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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem 5.9.6. Exchangeable Models\n",
"\n",
"1. In the divorce rate example of Section 5.2, set up a prior distribution for the values $y_1 \\ldots, y_8$ that allows for one low value (Utah) and one high value (Nevada), with independent and identical distributions for the other six values. This prior distribution should be exchangeable, because it is not known which of the eight states correspond to Utah and Nevada. \n",
"\n",
"2. Determine the posterior distribution for $y_8$ under this model given the observed values of $y_1, \\ldots, y_7$ given in the example. This posterior distribution should probably have two or three modes, corresponding to the possibilities that the missing state is Utah, Nevada, or one of the other six. \n",
"\n",
"3. Now consider the entire set of eight data points, including the value for $y_8$ given at the end of the example. Are these data consistent with the prior distribution you gave in part (1) above? In particular, did your prior distribution allow for the possibility that the actual data have an outlier (Nevada) at the high end, but no outlier at the low end?\n",
"\n",
"The states are Arizona, Colorado, Idaho, Montana, Nevada, New Mexico, Utah, and Wyoming.\n",
"\n",
"The rates from seven of these states are 5.8, 6.6,7.8,5.6,7.0,7.1,5.4 divorces per 1000 population per year. \n",
"\n",
"Gelman, Andrew; Carlin, John B.; Stern, Hal S.; Dunson, David B.; Vehtari, Aki; Rubin, Donald B.. Bayesian Data Analysis, Third Edition (Chapman & Hall/CRC Texts in Statistical Science) (Page 135). CRC Press. Kindle Edition. "
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"mean: 6.471428571428571 variance: 0.6877551020408161\n"
]
}
],
"source": [
"from scipy.stats import norm\n",
"from itertools import permutations\n",
"import matplotlib.pyplot as plt\n",
"\n",
"rates=np.array([5.8,6.6,7.8,5.6,7.0,7.1,5.4])\n",
"print('mean:',rates.mean(),'variance:',rates.var())\n"
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {},
"outputs": [],
"source": [
"s=range(8)\n",
"def prior(x):\n",
" L=0\n",
" for i,j in permutations(s,2):\n",
" L0=1\n",
" L0=L0*norm.pdf(x[i],loc=8.7,scale=.8)\n",
" L0=L0*norm.pdf(x[j],loc=4.3,scale=.8)\n",
" for k in s:\n",
" if k!=i and k!=j:\n",
" L0=L0*norm.pdf(x[k],loc=6.5,scale=.8)\n",
" L=L+L0\n",
" return(L)\n",
"\n",
"def like(x):\n",
" return prior(np.append(x,rates))"
]
},
{
"cell_type": "code",
"execution_count": 77,
"metadata": {},
"outputs": [],
"source": [
"x=np.linspace(0.0,15.0,1000)\n",
"y=np.array([like(i) for i in x])"
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x1a1977e748>]"
]
},
"execution_count": 78,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(x,y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I have a lot of questions about this problem, starting with: have I computed the right thing? I am not sure.\n",
"As far as the last part, No, my prior distribution did not allow for a high value without a low value; it expected one of each."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}