{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# MCMC: Metropolis-Hastings algorithm and diagnostics"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Florent Leclercq,
\n",
"Imperial Centre for Inference and Cosmology, Imperial College London,
\n",
"florent.leclercq@polytechnique.org"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from scipy.stats import norm, binom, beta\n",
"from matplotlib import pyplot as plt\n",
"from cycler import cycler\n",
"np.random.seed(123456)\n",
"%matplotlib inline\n",
"plt.rcParams.update({'lines.linewidth': 2})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this notebook we consider a Bernoulli experiment (a series of $N_{\\mathrm{trials}}$ independent experiments, each with its own boolean-valued outcome). The target parameter is the success rate $\\theta$. The likelihood for this problem is a [binomial distribution](https://en.wikipedia.org/wiki/Binomial_distribution) and the [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution) provides a family of conjuguate priors for Bayesian inference."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Generate data"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"33"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"groundtruth = 0.38\n",
"Ntrials = 100\n",
"Nsuccesses = binom(Ntrials, groundtruth).rvs()\n",
"Nsuccesses"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Analytic solution"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If the likelihood is a binomial distribution with $N_{\\mathrm{successes}}$ for $N_{\\mathrm{trials}}$, and if the prior is a beta distribution with parameters ($\\alpha$, $\\beta$), then the posterior is a beta distribution with parameters\n",
"\\begin{equation}\n",
"\\alpha' = \\alpha+N_{\\mathrm{successes}}, \\quad \\beta' = \\beta + N_{\\mathrm{trials}} - N_{\\mathrm{successes}}\n",
"\\end{equation}\n",
"(see for example https://en.wikipedia.org/wiki/Conjugate_prior#When_likelihood_function_is_a_discrete_distribution)."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def target_pdf(theta,Ntrials,Nsuccesses,lh,prior):\n",
" if theta < 0 or theta > 1:\n",
" return 0\n",
" else:\n",
" return lh(Ntrials,theta).pmf(Nsuccesses)*prior.pdf(theta)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"a = 10\n",
"b = 10\n",
"lh = binom\n",
"prior = beta(a,b)\n",
"posterior = beta(a+Nsuccesses, b+Ntrials-Nsuccesses)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
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\n",
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