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aflaxman/2014_05_13a_pymc_self-study_stackoverflow_question.ipynb

Created May 13, 2014 17:59
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2014_05_13a_pymc_self-study_stackoverflow_question.ipynb
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"name": "",
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"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np, pymc as pm, seaborn as sns\n",
"%matplotlib inline\n",
"import matplotlib as mpl, matplotlib.pyplot as plt, mpld3\n",
"mpld3.enable_notebook()\n",
"\n",
"mpl.rcParams['figure.figsize'] = (10, 4)\n",
"np.random.seed(123456)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"data = np.zeros(1000) # observed data: zero failures out of 1000 devices\n",
"p = pm.Uniform('p', 0, 1) # model the failure rate as a uniform distribution from 0 to 1\n",
"obs = pm.Bernoulli('obs', p, value=data, observed=True) # each device can fail or not fail. i.e. the observations follow a Bernoulli distribution\n",
"model = pm.Model([obs, p])\n",
"\n",
"mcmc = pm.MCMC(model)\n",
"mcmc.sample(40000, 10000, 1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-------- 21% ] 8444 of 40000 complete in 0.5 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-------------- 37% ] 15009 of 40000 complete in 1.0 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------52% ] 20991 of 40000 complete in 1.5 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------67%----- ] 26838 of 40000 complete in 2.0 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------81%----------- ] 32656 of 40000 complete in 2.5 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------96%---------------- ] 38582 of 40000 complete in 3.0 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------100%-----------------] 40000 of 40000 complete in 3.1 sec"
]
}
],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print np.percentile(mcmc.trace('p')[:], [2.5, 97.5])\n",
"print p.stats()['95% HPD interval'] # alternative approach to interval prediction"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[2.6165440508793241e-05, 0.0036806413183323641]\n",
"[ 7.48379837e-08 2.95055578e-03]\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Analytic Solution: beta dist and binomial dist are conjugate\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Uniform(0,1) is same distribution at Beta(1,1)\n",
"\n",
"u = np.random.uniform(low=0, high=1, size=1000000)\n",
"b = np.random.beta(a=1, b=1, size=1000000)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "code",
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"input": [
"fig, ax = plt.subplots(1, 2, sharex=True, sharey=True)\n",
"sns.distplot(u, bins=10, ax=ax[0], kde=True, axlabel='Uniform(0,1)')\n",
"sns.distplot(b, bins=10, ax=ax[1], kde=True, axlabel='Beta(1,1)')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 5,
"text": [
"<matplotlib.axes.AxesSubplot at 0x5a9e950>"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
"/homes/abie/anaconda/lib/python2.7/site-packages/matplotlib/font_manager.py:1236: UserWarning: findfont: Font family ['Arial'] not found. Falling back to Bitstream Vera Sans\n",
" (prop.get_family(), self.defaultFamily[fontext]))\n"
]
},
{
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"<style>\n",
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"</style>\n",
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"<div id=\"fig_el16646385555368178032434\"></div>\n",
"<script>\n",
"function mpld3_load_lib(url, callback){\n",
" var s = document.createElement('script');\n",
" s.src = url;\n",
" s.async = true;\n",
" s.onreadystatechange = s.onload = callback;\n",
" s.onerror = function(){console.warn(\"failed to load library \" + url);};\n",
" document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
"}\n",
"\n",
"if(typeof(mpld3) !== \"undefined\" && mpld3._mpld3IsLoaded){\n",
" // already loaded: just create the figure\n",
" !function(mpld3){\n",
" \n",
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" }(mpld3);\n",
