2の可視化\n", "df_b2 = pd.DataFrame(samples['beta2'][0], columns=['ch1', 'ch2', 'ch3'])" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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PtwwjK2m46oc+jYkvfi4OvOtFhBAIFxfhDg3pICFS8O2TctyJBRVBXMTIKn+3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\nhR52BdeCjxwOOCL5lL7akUgpeIqQ8yg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soWjUp6pU7IY2R3AM9iUKft3MFPp8gYlNXlwv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\nFEUjotnPT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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df_b2.plot()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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W+ntKqXcAnyf3fH1ba/2/rat0eRbp3zfJfUTdChwA/l5r/S+WFbtE\n8/WNXDiMkjsivfx++7rW+ksWlbosizx3vwh8FpghN43wM9ZVujwL9e+qNuuAL2ut37nQfcleKEII\nYVPlelJOCCHKngS4EELYlAS4EELYlAS4EELYlAS4EELYlAS4EELYlAS4EELYlAS4EELY1P8H8PqE\nmEE5LrsAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sns.distplot(df_b2.values.flatten())\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 図9.6のプロット\n", "準備が整ったので、目標の図9.6をプロットしてみましょう。\n", "\n", "各サンプリング値から平均λ(beta1, beta2から求まる)の曲線をプロットする関数add_meanを定義します。\n", "\n", "次に、入力データをプロットし、サンプルのλの予測値から曲線をプロットし、最後にbeta1, beta2の中央値を\n", "使った曲線をプロットします。" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def add_mean(beta1, beta2, alpha, color):\n", " plt.plot(d.x, np.exp(beta1 + beta2*(d.x - d.x.mean())).values, c=color, alpha =alpha)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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OyjKAYedFEhJd59D3DloPvqxDTKGBl9U770DKcoS1tRGco9cWZ0dZSw9AI8tK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\nGyzuRrsdNt5DndCtdb7EGkUy8AE8r4LnlQ3D7DoUfg+wIeRomo02P24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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 入力データのプロット\n", "plt.scatter(d.x, d.y, c='red', zorder=3)\n", "# サンプルのλの予測値をプロット\n", "for (beta1, beta2) in zip(df_b1.values.flatten(), df_b2.values.flatten()):\n", " add_mean(beta1, beta2, 0.02, 'gray')\n", "# 中央値を使ったプロット\n", "beta1_median = np.median(df_b1.values.flatten())\n", "beta2_median = np.median(df_b2.values.flatten())\n", "add_mean(beta1_median, beta2_median, 1.0, 'blue')\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "beta1とbeta2の関係もプロットしてみます。\n", "この結果からbeta1とbeta2の間には相関がないことが分かります。" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Xy+rqBMFgjGCwzsjI4+iret1iZibN+HgFxwnR2ZnE7489YZS2spsfbedq52kr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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(df_b1.values.flatten(), df_b2.values.flatten(), alpha = 0.3)\n", "plt.xlabel(\"Beta1\")\n", "plt.ylabel(\"Beta2\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 共役な事前分布\n", "パラメータの分布が予測できる場合には、その共役な事前分布を使ってギブスサンプリングします。" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
パラメータ共役な事前分布
正規分布の平均正規分布
正規分布の分散逆ガンマ分布
多変量正規分布の分散共分散行列逆ウィシャート分布
ガンマ分布のパラメータガンマ分布
ポアソン分布の平均ガンマ分布
二項分布の生起確率ベータ分布
多項分布の生起確率ディリクレ分布
" ], "text/plain": [ "<__main__.Table2Html instance at 0x7f0753f4d368>" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hdr = [\"パラメータ\", \"共役な事前分布\"]\n", "tbl = [\n", " [\"正規分布の平均\", \"正規分布\"],\n", " [\"正規分布の分散\", \"逆ガンマ分布\"],\n", " [\"多変量正規分布の分散共分散行列\", \"逆ウィシャート分布\"],\n", " [\"ガンマ分布のパラメータ\", \"ガンマ分布\"],\n", " [\"ポアソン分布の平均\", \"ガンマ分布\"],\n", " [\"二項分布の生起確率\", \"ベータ分布\"],\n", " [\"多項分布の生起確率\", \"ディリクレ分布\"]\n", "]\n", "Table2Html(tbl, header=hdr)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "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 }