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{
"metadata": {
"name": "",
"signature": "sha256:7b61dfeaae74223d1024ed82279564238d3f26d45580b2c8b4534e01a92394b4"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"import matplotlib.pyplot as plt, numpy as np, seaborn as sns, \\\n",
" powerlaw, pymc as pm\n",
"%matplotlib inline"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# set random seed for reproducibility\n",
"np.random.seed(12345)\n",
"\n",
"# simulate data from power law distribution\n",
"test = powerlaw.Power_Law(xmin = 1., parameters = [1.5])\n",
"simulated = test.generate_random(1000)\n",
"\n",
"# fit with powerlaw package\n",
"fit = powerlaw.Fit(simulated, xmin=1.)\n"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 12
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# PyMC model with xmin fixed\n",
"xmin = 1.\n",
"alpha = pm.Exponential('alpha', 1.5)\n",
"\n",
"@pm.stochastic(observed=True)\n",
"def power_law(value=simulated, alpha=alpha, xmin=xmin):\n",
" return np.sum(np.log((alpha-1) * xmin**(alpha-1) * value**-alpha))\n",
"\n",
"model = pm.MCMC([alpha,xmin,power_law])\n",
"model.sample(iter=5000, burn=0, thin=1) # 5000 iterations with 0 burn-in is not enough"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [---------------- 44% ] 2228 of 5000 complete in 0.5 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------87%------------- ] 4384 of 5000 complete in 1.0 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------100%-----------------] 5000 of 5000 complete in 1.1 sec"
]
}
],
"prompt_number": 13
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"pm.Matplot.plot(model)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plotting alpha\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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4nJTysoio7ZjlsjpERHc75mQRWT6uZExERETUDkw3XMiuLCIiIurEmJNFRGSGmJNFZPlM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\nOcM3KkoAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x7f9e45dab8d0>"
]
}
],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# PyMC model with xmin fixed\n",
"xmin = 1.\n",
"alpha = pm.Exponential('alpha', 1.5)\n",
"\n",
"@pm.stochastic(observed=True)\n",
"def power_law(value=simulated, alpha=alpha, xmin=xmin):\n",
" return np.sum(np.log((alpha-1) * xmin**(alpha-1) * value**-alpha))\n",
"\n",
"model = pm.MCMC([alpha,xmin,power_law])\n",
"model.sample(iter=20000, burn=10000, thin=10) # in this case the burn-in is the important part,\n",
" # but I'll run it for longer anyway, and thin to keep\n",
" # just 1000 samples for fast computation"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [---- 12% ] 2405 of 20000 complete in 0.5 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [--------- 24% ] 4808 of 20000 complete in 1.0 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [------------- 36% ] 7208 of 20000 complete in 1.5 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------48% ] 9602 of 20000 complete in 2.0 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------59%-- ] 11977 of 20000 complete in 2.5 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------71%------- ] 14346 of 20000 complete in 3.0 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------83%----------- ] 16718 of 20000 complete in 3.5 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------95%---------------- ] 19094 of 20000 complete in 4.0 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------100%-----------------] 20000 of 20000 complete in 4.2 sec"
]
}
],
"prompt_number": 15
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"pm.Matplot.plot(model)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plotting alpha\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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VD461Rb7lxn3HbQWKqezKL4zpEXp1aobmUeLLpVJw9tmQ7OQVSsXwsD2JZ69J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\ncb0uLy9HZmYmHn74YZSXl6O8vBxLly6VMUJlYQKmTh1R43CqPZBPDO/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8xenP8aKEOD0d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\niEgm/x9fGj87F7jHwAAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x7f9e3c0c7ad0>"
]
}
],
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"xmin = pm.Uninformative('xmin', value=0.1)\n",
"alpha = pm.Exponential('alpha', 1.5)\n",
"\n",
"@pm.stochastic(observed=True)\n",
"def power_law(value=simulated, alpha=alpha, xmin=xmin):\n",
" if value.min() < xmin:\n",
" return -np.inf\n",
" return np.sum(np.log((alpha-1) * xmin**(alpha-1) * value**-alpha))\n",
"\n",
"model = pm.MCMC([alpha,xmin,power_law])\n",
"model.sample(iter=5000, burn=2500)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [----------- 30% ] 1523 of 5000 complete in 0.5 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------58%-- ] 2913 of 5000 complete in 1.0 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------84%------------ ] 4226 of 5000 complete in 1.5 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------100%-----------------] 5000 of 5000 complete in 1.8 sec"
]
}
],
"prompt_number": 17
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"pm.Matplot.plot(model)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plotting xmin\n",
"Plotting"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" alpha\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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3yIFyJHeon1cGXqbykQDjD3+2+yh8gB/CQvwQ5K9ppTHVtdapE5So1Wrjlize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\nl4iIiIifKPESERER8ZP/D5wWISkpj9BUAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x7f9e45dab8d0>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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43SxsVi4wTGyHmkNJOUu/wUJMWQMGLM/b49HyKCsIb5qaNC1mivUhjMNM/Sb6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\nEank/wCvxe89TTSWFAAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x7f9e3c0632d0>"
]
}
],
"prompt_number": 18
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# PyMC model with xmin as an additional parameter\n",
"xmin = pm.Uniform('xmin', 0., 10., value=1.)\n",
"alpha = pm.Uniform('alpha', 1., 10.)\n",
"\n",
"@pm.stochastic(observed=True)\n",
"def power_law(value=simulated, alpha=alpha, xmin=xmin):\n",
" # xmin must be less than all data values\n",
" if xmin > np.min(value):\n",
" return -np.inf\n",
" \n",
" return np.sum(np.log(alpha-1) + (alpha-1)*np.log(xmin) + -alpha*np.log(value))\n",
"\n",
"model = pm.MCMC([alpha,xmin,power_law])\n",
"model.sample(iter=20000, burn=10000, thin=10)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [----- 13% ] 2725 of 20000 complete in 0.5 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [--------- 25% ] 5032 of 20000 complete in 1.0 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [------------- 35% ] 7188 of 20000 complete in 1.5 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------46% ] 9323 of 20000 complete in 2.0 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------57%- ] 11426 of 20000 complete in 2.5 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------67%----- ] 13518 of 20000 complete in 3.0 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------77%--------- ] 15588 of 20000 complete in 3.5 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------88%------------- ] 17662 of 20000 complete in 4.0 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------98%----------------- ] 19735 of 20000 complete in 4.5 sec"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\r",
" [-----------------100%-----------------] 20000 of 20000 complete in 4.6 sec"
]
}
],
"prompt_number": 19
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"pm.Matplot.plot(model)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plotting alpha\n",
"Plotting"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" xmin\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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3XZ2eV47RYOQ853jss13nsff4dXwwLx2lpfbLdkVFlbzXOVJcYr9z9f1vTuLu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\nIiKSCQsxIiIiIpn8L4OtQVSiHmtyAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x7f9e33f75150>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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hrY9/dFzQCdhCdHQXd8lEPSEDuxqktq+xFKZeXyM8WbZDDZtlGyQQEQRBDGgc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\ngg==\n",
"text": [
"<matplotlib.figure.Figure at 0x7f9e3c381510>"
]
}
],
"prompt_number": 20
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print 'alpha:', fit.alpha, 'vs', alpha.trace().mean()\n",
"print ' xmin:', fit.xmin, 'vs', xmin.trace().mean()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"alpha: 1.49787599133 vs 1.49828919861\n",
" xmin: 1.0 vs 0.998160020389\n"
]
}
],
"prompt_number": 21
}
],
"metadata": {}
}
]
}
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