{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 線形回帰モデル - pystan" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from __future__ import division\n", "import os\n", "import sys\n", "import glob\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "%matplotlib inline\n", "%precision 4\n", "#plt.style.use('ggplot')\n", "import seaborn as sns\n", "sns.set_style('white')\n", "sns.set_context('paper')\n", "\n", "np.random.seed(1234)\n", "import pystan\n", "import scipy.stats as stats\n", "\n", "import scipy.stats as stats" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 線形回帰モデルのパラメータ推定\n", "\n", "普通の伝統的な統計学では以下の線形回帰式を用いて回帰パラメータ$a$, $b$を推定する.\n", "\n", "$$\n", "y \\sim ax + b\n", "$$\n", "\n", "確率論的プログラミングにおいては,,\n", "\n", "$$y = ax + b + \\epsilon$$\n", "\n", "という線型モデルを次の形式に解釈することでモデリングを行う.\n", "\n", "$$\n", "y \\sim \\mathcal{N}(ax + b, \\sigma^2)\n", "$$\n", "\n", "推定するパラメータは$a$, $b$ と $\\sigma$で,それぞれの事前分布は次のように決めるとする.\n", "\n", "$$\n", "a \\sim \\mathcal{N}(0, 100) \\\\\n", "b \\sim \\mathcal{N}(0, 100) \\\\\n", "\\sigma \\sim \\mathcal{U}(0, 20)\n", "$$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "lin_reg_code = \"\"\"\n", "data {\n", " int n; \n", " real x[n];\n", " real y[n]; \n", "}\n", "transformed data {}\n", "parameters {\n", " real a;\n", " real b;\n", " real sigma;\n", "}\n", "transformed parameters {\n", " real mu[n];\n", " for (i in 1:n) {\n", " mu[i] <- a*x[i] + b;\n", " }\n", "}\n", "model {\n", " sigma ~ uniform(0, 20);\n", " y ~ normal(mu, sigma);\n", "}\n", "generated quantities {}\n", "\"\"\"\n", "\n", "n = 11\n", "_a = 6\n", "_b = 2\n", "x = np.linspace(0, 1, n)\n", "y = _a*x + _b + np.random.randn(n)\n", "\n", "lin_reg_dat = {\n", " 'n': n,\n", " 'x': x,\n", " 'y': y\n", " }\n", "\n", "fit = pystan.stan(model_code=lin_reg_code, data=lin_reg_dat, iter=1000, chains=1)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Inference for Stan model: anon_model_4bdbb0aeaf5fafee91f7aa8b257093f2.\n", "1 chains, each with iter=1000; warmup=500; thin=1; \n", "post-warmup draws per chain=500, total post-warmup draws=500.\n", "\n", " mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat\n", "a 5.74 0.15 1.3 3.03 4.9 5.82 6.59 8.25 80 1.0\n", "b 2.06 0.09 0.78 0.57 1.54 2.03 2.52 3.77 78 1.0\n", "sigma 1.38 0.04 0.4 0.81 1.09 1.3 1.58 2.33 89 1.0\n", "mu[0] 2.06 0.09 0.78 0.57 1.54 2.03 2.52 3.77 78 1.0\n", "mu[1] 2.63 0.08 0.68 1.34 2.19 2.6 3.02 4.08 80 1.0\n", "mu[2] 3.2 0.06 0.58 2.09 2.83 3.17 3.53 4.44 85 1.0\n", "mu[3] 3.78 0.05 0.5 2.73 3.47 3.76 4.08 4.82 95 1.0\n", "mu[4] 4.35 0.04 0.44 3.49 4.07 4.35 4.63 5.22 115 1.0\n", "mu[5] 4.93 0.03 0.42 4.1 4.64 4.92 5.2 5.78 150 1.0\n", "mu[6] 5.5 0.03 0.43 4.7 5.22 5.51 5.78 6.41 163 1.0\n", "mu[7] 6.07 0.04 0.49 5.15 5.75 6.08 6.39 7.09 156 1.0\n", "mu[8] 6.65 0.05 0.56 5.63 6.28 6.63 7.02 7.8 143 1.0\n", "mu[9] 7.22 0.06 0.66 5.94 6.81 7.21 7.66 8.54 131 1.0\n", "mu[10] 7.8 0.07 0.76 6.34 7.29 7.76 8.28 9.32 116 1.0\n", "lp__ -8.09 0.16 1.47 -11.87 -8.82 -7.75 -7.03 -6.32 88 1.01\n", "\n", "Samples were drawn using NUTS(diag_e) at Tue Oct 6 10:44:55 2015.\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" ] } ], "source": [ "print(fit)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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lGb6fmi8jORJKlcb+fJgTjNbWVlRXV6OpqQkzZszw6rmFAo+UYPUYjtoAZ+cU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\nKD/XzHGes/YsP6PD1bjW1CUogwsbV5aiUmH/HvNzuNsPZcO3ZmlqnN6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