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@aflaxman
Created November 11, 2013 21:10
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PyMC3 Gelman-Rubin convergence diagnostic on a simple case
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{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"!date"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Mon Nov 11 13:09:19 PST 2013\r\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import pymc as mc"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"n = 500\n",
"m = 5"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%%time\n",
"\n",
"np.random.seed(123456)\n",
"with mc.Model() as model:\n",
" theta = mc.Normal('theta', 1., 1.)\n",
" \n",
" ptrace = mc.psample(draws=n,\n",
" start=[{'theta':1+.25*randn()} for j in range(m)],\n",
" step=mc.Metropolis(scaling=.5, tune=False),\n",
" threads=m,\n",
" random_seeds=123456+arange(m))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"CPU times: user 325 ms, sys: 54 ms, total: 379 ms\n",
"Wall time: 1.43 s\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mc.gelman_rubin(ptrace)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 6,
"text": [
"{'theta': 1.0289896318833507}"
]
}
],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mean(ptrace['theta'])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 7,
"text": [
"1.1914695220942182"
]
}
],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mc.traceplot(ptrace)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
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rA3bscP5c5eU0RmKmOP5c1dVkrdBTTOrqqP8bN9qmpRaVLD34GEA9Tpyg+D2t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\nKFUwdzrHvAAAAABJRU5ErkJggg==\n",
"prompt_number": 8,
"text": [
"<matplotlib.figure.Figure at 0x9f88910>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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rA3bscP5c5eU0RmKmOP5c1dVkrdBTTOrqqP8bN9qmpRaVLD34GEA9Tpyg+D2t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\nKFUwdzrHvAAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x9f88910>"
]
}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Running longer gets the mean more accurately."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%%time\n",
"\n",
"np.random.seed(123456)\n",
"with mc.Model() as model:\n",
" theta = mc.Normal('theta', 1., 1.)\n",
" \n",
" ptrace = mc.psample(draws=n*50,\n",
" start=[{'theta':1+.25*randn()} for j in range(m)],\n",
" step=mc.Metropolis(scaling=.5, tune=False),\n",
" threads=m,\n",
" random_seeds=123456+arange(m))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"CPU times: user 559 ms, sys: 81 ms, total: 640 ms\n",
"Wall time: 8.89 s\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mc.gelman_rubin(ptrace)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 10,
"text": [
"{'theta': 1.0002930403991559}"
]
}
],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mean(ptrace['theta'])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 11,
"text": [
"0.99987846236776967"
]
}
],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mc.traceplot(ptrace)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"png": 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/DywxppUhdJV+Xev1wYP6lj+eggJxl9Pycn03QTGkutnySiD/PrLEmGmWIj+f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\n2dlZ7WsfEBAAX19fnD17Vi5R7R7dHnW54TjmCvj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14QtRedpSgyyz2cyDLBVWqxWVlZVo\naGhAQ0MDLl26JDokTRkaGoIkSaitrUVvb6/ocDRpfHwcRUVFOHDggFyPhoeHRYelaaOjo7y6YAZT\nU1Ow2+2oq6vD8ePHMT8/LzqkjLT+nFBro8plh5uamlYtO9ze3i4vbazstPb398tLPD98+FA+rlza\nONcdwfUo21OmZaNdLhdsNhuOHDmC2dlZ+e97enpQW1sLSZLw+vVr+biIvKar+3rPU2dnJ6xWK2pq\nanD69GksLS3pLk9nzpzB7t27sX37dphMJvT39xckL5mukesyPXjwIGOfMNv7v5kc56pMJSUlcp6U\nUscDovJUBOj8C6WMMcYYY4wxpiG6mJPFGGOMMcYYY3rBgyzGGGOMMcYYyyEeZDHGGGOMMcZYDvEg\nizHGGGOMMcZyiAdZjDHGGGOMMZZD/wBTnyAaI7MohgAAAABJRU5ErkJggg==\n",
"prompt_number": 12,
"text": [
"<matplotlib.figure.Figure at 0xa1f0550>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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/DywxppUhdJV+Xev1wYP6lj+eggJxl9Pycn03QTGkutnySiD/PrLEmGmWIj+f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\n2dlZ7WsfEBAAX19fnD17Vi5R7R7dHnW54TjmCvj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14QtRedpSgyyz2cyDLBVWqxWVlZVo\naGhAQ0MDLl26JDokTRkaGoIkSaitrUVvb6/ocDRpfHwcRUVFOHDggFyPhoeHRYelaaOjo7y6YAZT\nU1Ow2+2oq6vD8ePHMT8/LzqkjLT+nFBro8plh5uamlYtO9ze3i4vbazstPb398tLPD98+FA+rlza\nONcdwfUo21OmZaNdLhdsNhuOHDmC2dlZ+e97enpQW1sLSZLw+vVr+biIvKar+3rPU2dnJ6xWK2pq\nanD69GksLS3pLk9nzpzB7t27sX37dphMJvT39xckL5mukesyPXjwIGOfMNv7v5kc56pMJSUlcp6U\nUscDovJUBOj8C6WMMcYYY4wxpiG6mJPFGGOMMcYYY3rBgyzGGGOMMcYYyyEeZDHGGGOMMcZYDvEg\nizHGGGOMMcZyiAdZjDHGGGOMMZZD/wBTnyAaI7MohgAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0xa1f0550>"
]
}
],
"prompt_number": 12
}
],
"metadata": {}
}
]
}
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