"}else if(typeof define === \"function\" && define.amd){\n",
" // require.js is available: use it to load d3/mpld3\n",
" require.config({paths: {d3: \"https://mpld3.github.io/js/d3.v3.min\"}});\n",
" require([\"d3\"], function(d3){\n",
" window.d3 = d3;\n",
" mpld3_load_lib(\"https://mpld3.github.io/js/mpld3.v0.3git.js\", function(){\n",
" \n",
" mpld3.draw_figure(\"fig_el16646385555368178032434\", {\"axes\": [{\"xlim\": [-0.20000000000000001, 1.2000000000000002], \"yscale\": \"linear\", \"axesbg\": \"#EAEAF2\", \"texts\": [{\"v_baseline\": \"hanging\", \"h_anchor\": \"middle\", \"color\": \"#262626\", \"text\": \"Uniform(0,1)\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 11.0, \"position\": [0.5, -0.094086021505376358], \"rotation\": -0.0, \"id\": \"el1664694886352\"}], \"zoomable\": true, \"images\": [], \"xdomain\": [-0.20000000000000001, 1.2000000000000002], \"ylim\": [0.0, 1.2000000000000002], \"paths\": [{\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data02\", \"id\": \"el1664697062672\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data03\", \"id\": \"el1664697059984\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data04\", \"id\": \"el1664697074192\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data05\", \"id\": \"el1664697084112\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data06\", \"id\": \"el1664697085776\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data07\", \"id\": \"el1664697087440\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data08\", \"id\": \"el1664697101456\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data09\", \"id\": \"el1664697103120\"}, {\"edgecolor\": \"#000000\", 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1.002602475966827], [0.8030798739803237, 0.9988664540681487], [0.8118648016361452, 0.9957367178445129], [0.8206497292919666, 0.994159948527098], [0.8294346569477881, 0.9942706905984415], [0.8382195846036095, 0.9954472940179349], [0.847004512259431, 0.9967759205824014], [0.8557894399152524, 0.9975365055458141], [0.8645743675710739, 0.9975213886524734], [0.8733592952268953, 0.9971193208390992], [0.8821442228827168, 0.997026393561357], [0.8909291505385382, 0.9976607456482085], [0.8997140781943597, 0.9987787953154912], [0.9084990058501811, 0.9996845051717805], [0.9172839335060026, 0.9997796666571924], [0.926068861161824, 0.9988916661624355], [0.9348537888176455, 0.9971080807275744], [0.943638716473467, 0.9940718510770693], [0.9524236441292884, 0.9875433289864757], [0.9612085717851098, 0.9712113115153487], [0.9699934994409312, 0.9330901351308589], [0.9787784270967528, 0.8577992052871066], [0.9875633547525742, 0.7352685312805393], [0.9963482824083956, 0.572003214059279], [1.005133210064217, 0.39417492233646234], [1.0139181377200386, 0.23590217344677067], [1.02270306537586, 0.12078432606021017], [1.0314879930316814, 0.052336282847473936], [1.0402729206875028, 0.019051698481422852], [1.0490578483433244, 0.0058428169529865515], [1.0578427759991458, 0.0017741786154863437]]}, \"id\": \"el1664638555536\"});\n",
" });\n",
" });\n",
"}else{\n",
" // require.js not available: dynamically load d3 & mpld3\n",
" mpld3_load_lib(\"https://mpld3.github.io/js/d3.v3.min.js\", function(){\n",
" mpld3_load_lib(\"https://mpld3.github.io/js/mpld3.v0.3git.js\", function(){\n",
" \n",
" mpld3.draw_figure(\"fig_el16646385555368178032434\", {\"axes\": [{\"xlim\": [-0.20000000000000001, 1.2000000000000002], \"yscale\": \"linear\", \"axesbg\": \"#EAEAF2\", \"texts\": [{\"v_baseline\": \"hanging\", \"h_anchor\": \"middle\", \"color\": \"#262626\", \"text\": \"Uniform(0,1)\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 11.0, \"position\": [0.5, -0.094086021505376358], \"rotation\": -0.0, \"id\": \"el1664694886352\"}], \"zoomable\": true, \"images\": [], \"xdomain\": [-0.20000000000000001, 1.2000000000000002], \"ylim\": [0.0, 