{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Demonstration: Metropolis-Hasting MCMC sampling of a Poisson distribution " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook was adapted from Example 1, section 12.2 in Gregory's *Bayesian Logical Data Analysis for the Physical Sciences* {cite}`Gregory2005`." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "The Poisson discrete random variable from scipy.stats is defined by (see [documentation](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.poisson.html))\n", "\n", "$$\n", "p(k|\\mu) = \\frac{\\mu^k e^{-\\mu}}{k!} \\quad \\mbox{for }k\\geq 0 \\;.\n", "$$\n", "\n", "where $k$ is an integer and $\\mu$ is called the shape parameter. The mean and variance of this distribution are both equal to $\\mu$. (Note: Gregory uses a different notation, but we'll stay consistent with scipy.stats.)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "By \"sampling a Poisson distribution\" we mean we will obtain a set of $k$ values: $\\{k_1, k_2, k_3, \\ldots\\}$ that follow this distribution. That is, for a particular $k_i$, the probability to get that value should be what we get by evaluating $p(k_i|\\mu)$. We know we've succeeded if we make a histogram of our set of $k_i$s and it looks like $p(k|\\mu)$ (scaled to line up or else our histogram needs to be normalized to one).\n", "\n", "The method we'll use is generically called Markov chain Monte Carlo or MCMC. A Markov chain starts with some initial value, and then each successive value is generated from the previous one. But it is not deterministic: when the new value is chosen, there is a random number involved. The particular version of MCMC used here is called Metropolis-Hasting. You may be familiar with this from a statistical mechanics class, where it is typically applied to the Ising model." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "We'll do the Metropolis-Hasting sampling as follows:\n", "1. Choose an initial $k$ (call it $k_0$), having already fixed $\\mu$.\n", "2. Given $k_i$, sample a uniform random number $x$ from 0 to 1 (so $x \\sim U(0,1)$) and propose $k' = k_i + 1$ if the $x > 0.5$, otherwise propose $k' = k_i - 1$.\n", "3. Compute the Metropolis ratio $r = p(k'|\\mu)\\, /\\, p(k_i|\\mu)$ using the discrete Poisson distribution.\n", "4. Given another uniform random number $y \\sim U(0,1)$, $k_{i+1} = k'$ if $y \\leq r$, else $k_{i+1} = k_i$ (i.e., keep the same value for the next $k$).\n", "5. Repeat 2.-4. until you think you have enough samples of $k$.\n", "6. When graphing the posterior or calculating averages, skip the first values until the sampling has equilibrated (this is generally called the \"burn-in\" or \"warm-up\").\n", "\n", "In practice we'll carry this out by generating all our uniform random numbers at the beginning using `scipy.stats.uniform.rvs`." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "%matplotlib inline \n", "\n", "import numpy as np\n", "from math import factorial\n", "\n", "# We'll get our uniform distributions from stats, but there are other ways.\n", "import scipy.stats as stats \n", "\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "def poisson(k, mu):\n", " \"\"\"\n", " Returns a Poisson distribution value for k with mean mu\n", " \"\"\"\n", " return mu**k * np.exp(-mu) / factorial(k) " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "In the following we have the steps 1-6 defined above marked in the code. *Step through the implementation and ask questions about what you don't understand.*" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "# 1. Set mu and k0\n", "mu = 3.\n", "k0 = 10.\n", "\n", "num_steps = 1000 # number of MCMC steps we'll take\n", "# generate the two sets of uniform random numbers we'll need for 2. and 4.\n", "uniform_1 = stats.uniform.rvs(size=num_steps) \n", "uniform_2 = stats.uniform.rvs(size=num_steps)\n", "\n", "k_array = np.zeros(num_steps, dtype=int)\n", "k_array[0] = k0" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "# 5. Loop through steps 2-4\n", "for i in range(num_steps-1): # num_steps-1 so k_array[i+1] is always defined\n", " # 2. Propose a step\n", " k_now = k_array[i]\n", " if uniform_1[i] > 0.5:\n", " kp = k_now + 1 # step to the right\n", " else:\n", " kp = max(0, k_now - 1) # step to the left, but don't go below zero\n", " \n", " # 3. Calculate Metropolis ratio\n", " metropolis_r = poisson(kp, mu) / poisson(k_now, mu)\n", " # 4. Accept or reject\n", " if uniform_2[i] <= metropolis_r:\n", " k_array[i+1] = kp\n", " else:\n", " k_array[i+1] = k_now\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 6. Choose how many steps to skip\n", "warm_up_steps = 100\n", "\n", "fig = plt.figure(figsize=(10,10))\n", "\n", "# Plot the trace (that means k_i for i=0 to num_steps)\n", "ax_trace = fig.add_subplot(1, 1,1) \n", "ax_trace.plot(range(num_steps), k_array, color='blue')\n", "ax_trace.set_ylim(0, 12)\n", "ax_trace.set_xlabel(r'$i$')\n", "ax_trace.set_ylabel(r'$k_i$')\n", "trace_title = rf'MCMC trace for Poisson distribution with $\\mu = ${mu:.1f}'\n", "ax_trace.set_title(trace_title);" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(10,10))\n", "# Plot the Poisson distribution\n", "ax_plot = fig.add_subplot(1, 1, 1)\n", "bin_num = 12\n", "n_pts = range(bin_num)\n", " \n", "# Scale exact result to the histogram, accounting for warm_up_steps \n", "poisson_pts = [(num_steps - warm_up_steps) * poisson(n, mu) for n in n_pts] \n", " \n", "# Plot the exact distribution \n", "ax_plot.plot(n_pts, poisson_pts, marker='o', color='black') \n", "# Histogram k_i beyond the warm-up period\n", "ax_plot.hist(k_array[warm_up_steps:], bins=n_pts,\n", " align='left', rwidth=0.2, color='red')\n", "ax_plot.set_xlim(-1, bin_num)\n", "ax_plot.set_xlabel(r'$k$')\n", "plot_title = rf'$\\mu = ${mu:.1f} # steps = {num_steps:d},' \\\n", " + ' # warm-up steps = {warm_up_steps:d}'\n", "ax_plot.set_title(plot_title)\n", "\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "*What do you observe about these plots?*" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " MCMC mean = 2.93\n", "Exact mean = 3.00\n", " MCMC sd = 1.58\n", " Exact sd = 1.73\n" ] } ], "source": [ "# Check the mean and standard deviations from the samples against exac\n", "print(f' MCMC mean = {np.mean(k_array[warm_up_steps:]):.2f}')\n", "print(f'Exact mean = {stats.poisson.mean(mu=mu):.2f}')\n", "print(f' MCMC sd = {np.std(k_array[warm_up_steps:]):.2f}')\n", "print(f' Exact sd = {stats.poisson.std(mu=mu):.2f}') " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "* *How do you expect the accuracy of the estimate of the mean scales with the number of points? How would you test it?* \n", "\n", "* *Record values of the MCMC mean for `num_steps` = 1000, 4000, and 16000, running each 10-20 times. Explain what you find.* \n", "\n", "* *Calculate the mean and standard deviations of the means you found (using `np.mean()` and `np.std()`. Explain your results.