{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Rosenbrock toy distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This function (further described [here](http://pints.readthedocs.io/en/latest/toy/rosenbrock.html)) which can be used to define a normalisable probability density function:\n", "\n", "$ p(x, y) \\propto \\frac{1}{1 + \\text{RosenbrockError}(x,y)}, $\n", "\n", "that is,\n", "\n", "$ p(x, y) \\propto \\frac{1}{\\left(1 + (1 - x)^2 + 100 (y - x^2)^2) \\right)}, $\n", "\n", "which we term the `RosenbrockLogPDF`.\n", "\n", "We now plot this function." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from __future__ import print_function\n", "import pints\n", "import pints.toy\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pints.plot\n", "\n", "# Create Rosenbrock log pdf\n", "log_pdf = pints.toy.RosenbrockLogPDF()\n", "\n", "# Contour plot of pdf\n", "levels = np.linspace(0, 1, 20)\n", "x = np.linspace(-2, 4, 400)\n", "y = np.linspace(-1, 12, 400)\n", "X, Y = np.meshgrid(x, y)\n", "Z = np.exp([[log_pdf([i, j]) for i in x] for j in y])\n", "plt.contour(X, Y, Z, levels = levels)\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Turn into Bayesian problem by using the inverse Rosenbrock function as a likelihood\n", "\n", "Then use Hamiltonian Monte Carlo to sample from the posterior distribution" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Running...\n", "Done!\n", "R-hat:\n", "[1.003652855160633, 1.0067509462132447]\n" ] } ], "source": [ "# Create an adaptive covariance MCMC routine\n", "x0 = np.random.uniform([1, 1], [1.1, 1.1], size=(4, 2))\n", "sigma0 = [0.5, 0.5]\n", "\n", "# Use suggested prior bounds\n", "bounds = log_pdf.suggested_bounds()\n", "\n", "# Create a uniform prior over both the parameters\n", "log_prior = pints.UniformLogPrior(\n", " bounds[0], bounds[1]\n", ")\n", "\n", "# Create a posterior log-likelihood (log(likelihood * prior))\n", "log_posterior = pints.LogPosterior(log_pdf, log_prior)\n", "\n", "mcmc = pints.MCMCController(log_posterior, 4, x0, method=pints.HamiltonianMCMC, sigma0=sigma0)\n", "\n", "# Stop after 4000 iterations\n", "mcmc.set_max_iterations(4000)\n", "\n", "# Disable logging\n", "mcmc.set_log_to_screen(False)\n", "\n", "# Run!\n", "print('Running...')\n", "chains = mcmc.run()\n", "print('Done!')\n", "\n", "# Discard warm-up\n", "chains = [chain[1000:] for chain in chains]\n", "\n", "print('R-hat:')\n", "print(pints.rhat_all_params(chains))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We inspect the results by creating a scatter plot of the samples. Hamiltonian Monte Carlo does pretty well although struggles to sample from the thin tails" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "stacked = np.vstack(chains)\n", "plt.contour(X, Y, Z, levels=levels, colors='k', alpha=0.5)\n", "plt.scatter(stacked[:,0], stacked[:,1], marker='.', alpha=0.2)\n", "plt.xlim(-2, 4)\n", "plt.ylim(-1, 12)\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the path of one of the chains" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "chain = chains[0]\n", "\n", "plt.contour(X, Y, Z, levels=levels, colors='k', alpha=0.5)\n", "plt.plot(chain[0:1000,0], chain[0:1000,1])\n", "plt.xlim(-2, 4)\n", "plt.ylim(-1, 12)\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calculate normed distance of sample mean and sample covariance from true values" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print('Normed distance = ' + str(log_pdf.distance(stacked)))" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.8" } }, "nbformat": 4, "nbformat_minor": 2 }