1.2000000000000002], \"paths\": [{\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data02\", \"id\": \"el1664697062672\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data03\", \"id\": \"el1664697059984\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data04\", \"id\": \"el1664697074192\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data05\", \"id\": \"el1664697084112\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data06\", \"id\": \"el1664697085776\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data07\", \"id\": \"el1664697087440\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data08\", \"id\": \"el1664697101456\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data09\", \"id\": \"el1664697103120\"}, {\"edgecolor\": \"#000000\", 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\"10,0\", \"gridOn\": true}, \"fontsize\": 10.0, \"position\": \"left\", \"nticks\": 8, \"tickvalues\": null}], \"lines\": [{\"color\": \"#4C72B0\", \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 2, \"alpha\": 1, \"xindex\": 0, \"linewidth\": 1.75, \"data\": \"data01\", \"id\": \"el1664697134608\"}], \"markers\": [], \"id\": \"el1664694534544\", \"ydomain\": [0.0, 1.2000000000000002], \"collections\": [], \"xscale\": \"linear\", \"bbox\": [0.125, 0.125, 0.35227272727272724, 0.77500000000000002]}, {\"xlim\": [-0.20000000000000001, 1.2000000000000002], \"yscale\": \"linear\", \"axesbg\": \"#EAEAF2\", \"texts\": [{\"v_baseline\": \"hanging\", \"h_anchor\": \"middle\", \"color\": \"#262626\", \"text\": \"Beta(1,1)\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 11.0, \"position\": [0.5, -0.094086021505376358], \"rotation\": -0.0, \"id\": \"el1664695041552\"}], \"zoomable\": true, \"images\": [], \"xdomain\": [-0.20000000000000001, 1.2000000000000002], \"ylim\": [0.0, 1.2000000000000002], \"paths\": [{\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data13\", \"id\": \"el1664697133776\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data14\", \"id\": \"el1664697141392\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data15\", \"id\": \"el1664697143056\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data16\", \"id\": \"el1664697144720\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data17\", \"id\": \"el1664698600528\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data18\", \"id\": \"el1664698602192\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data19\", \"id\": \"el1664698612112\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data20\", \"id\": \"el1664698613776\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data21\", \"id\": \"el1664698615056\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data22\", \"id\": \"el1664698633552\"}], \"sharey\": [\"el1664694534544\"], \"sharex\": [\"el1664694534544\"], \"axesbgalpha\": null, \"axes\": [{\"scale\": \"linear\", \"tickformat\": null, \"grid\": {\"color\": \"#FFFFFF\", \"alpha\": 1.0, \"dasharray\": \"10,0\", \"gridOn\": true}, \"fontsize\": 10.0, \"position\": \"bottom\", \"nticks\": 9, \"tickvalues\": null}, {\"scale\": \"linear\", \"tickformat\": \"\", \"grid\": {\"color\": \"#FFFFFF\", \"alpha\": 1.0, \"dasharray\": \"10,0\", \"gridOn\": true}, \"fontsize\": 10.0, \"position\": \"left\", \"nticks\": 8, \"tickvalues\": null}], \"lines\": [{\"color\": \"#4C72B0\", \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 2, \"alpha\": 1, \"xindex\": 0, \"linewidth\": 1.75, \"data\": \"data12\", \"id\": \"el1664698645328\"}], \"markers\": [], \"id\": \"el1664695021392\", \"ydomain\": [0.0, 1.2000000000000002], \"collections\": [], \"xscale\": \"linear\", \"bbox\": [0.54772727272727262, 0.125, 0.35227272727272729, 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" });\n",
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"</script>"
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Bsnvii+k+m2j+GrN/eeHChWhubsbx48eh6zp2796NZcuWDTlm2bJleP/992EY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\nV1yR/XlXXnllTnHNmzcPQKaoSyaTQ16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"text": [
"<matplotlib.figure.Figure at 0x24c4f90>"
]
}
