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@Tillsten
Created September 4, 2015 12:55
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{
"cells": [
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import emcee\n",
"\n",
"np.random.seed(42)\n",
"theta_true = (25, 0.5)\n",
"xdata = 100 * np.random.random(20)\n",
"ydata = theta_true[0] + theta_true[1] * xdata\n",
"\n",
"# add scatter to points\n",
"xdata = np.random.normal(xdata, 10)\n",
"ydata = np.random.normal(ydata, 10)"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Create some convenience routines for plotting\n",
"\n",
"def compute_sigma_level(trace1, trace2, nbins=20):\n",
" \"\"\"From a set of traces, bin by number of standard deviations\"\"\"\n",
" L, xbins, ybins = np.histogram2d(trace1, trace2, nbins)\n",
" L[L == 0] = 1E-16\n",
" logL = np.log(L)\n",
"\n",
" shape = L.shape\n",
" L = L.ravel()\n",
"\n",
" # obtain the indices to sort and unsort the flattened array\n",
" i_sort = np.argsort(L)[::-1]\n",
" i_unsort = np.argsort(i_sort)\n",
"\n",
" L_cumsum = L[i_sort].cumsum()\n",
" L_cumsum /= L_cumsum[-1]\n",
" \n",
" xbins = 0.5 * (xbins[1:] + xbins[:-1])\n",
" ybins = 0.5 * (ybins[1:] + ybins[:-1])\n",
"\n",
" return xbins, ybins, L_cumsum[i_unsort].reshape(shape)\n",
"\n",
"\n",
"def plot_MCMC_trace(ax, xdata, ydata, trace, scatter=False, **kwargs):\n",
" \"\"\"Plot traces and contours\"\"\"\n",
" xbins, ybins, sigma = compute_sigma_level(trace[0], trace[1])\n",
" ax.contour(xbins, ybins, sigma.T, levels=[0.683, 0.955], **kwargs)\n",
" if scatter:\n",
" ax.plot(trace[0], trace[1], ',k', alpha=0.1)\n",
" ax.set_xlabel(r'$\\alpha$')\n",
" ax.set_ylabel(r'$\\beta$')\n",
" \n",
" \n",
"def plot_MCMC_model(ax, xdata, ydata, trace):\n",
" \"\"\"Plot the linear model and 2sigma contours\"\"\"\n",
" ax.plot(xdata, ydata, 'ok')\n",
"\n",
" alpha, beta = trace[:2]\n",
" xfit = np.linspace(-20, 120, 10)\n",
" yfit = alpha[:, None] + beta[:, None] * xfit\n",
" mu = yfit.mean(0)\n",
" sig = 2 * yfit.std(0)\n",
"\n",
" ax.plot(xfit, mu, '-k')\n",
" ax.fill_between(xfit, mu - sig, mu + sig, color='lightgray')\n",
"\n",
" ax.set_xlabel('x')\n",
" ax.set_ylabel('y')\n",
"\n",
"\n",
"def plot_MCMC_results(xdata, ydata, trace, colors='k'):\n",
" \"\"\"Plot both the trace and the model together\"\"\"\n",
" fig, ax = plt.subplots(1, 2, figsize=(10, 4))\n",
" plot_MCMC_trace(ax[0], xdata, ydata, trace, True, colors=colors)\n",
" plot_MCMC_model(ax[1], xdata, ydata, trace)"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Wall time: 2.75 s\n",
"done\n",
"Wall time: 3.85 s\n",
"done\n"
]
},
{
"data": {
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A/ggSG8quXWuzwtXeK0nXS2bUJKltEkKQl5dHXl6eWQRov//+O+Hh4WRmZjJnzhwefPBB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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xd0ff898>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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Li8WLF+Ph4XFT4dS2rgiW3H5IESeRSFqSxlqHFBYWsnDhQnr06MFrr72Gh4cHUPc86tu3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\n9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2scr7zySkBb2RoCbYkLKjU1NVJRUSHbtm2T/Px8eeyxx6RLly4yc+ZMKSgokC+++EJO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\nkzillFJKqRD0/wHfkULqGg6hGQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xb690eb8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def log_prior(theta):\n",
" alpha, beta, sigma = theta\n",
" if sigma < 0:\n",
" return -np.inf # log(0)\n",
" else:\n",
" return -1.5 * np.log(1 + beta ** 2) - np.log(sigma)\n",
"\n",
"def log_likelihood(theta, x, y): \n",
" alpha, beta, sigma = theta\n",
" y_model = alpha + beta * x\n",
" return -0.5 * np.sum(np.log(2 * np.pi * sigma ** 2) + (y - y_model) ** 2 / sigma ** 2)\n",
"\n",
"def log_posterior(theta, x, y):\n",
" if len(theta) == 2:\n",
" theta = np.hstack((theta, 1))\n",
" return log_prior(theta) + log_likelihood(theta, x, y)\n",
"\n",
"ndim = 3 # number of parameters in the model\n",
"nwalkers = 50 # number of MCMC walkers\n",
"nburn = 1000 # \"burn-in\" period to let chains stabilize\n",
"nsteps = 2000 # number of MCMC steps to take\n",
"\n",
"# set theta near the maximum likelihood, with \n",
"np.random.seed(0)\n",
"starting_guesses = np.random.random((nwalkers, ndim))\n",
"sampler = emcee.EnsembleSampler(nwalkers, ndim, log_posterior, args=[xdata, ydata])\n",
"%time sampler.run_mcmc(starting_guesses, nsteps)\n",
"print(\"done\")\n",
"\n",
"# sampler.chain is of shape (nwalkers, nsteps, ndim)\n",
"# we'll throw-out the burn-in points and reshape:\n",
"emcee_trace = sampler.chain[:, nburn:, :].reshape(-1, ndim).T\n",
"plot_MCMC_results(xdata, ydata, emcee_trace)\n",
"\n",
"\n",
"ndim = 2 # number of parameters in the model\n",
"nwalkers = 50 # number of MCMC walkers\n",
"nburn = 1000 # \"burn-in\" period to let chains stabilize\n",
"nsteps = 2000 # number of MCMC steps to take\n",
"\n",
"# set theta near the maximum likelihood, with \n",
"np.random.seed(0)\n",
"starting_guesses = np.random.random((nwalkers, ndim))\n",
"sampler = emcee.EnsembleSampler(nwalkers, ndim, log_posterior, args=[xdata, ydata])\n",
"%time sampler.run_mcmc(starting_guesses, nsteps)\n",
"print(\"done\")\n",
"\n",
"# sampler.chain is of shape (nwalkers, nsteps, ndim)\n",
"# we'll throw-out the burn-in points and reshape:\n",
"emcee_trace = sampler.chain[:, nburn:, :].reshape(-1, ndim).T\n",
"plot_MCMC_results(xdata, ydata, emcee_trace)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.8"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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