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"cells": [
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"cell_type": "markdown",
"metadata": {},
"source": [
"# Hierarchical Bayesian Inference of Binomial Probabilities (BDA 5.3) #\n",
"\n",
"This notebook attempts to reproduce analysis in Chapter 5.3 of the book 'Bayesian Data Analysis' by Gelman et al (3rd Edition). \n",
"\n",
"Here, we are given $J=71$ observations of binomial outcomes $(y_1,N_1), \\ldots, (y_J,N_J)$ where $y_j \\sim \\text{Bin}(N_j, \\theta_j)$. We assume conjugate prior $\\theta_j \\sim \\text{Beta}(\\alpha,\\beta)$, and a \"reasonable\" hyperprior density $p(\\alpha,\\beta) \\propto (\\alpha+\\beta)^{-5/2}$; refer to the chapter regarding why this is a reasonable choice. Given this hierarchical model, we perform fully Bayesian analysis."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"% pylab inline"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# load data from Andrew's homepage\n",
"from pandas import *\n",
"tumor_df = read_csv(\"http://www.stat.columbia.edu/~gelman/book/data/rats.asc\",\n",
" index_col=False, skiprows=2, delim_whitespace=True)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# the data roughly looks like follows\n",
"tumor_df.head(20)"
],
"language": "python",
"metadata": {},
"outputs": [
{
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