],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# After observing 0 successes from 1000 binomially distributed trials, the posterior of p is still beta-distributed\n",
"# with p_posterior ~ Beta(1,1001)\n",
"\n",
"p_posterior = np.random.beta(a=1, b=1001, size=1000000)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, ax = plt.subplots(1, 2, sharex=True, sharey=True)\n",
"sns.distplot(p.trace(), bins=10, ax=ax[0], kde=True, axlabel='MCMC Samples')\n",
"sns.distplot(p_posterior, bins=10, ax=ax[1], kde=True, axlabel='Beta(1,1001)')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 7,
"text": [
"<matplotlib.axes.AxesSubplot at 0x60dea10>"
]
},
{
"html": [
"\n",
"\n",
"<style>\n",
"\n",
"</style>\n",
"\n",
"<div id=\"fig_el16646987744165898207548\"></div>\n",
"<script>\n",
"function mpld3_load_lib(url, callback){\n",
" var s = document.createElement('script');\n",
" s.src = url;\n",
" s.async = true;\n",
" s.onreadystatechange = s.onload = callback;\n",
" s.onerror = function(){console.warn(\"failed to load library \" + url);};\n",
" document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
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" // already loaded: just create the figure\n",
" !function(mpld3){\n",
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" }(mpld3);\n",
"}else if(typeof define === \"function\" && define.amd){\n",
" // require.js is available: use it to load d3/mpld3\n",
" require.config({paths: {d3: \"https://mpld3.github.io/js/d3.v3.min\"}});\n",
" require([\"d3\"], function(d3){\n",
" window.d3 = d3;\n",
" mpld3_load_lib(\"https://mpld3.github.io/js/mpld3.v0.3git.js\", function(){\n",
" \n",
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[0.004008132415891356, 38.02121040317658], [0.0026720886797414953, 38.02121040317658]], \"data14\": [[0.0013360449435916336, 0.0], [0.0026720886797414953, 0.0], [0.0026720886797414953, 145.17189426667417], [0.0013360449435916336, 145.17189426667417]], \"data17\": [[0.005344176152041218, 0.0], [0.00668021988819108, 0.0], [0.00668021988819108, 2.520875558838904], [0.005344176152041218, 2.520875558838904]], \"data16\": [[0.004008132415891356, 0.0], [0.005344176152041218, 0.0], [0.005344176152041218, 9.953266977862157], [0.004008132415891356, 9.953266977862157]], \"data11\": [[0.009022025812986077, 0.0], [0.010024464810208564, 0.0], [0.010024464810208564, 0.03325223123371283], [0.009022025812986077, 0.03325223123371283]], \"data10\": [[0.00801958681576359, 0.0], [0.009022025812986076, 0.0], [0.009022025812986076, 0.09975669370113867], [0.00801958681576359, 0.09975669370113867]], \"data13\": [[1.2074417724342035e-09, 0.0], [0.0013360449435916339, 0.0], [0.0013360449435916339, 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[0.012014933640276748, 0.0], [0.012122705635268377, 0.11814465505989347], [0.012230477630260007, 0.0], [0.012338249625251638, 0.1623020185816486], [0.012446021620243266, 0.0], [0.012553793615234897, 0.22168669785419937], [0.012661565610226527, 0.0], [0.012769337605218156, 0.32825979519391524], [0.012877109600209786, 0.0], [0.012984881595201414, 0.5292158043715087], [0.013092653590193045, 0.0], [0.013200425585184675, 0.9359741868813742], [0.013308197580176304, 0.0], [0.013415969575167934, 1.8713139546087723], [0.013523741570159563, 0.0]]}, \"id\": \"el1664698774416\"});\n",
" });\n",
" });\n",
"}else{\n",
" // require.js not available: dynamically load d3 & mpld3\n",
" mpld3_load_lib(\"https://mpld3.github.io/js/d3.v3.min.js\", function(){\n",
" mpld3_load_lib(\"https://mpld3.github.io/js/mpld3.v0.3git.js\", function(){\n",
" \n",
