{ "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10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10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10.4です。\n", "\n", "![図9.6](images/Fig10.4.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": 2, "metadata": { "collapsed": true }, "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", "サポートページから10章のデータをダウンロードします。\n", "\n", "### データの素性をみる\n", "いつものようにデータを読み込んだら、ルーティンとしてdescribeと可視化をしましょう。\n", "\n", "describeの結果からも分かるとおり、分散(9.93)が大きく、可視化の結果からは山が2つの分布をしています。" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "d = pd.read_csv('http://hosho.ees.hokudai.ac.jp/~kubo/stat/iwanamibook/fig/hbm/data7a.csv')" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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mean50.5000004.030000
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" ], "text/plain": [ " id y\n", "count 100.000000 100.000000\n", "mean 50.500000 4.030000\n", "std 29.011492 3.150934\n", "min 1.000000 0.000000\n", "25% 25.750000 1.000000\n", "50% 50.500000 4.000000\n", "75% 75.250000 7.000000\n", "max 100.000000 8.000000" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# RのsummaryのようにPandasのDataFrameの情報を出力するには、describeを使用\n", "print \"分散=\", d.y.var()\n", "d.describe()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 生存種子数yのヒストグラムと確率密度分布をプロット\n", "sns.distplot(d.y, bins=9)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 最尤推定\n", "statmodelsのGLMを使って二項分布の最尤推定をします。\n", "\n", "求まった切片(0.015)から、qの最尤推定値は以下の様に求まります。\n", "$$\n", "\\hat{q} = \\frac{1}{1 + exp(-0.015)} = 0.504\n", "$$\n", "\n", "二項分布の分散は、$Nqp = 2.0$ですが、データの分散は9.93で過分散となっています。" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Model: GLM AIC: 763.9388
Link Function: logit BIC: 175.5773
Dependent Variable: ['y', 'NmY'] Log-Likelihood: -380.97
Date: 2016-08-21 07:29 LL-Null: -380.97
No. Observations: 100 Deviance: 631.49
Df Model: 0 Pearson chi2: 491.
Df Residuals: 99 Scale: 1.0000
Method: IRLS
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Coef. Std.Err. z P>|z| [0.025 0.975]
Intercept 0.0150 0.0707 0.2121 0.8320 -0.1236 0.1536
" ], "text/plain": [ "\n", "\"\"\"\n", " Results: Generalized linear model\n", "=============================================================\n", "Model: GLM AIC: 763.9388\n", "Link Function: logit BIC: 175.5773\n", "Dependent Variable: ['y', 'NmY'] Log-Likelihood: -380.97 \n", "Date: 2016-08-21 07:29 LL-Null: -380.97 \n", "No. Observations: 100 Deviance: 631.49 \n", "Df Model: 0 Pearson chi2: 491. \n", "Df Residuals: 99 Scale: 1.0000 \n", "Method: IRLS \n", "--------------------------------------------------------------\n", " Coef. Std.Err. z P>|z| [0.025 0.975]\n", "--------------------------------------------------------------\n", "Intercept 0.0150 0.0707 0.2121 0.8320 -0.1236 0.1536\n", "=============================================================\n", "\n", "\"\"\"" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# statmodelsのGLMを使って解析する\n", "# N-yのカラムを追加\n", "N = 8\n", "d['NmY'] = N - d.y\n", "fit = smf.glm('y + NmY ~ 1', data=d, family=sm.families.Binomial()).fit()\n", "fit.summary2()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.50374992968908194" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# statmodelsの解析結果を使って生存率qを求める\n", "q = 1/(1+np.exp(-0.015)); q" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "1.9998875042186155" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 二項分布の分散=Nqp\n", "N*q*(1-q)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 二項分布との比較\n", "二項分布の最尤推定値$\\hat{q} = 0.504$から求まる分布とデータのヒストグラムを重ね合わせてみましょう。\n", "\n", "二項分布では観測データを説明できていないことが分かります。" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from math import factorial as fac\n", "\n", "def binomial(x, y):\n", " try:\n", " binom = fac(x) // fac(y) // fac(x - y)\n", " except ValueError:\n", " binom = 0\n", " return binom\n", "# 二項分布を定義\n", "def _p(q, y, N):\n", " return binomial(N, y)*q**y*(1-q)**(N-y)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Y = range(9)\n", "q = 0.504\n", "N=8\n", "prob = [_p(q, y, N)*100 for y in Y]\n", "df = pd.DataFrame(zip(Y, prob), columns = ['Y', 'prob'])\n", "ax = d.y.hist(bins=9)\n", "df.plot(kind='scatter', x = 'Y', y='prob', color='red', zorder=2, ax=ax)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 階層ベイズモデルの推定・予測\n", "二項分布との乖離を生んだのは個体差$r_i$だと仮定して階層ベイズモデルを作成します。\n", "\n", "以下に久保本の10.3.1のモデルを示します。jagsではWinBugsのモデルがほぼそのまま使えるのでとても便利です。\n", "- 個体差の標準偏差sは、[0..10000]の一様分布の無情報事前分布から推定\n", "- 個体差$r_i$は、標準偏差sの正規分布からサンプリング\n", "- logistic関数の$q_i = \\beta + r+i$から計算し、$q_i$とsから二項分布をサンプリング" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "N=len(d.y)\n", "code = '''\n", "model {\n", " for (i in 1:N) {\n", " Y[i] ~ dbin(q[i], 8) # 二項分布\n", " logit(q[i]) <- beta + r[i] # 生存率\n", " }\n", " beta ~ dnorm(0, 1.0E-4) # 無情報事前分布\n", " for (i in 1:N) {\n", " r[i] ~ dnorm(0, tau) # 階層事前分布\n", " }\n", " tau <- 1 / (s * s) # tau は分散の逆数\n", " s ~ dunif(0, 1.0E+4) # 無情報事前分布\n", "}\n", "'''" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "事前サンプリングのデフォルト 1000では、$\\beta$がばらついたので、adapt=3000としてモデルを作成しました。" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "adapting: iterations 1374 of 9000, elapsed 0:00:01, remaining 0:00:04\n", "adapting: iterations 3180 of 9000, elapsed 0:00:02, remaining 0:00:03\n", "adapting: iterations 5016 of 9000, elapsed 0:00:03, remaining 0:00:02\n", "adapting: iterations 6870 of 9000, elapsed 0:00:04, remaining 0:00:01\n", "adapting: iterations 8730 of 9000, elapsed 0:00:05, remaining 0:00:00\n", "adapting: iterations 9000 of 9000, elapsed 0:00:05, remaining 0:00:00\n" ] } ], "source": [ "model = pyjags.Model(code, data=dict(Y=d.y, N=N), chains=3, adapt=3000)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sampling: iterations 1320 of 1500, elapsed 0:00:01, remaining 0:00:00\n", "sampling: iterations 1500 of 1500, elapsed 0:00:01, remaining 0:00:00\n" ] } ], "source": [ "samples = model.sample(500, vars=['beta', 's'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### サンプリング結果の可視化\n", "計算された$\\beta$とsを可視化してみましょう。" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# betaの可視化\n", "df_beta = pd.DataFrame(samples['beta'][0], columns=['ch1', 'ch2', 'ch3'])" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Q3Y6ktj65BG/ZViCLRh+ngrfqeN4TheX2riKSjMSS00FisYCC5zHy9JPe3+GC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\ng82fZPnT29az721qAoQg5zdhjzMHb3S1Sl7kT4grZeo+o2jEhO0RLVV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OAAAg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\nz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df_beta.plot()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sns.distplot(df_beta.values.flatten())\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.00734923506843 0.0115458634885\n" ] } ], "source": [ "print np.median(df_beta.values.flatten()), df_beta.values.flatten().mean()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# betaの可視化\n", "df_s = pd.DataFrame(samples['s'][0], columns=['ch1', 'ch2', 'ch3'])" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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IQ7UynYSgRtTAWGN81u1gc0itSNs+5Ai0CSO+SJ6OTsz3Pl/mKrdgY5of3bodP/lN9qSr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\nsIGUVr53Z+d5zWZzCwDMzs4+CCBoNpuT6uvD8Bn4ZvXZ+swpU5u2iYr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dsxp5VlrRQM4c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\nA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hgGTiFQr4Q4ckKuqDVR0ZJoJ+5iub+C8fJ4dn8A6BryytoBij8Ac4G8Wgpw+MQquOq8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\nDrLx8SpKBVtQb3LCf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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df_s.plot()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sns.distplot(df_s.values.flatten())\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2.9579209966 2.99092478911\n" ] } ], "source": [ "print np.median(df_s.values.flatten()), df_s.values.flatten().mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 階層ベイズモデルの事後分布の計算\n", "ここからは、Sageの数値計算を使って計算します。%load_ext sageでSageの関数を利用可能にします。\n", "\n", "生存種子数yの確率分布は、二項分布$p(y\\,| \\,\\beta, r)$と正規分布$p(r \\,|\\, s)$の無限混合分付であり、以下の様にあらわされます。\n", "$$\n", "p(y\\,|\\,\\beta, s) = \\int_{-\\infty}^{\\infty} p(y\\,| \\,\\beta, r)\\,p(r \\,|\\, s)\\, dr\n", "$$" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# ここからSageの関数を使用します\n", "%load_ext sage" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 生存種子数yの確率分布をプロット\n", "Sageの計算処理を使って、$p(y\\,| \\,\\beta, r)\\,p(r \\,|\\, s)$をプロットしてみます。" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# p(y | beta, r)p(r | s)を_rで定義 \n", "def _gauss(r, s):\n", " return 1/(sqrt(2*pi)*s)*e^(-r^2/(2*s*s))\n", "def _r(y, beta, r, s):\n", " q = 1/(1+exp(-beta -r))\n", " return _p(q, y, 8)*_gauss(r, s)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "<__main__.Graphics2Html instance at 0x7f61f26075a8>" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Yを0..8に変えて分布を計算する\n", "r = var('r')\n", "beta_med = np.median(df_beta.values.flatten())\n", "s_med = np.median(df_s.values.flatten())\n", "plts = Graphics()\n", "for y in (0..8):\n", " plts += plot(_r(y, beta_med, r, s_med), [r, -10, 10], figsize=5)\n", "# python2カーネルでsageのGraphicsを表示\n", "Graphics2Html(plts)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$p(y\\,| \\,\\beta, r)\\,p(r \\,|\\, s)$の分布からrを-20から20の範囲で数値積分すれば、y毎の生存種子数yの確率分布が計算できることが分かります。" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# 上記確率分布をrについて積分する、数値積分の範囲を上記の図から-20から20とした\n", "def _rInt(y, beta, s):\n", " (s, e) = numerical_integral(lambda r : _r(y, beta, r, s), -20, 20)\n", " return s" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "y毎の生存種子数yの確率分布に100を掛けて、データのヒストグラムと" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "prob = [_rInt(y, beta_med, s_med)*100 for y in range(9)]\n", "df = pd.DataFrame(zip(Y, prob), columns = ['Y', 'prob'])\n", "ax = d.y.hist(bins=9)\n", "df.plot(kind='scatter', x = 'Y', y='prob', color='red', zorder=2, ax=ax)\n", "plt.show()" ] }, { "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": "2.7.13" } }, "nbformat": 4, "nbformat_minor": 0 }