*\n", "\n", "* *Predict what you will find from 10 runs at `num_steps` = 100,000. What did you actually find?*" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1000 [10]: 3.05 +/- 0.30\n", "1000 [10]: 2.96 +/- 0.16\n", "1000 [20]: 3.00 +/- 0.24\n", " \n", "4000 [10]: 3.05 +/- 0.07\n", "4000 [10]: 2.97 +/- 0.11\n", "4000 [20]: 3.01 +/- 0.10\n", " \n", "16000 [10]: 3.04 +/- 0.06\n", "16000 [10]: 2.98 +/- 0.07\n", "16000 [20]: 3.01 +/- 0.07\n", " \n", "100000 [10]: 2.990 +/- 0.024\n", "100000 [10]: 3.005 +/- 0.012\n", "100000 [20]: 2.997 +/- 0.020\n" ] } ], "source": [ "# Sample results with 1000, 4000, 16000, 100000 \n", "# These are recorded results. Try to extract your own series.\n", "\n", "mean1000 = np.array([3.18, 2.83, 3.45, 2.78, 2.51, 2.81, 2.99, 3.29, 3.19, 3.46])\n", "print(f'1000 [10]: {np.mean(mean1000):.2f} +/- {np.std(mean1000):.2f}')\n", "mean1000b = np.array([2.86, 3.20, 3.13, 2.79, 3.04, 3.17, 2.93, 2.95, 2.80, 2.73])\n", "print(f'1000 [10]: {np.mean(mean1000b):.2f} +/- {np.std(mean1000b):.2f}')\n", "mean1000c = np.concatenate([mean1000, mean1000b])\n", "print(f'1000 [20]: {np.mean(mean1000c):.2f} +/- {np.std(mean1000c):.2f}')\n", "\n", "print(' ')\n", "\n", "mean4000 = np.array([3.05, 3.07, 2.90, 3.10, 3.04, 3.02, 3.06, 3.04, 2.99, 3.18])\n", "print(f'4000 [10]: {np.mean(mean4000):.2f} +/- {np.std(mean4000):.2f}')\n", "mean4000b = np.array([3.04, 2.91, 3.02, 3.00, 2.87, 2.92, 2.76, 3.17, 3.01, 3.04])\n", "print(f'4000 [10]: {np.mean(mean4000b):.2f} +/- {np.std(mean4000b):.2f}')\n", "mean4000c = np.concatenate([mean4000, mean4000b])\n", "print(f'4000 [20]: {np.mean(mean4000c):.2f} +/- {np.std(mean4000c):.2f}')\n", "\n", "print(' ')\n", "\n", "mean16000 = np.array([3.08, 3.01, 3.04, 2.93, 3.11, 2.98, 3.05, 3.12, 3.04, 3.08])\n", "print(f'16000 [10]: {np.mean(mean16000):.2f} +/- {np.std(mean16000):.2f}')\n", "mean16000b = np.array([3.05, 2.98, 2.99, 2.89, 3.04, 3.11, 2.90, 2.92, 2.94, 2.98])\n", "print(f'16000 [10]: {np.mean(mean16000b):.2f} +/- {np.std(mean16000b):.2f}')\n", "mean16000c = np.concatenate([mean16000, mean16000b])\n", "print(f'16000 [20]: {np.mean(mean16000c):.2f} +/- {np.std(mean16000c):.2f}')\n", "\n", "print(' ')\n", "\n", "mean100000 = np.array([3.00, 3.02, 2.95, 3.01, 3.00, 3.00, 2.99, 3.00, 2.94, 2.99])\n", "print(f'100000 [10]: {np.mean(mean100000):.3f} +/- {np.std(mean100000):.3f}')\n", "mean100000b = np.array([3.03, 3.01, 3.01, 3.01, 2.99, 3.01, 2.99, 3.01, 2.99, 3.00])\n", "print(f'100000 [10]: {np.mean(mean100000b):.3f} +/- {np.std(mean100000b):.3f}')\n", "mean100000c = np.concatenate([mean100000, mean100000b])\n", "print(f'100000 [20]: {np.mean(mean100000c):.3f} +/- {np.std(mean100000c):.3f}')\n", "\n", "# Should have kept 3 digits for 100000 runs\n", "# Basically we see the 1/np.sqrt(N) improvement in the standard deviation\n", "# of the predictions for the mean." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig,ax = plt.subplots(1,1)\n", "nsamples = np.array([1000,4000,16000,100000])\n", "stds = np.array([np.std(mean1000c),np.std(mean4000c),np.std(mean16000c),np.std(mean100000c)])\n", "ax.semilogx(nsamples,1/np.sqrt(nsamples)*0.25*np.sqrt(1000),label=r'$1/\\sqrt{N}$')\n", "ax.semilogx(nsamples,stds,'o',label=r'$\\sigma(N)$')\n", "ax.set_xlabel(r'$N$')\n", "ax.set_ylabel(r'$\\sigma$')\n", "ax.legend(loc='best');" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.17" } }, "nbformat": 4, "nbformat_minor": 4 }