" mpld3.draw_figure(\"fig_el16646987744165898207548\", {\"axes\": [{\"xlim\": [-0.002, 0.014], \"yscale\": \"linear\", \"axesbg\": \"#EAEAF2\", \"texts\": [{\"v_baseline\": \"hanging\", \"h_anchor\": \"middle\", \"color\": \"#262626\", \"text\": \"MCMC Samples\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 11.0, \"position\": [0.5, -0.094086021505376358], \"rotation\": -0.0, \"id\": \"el1664696957008\"}], \"zoomable\": true, \"images\": [], \"xdomain\": [-0.002, 0.014], \"ylim\": [0.0, 900.0], \"paths\": [{\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data02\", \"id\": \"el16646110697232\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data03\", \"id\": \"el16646110698320\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data04\", \"id\": \"el16646110712720\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data05\", \"id\": \"el16646110714384\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data06\", \"id\": \"el16646110694672\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data07\", \"id\": \"el16646110720592\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data08\", \"id\": \"el16646110722256\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data09\", \"id\": \"el16646110740368\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data10\", \"id\": \"el16646110742032\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data11\", \"id\": \"el16646110743312\"}], \"sharey\": [\"el16646101575184\"], \"sharex\": [\"el16646101575184\"], \"axesbgalpha\": null, \"axes\": [{\"scale\": \"linear\", \"tickformat\": null, \"grid\": {\"color\": \"#FFFFFF\", \"alpha\": 1.0, \"dasharray\": \"10,0\", \"gridOn\": true}, \"fontsize\": 10.0, \"position\": \"bottom\", \"nticks\": 9, \"tickvalues\": null}, {\"scale\": \"linear\", \"tickformat\": null, \"grid\": {\"color\": \"#FFFFFF\", \"alpha\": 1.0, \"dasharray\": \"10,0\", \"gridOn\": true}, \"fontsize\": 10.0, \"position\": \"left\", \"nticks\": 10, \"tickvalues\": null}], \"lines\": [{\"color\": \"#4C72B0\", \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 2, \"alpha\": 1, \"xindex\": 0, \"linewidth\": 1.75, \"data\": \"data01\", \"id\": \"el16646110668112\"}], \"markers\": [], \"id\": \"el1664638552976\", \"ydomain\": [0.0, 900.0], \"collections\": [], \"xscale\": \"linear\", \"bbox\": [0.125, 0.125, 0.35227272727272724, 0.77500000000000002]}, {\"xlim\": [-0.002, 0.014], \"yscale\": \"linear\", \"axesbg\": \"#EAEAF2\", \"texts\": [{\"v_baseline\": \"hanging\", \"h_anchor\": \"middle\", \"color\": \"#262626\", \"text\": \"Beta(1,1001)\", \"coordinates\": \"axes\", \"zorder\": 3, \"alpha\": 1, \"fontsize\": 11.0, \"position\": [0.5, -0.094086021505376358], \"rotation\": -0.0, \"id\": \"el16646101595344\"}], \"zoomable\": true, \"images\": [], \"xdomain\": [-0.002, 0.014], \"ylim\": [0.0, 900.0], \"paths\": [{\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data13\", \"id\": \"el16646110667856\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data14\", \"id\": \"el16646101609552\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, \"coordinates\": \"data\", \"dasharray\": \"none\", \"zorder\": 1, \"alpha\": 0.4, \"xindex\": 0, \"data\": \"data15\", \"id\": \"el16646101596624\"}, {\"edgecolor\": \"#000000\", \"facecolor\": \"#4C72B0\", \"edgewidth\": 0.3, \"pathcodes\": [\"M\", \"L\", \"L\", \"L\", \"Z\"], \"yindex\": 1, 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HO6ceyImIzFRoBn1YYb6do94+/IEQNmvWLjcpkjZiDsYuu+wyLrvsMgCKi4vZ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\nRCSNlIyJiIiIpNFPf3BHTFBkibcAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x5e32d90>"
]
}
],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print 'From MCMC'\n",
"print np.round(np.percentile(mcmc.trace('p')[:], [2.5, 97.5]), 5)\n",
"print np.round(p.stats()['95% HPD interval'], 5) # alternative approach to interval prediction\n",
"print\n",
"print 'From Beta(1,1001)'\n",
"print np.round(np.percentile(p_posterior, [2.5, 97.5]), 5)\n",
"print np.round(pm.utils.hpd(p_posterior, alpha=.05), 5) # alternative approach to interval prediction"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"From MCMC\n",
"[ 3.00000000e-05 3.68000000e-03]\n",
"[ 0. 0.00295]\n",
"\n",
"From Beta(1,1001)\n",
"[ 3.00000000e-05 3.68000000e-03]"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"[ 0. 0.00299]"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 8
}
],
"metadata": {}
}
]
}
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