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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"source": [
"This notebook is concerned with pseudo-marginal MCMC as introduced in [Estimation of Population Growth or Decline in Genetically Monitored Populations](http://www.genetics.org/content/164/3/1139), and discussed in Darren Wilkinson's [blog post](https://darrenjw.wordpress.com/2010/09/20/the-pseudo-marginal-approach-to-exact-approximate-mcmc-algorithms/) and [The pseudo-marginal approach for efficient Monte Carlo computations](http://projecteuclid.org/euclid.aos/1236693147).\n",
"\n",
"In the following, we try to draw samples from the univariate normal distribution with zero mean and unit variance. We employ three different approaches:\n",
"\n",
"* `do-not-reevaluate` as suggested in Wilkinson's blog post. This method does not reevaluate the distribution for the currently accepted state of the chain.\n",
"* `reevaluate-individual` as warned against in Wilkinson's blog post. This method reevaluates the distribution for the currently accepted state of the chain and the candidate independently.\n",
"* `reevaluate-both` which reevaluates the distribution for the currently accepted step but evaluates the distribution for the candidate using the *same* sample.\n",
"\n",
"As expected, `reevaluate-individual` does not sample from the correct target distribution. `do-not-reevaluate` samples the correct target distribution but mixes badly if the variance of the estimator is high. Intuitively, if the method encounters a very large value of the distribution, it will get stuck in that state for a long time (as simulated below by a heavy-tailed log-normal distribution). `reevaluate-both` samples from the correct distribution and mixes well because the only thing that matters to the algorithm are the ratio of the distribution and the current state and the proposal--the absolute value is irrelevant."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import numpy as np\n",
"from matplotlib import pyplot as plt, rcParams\n",
"import scipy.stats\n",
"%matplotlib inline\n",
"rcParams['figure.dpi'] = 144"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"class NoisyLikelihood:\n",
" \"\"\"\n",
" Evaluates the univariate normal likelihood with multiplicative noise.\n",
" \"\"\"\n",
" def __init__(self):\n",
" self.sample_factor()\n",
" \n",
" def __call__(self, x):\n",
" return np.exp(-0.5 * x * x) * self.factor\n",
" \n",
" def sample_factor(self, *_):\n",
" self.factor = np.random.lognormal(1, 3)\n",
" \n",
"noisy_likelihood = NoisyLikelihood()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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DSAcAAAAyhpAOAAAAZAwhHQAAAMgYQjoAAACQMYR0AAAAIGMI6QAAAEDGENIBAACAjCGk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"text/plain": [
"<matplotlib.figure.Figure at 0x1125aff60>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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BZuBRoB7YCXg3cC7wVTM7xjn3XIH1VgDTCtz/WolPRaQ4TWugs9W7PmoSjCr6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\nNZX0QGxNStIlPkrSI3J53qydpTrsFw9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LiIhIMmr1pFEAM01oJJFSkh5CxTqRrNJPp0jV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wXKCv1+J+EGnA8syPH8sXgXiLuBcbU+nlXYz0i+o4Ev+8t/Puv5S/3n74x7XwvUPdR3fJGy1lLi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\nQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1146d1518>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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Lzayca4lUVyQfvV+VlRpb6vuyyYPSj3vZFvansp0D0lgUpEvdmLigjXdd+zQX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\nJB0AAGYC4Rem66kXSDQAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1148281d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"METHODS = ['do-not-reevaluate', 'reevaluate-individual', 'reevaluate-both']\n",
"def summary_plot(method):\n",
"\n",
" assert method in METHODS, \"method must be one of %s not %s\" % (', '.join(METHODS), method)\n",
"\n",
" # Start the sampler at the mode\n",
" x = 0\n",
" likelihood = noisy_likelihood(x)\n",
"\n",
" xs = [x]\n",
" likelihoods = [likelihood]\n",
"\n",
" for i in range(10000):\n",
" # Draw a candidate\n",
" candidate_x = np.random.normal(0, 1) + x\n",
" noisy_likelihood.sample_factor()\n",
"\n",
" # Deal with reevaluation\n",
" if method == 'do-not-reevaluate':\n",
" pass # Nothing to be done here\n",
" elif method == 'reevaluate-individual':\n",
" likelihood = noisy_likelihood(x)\n",
" noisy_likelihood.sample_factor()\n",
" elif method == 'reevaluate-both':\n",
" likelihood = noisy_likelihood(x)\n",
" else:\n",
" raise ValueError(\"method must be one of %s not %s\" % (', '.join(METHODS), method))\n",
"\n",
" # Compute the acceptance ratio\n",
" candidate_likelihood = noisy_likelihood(candidate_x)\n",
" acceptance = candidate_likelihood / likelihood\n",
"\n",
" # Accept or reject\n",
" if np.random.uniform() < acceptance:\n",
" x = candidate_x\n",
" likelihood = candidate_likelihood\n",
"\n",
" xs.append(x)\n",
" likelihoods.append(likelihood)\n",
"\n",
" fig, (ax1, ax2) = plt.subplots(1, 2)\n",
" ax1.plot(xs)\n",
" ax2.hist(xs, bins=20, normed=True)\n",
" lin = np.linspace(-3, 3)\n",
" ax2.plot(lin, scipy.stats.norm.pdf(lin))\n",
" fig.suptitle(method)\n",
" \n",
"for method in METHODS:\n",
" summary_plot(method)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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