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@andyfaff
Created January 27, 2016 05:05
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fixing_sigma
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import emcee\n",
"from lmfit import Minimizer, Parameter, Parameters\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": 2,
"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": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"values from emcee direct - using sigma\n",
"27.4440439952 4.17508793111\n",
"0.436834137254 0.0781237188117\n",
"values from emcee - ignoring sigma"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/anz/miniconda3/envs/dev3/lib/python3.4/site-packages/matplotlib/collections.py:650: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n",
" if self._edgecolors_original != str('face'):\n",
"/Users/anz/miniconda3/envs/dev3/lib/python3.4/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n",
" if self._edgecolors == str('face'):\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"27.1084969127 0.396426223662\n",
"0.441064312956 0.00754150154749\n"
]
},
{
"data": {
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1vPrqq/j6+tJoaP8dIdRMUASAaX2x9kJxGTYVO80lKCgCadu2bbz++utMnDiR8PBwRowY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3CDc267b59hwGjgSuCQc+57Cd5Hsz5F0kCzPoOn+5dI95NLsz7/B7DLOfcH59xxYB1w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\nAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x109b5f400>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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FodFx+vRpnZ2drXfu3KnXrVun77jjDj1w4EC9ceNGvXPnTv3999/rU6dONfQ2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\nEieEEEIIEYT+P/i4d0Dgx6JQAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10a2bdf60>"
]
},
"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",
"sampler.run_mcmc(starting_guesses, nsteps)\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",
"print(\"values from emcee direct - using sigma\")\n",
"lv, uv = np.percentile(emcee_trace[0], [15.8, 84.2])\n",
"print(np.median(emcee_trace[0]), 0.5 * (uv - lv))\n",
"lv, uv = np.percentile(emcee_trace[1], [15.8, 84.2])\n",
"print(np.median(emcee_trace[1]), 0.5 * (uv - lv))\n",
"plot_MCMC_results(xdata, ydata, emcee_trace)\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",
"sampler2 = emcee.EnsembleSampler(nwalkers, ndim, log_posterior, args=[xdata, ydata])\n",
"sampler2.run_mcmc(starting_guesses, nsteps)\n",
"\n",
"# sampler.chain is of shape (nwalkers, nsteps, ndim)\n",
"# we'll throw-out the burn-in points and reshape:\n",
"emcee_trace = sampler2.chain[:, nburn:, :].reshape(-1, ndim).T\n",
"print(\"values from emcee - ignoring sigma\")\n",
"lv, uv = np.percentile(emcee_trace[0], [15.8, 84.2])\n",
"print(np.median(emcee_trace[0]), 0.5 * (uv - lv))\n",
"lv, uv = np.percentile(emcee_trace[1], [15.8, 84.2])\n",
"print(np.median(emcee_trace[1]), 0.5 * (uv - lv))\n",
"plot_MCMC_results(xdata, ydata, emcee_trace)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Now lets do it with the lmfit PR"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def resid (params):\n",
" return params['alpha'] + params['beta'] * xdata - ydata"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"params = Parameters()\n",
"params.add('alpha', value=1)\n",
"params.add('beta', value=1)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"mini = Minimizer(resid, params)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Without sigma\n",
"Parameters([('alpha', <Parameter 'alpha', value=27.117055897020652 +/- 0.396, bounds=[-inf:inf]>), ('beta', <Parameter 'beta', value=0.44117048125554958 +/- 0.00755, bounds=[-inf:inf]>)])\n",
"With sigma"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/anz/miniconda3/envs/dev3/lib/python3.4/site-packages/matplotlib/collections.py:650: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n",
" if self._edgecolors_original != str('face'):\n",
"/Users/anz/miniconda3/envs/dev3/lib/python3.4/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n",
" if self._edgecolors == str('face'):\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Parameters([('alpha', <Parameter 'alpha', value=26.998979843656901 +/- 4.21, bounds=[-inf:inf]>), ('beta', <Parameter 'beta', value=0.44481998809484524 +/- 0.082, bounds=[-inf:inf]>), ('__lnsigma', <Parameter '__lnsigma', value=2.3513960167668193 +/- 0.171, bounds=[-inf:inf]>)])\n"
]
},
{
"data": {
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SkhJ2797N7t27ycrKYvfu3ZhMJry9vQkMDORPf/oT/fr1+1XB2Th6dy3PR6G4UlQkTqFQ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WFLRkYGy5YtY8yYMdx4441ERETUOmmrze/ifOmYuNCxadOmWtdos1rfvvvuO4qKipg/fz7Hjh0j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\nKaVCkCZxSimllFIh6P8DVpQ/QYqT+xwAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x105bb33c8>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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AERERWsP1vLw8pk+fTkJCgla817iQrup6NY2xg0Yr3ZYtW1iwYAH9+vVjw4YN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\nUFpayvTp03FzcyM+Pp6SkhK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OnDnD6dOnWbduHV5eXtja2rJnzx4iIyNJSEjAy8uLu+66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\nIiISU0rURERERGLq/wGGlX7NSAQ2zwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x104baee10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# first without sigma\n",
"# DEFAULT is for is_weighted == True\n",
"res = mini.emcee(params=params, steps=2000, burn=1000, nwalkers=50, is_weighted=True)\n",
"print(\"Without sigma\")\n",
"print(res.params)\n",
"emcee_trace = res.chain.reshape(-1, 2).T\n",
"plot_MCMC_results(xdata, ydata, emcee_trace)\n",
"\n",
"# then with sigma\n",
"res = mini.emcee(params=params, steps=2000, burn=1000, nwalkers=50, is_weighted=False)\n",
"print(\"With sigma\")\n",
"print(res.params)\n",
"emcee_trace = res.chain[..., :-1].reshape(-1, 2).T\n",
"plot_MCMC_results(xdata, ydata, emcee_trace)"
]
},
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"source": [
"I would say that the two MC traces look fairly similar. If there are differences they are probably due to the fact that I'm using a uniform prior. The parameters look ok, the `__lnsigma` value gives an uncertainty (on each datapoint) of ~10."
]
}
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