{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " \n", "
\n", "\n", "# Banana Example\n", "Author(s): Paul Miles | Date Created: June 18, 2018\n", "\n", "This technical example constructs a non-Gaussian target distribution by twisting two first dimensions of Gaussian\n", "distribution. The Jacobian of the transformation is 1, so it is easy to calculate the right probability regions for the banana and study different adaptive methods.\n", "\n", "The basics of the model are as follows.\n", "$$B_f(x_i, a, b) = [ax_1, \\frac{x_2}{a}-b(a^2x_1^2 + a^2), x_3, ..., x_{npar}]$$\n", "$$B_f^{-1}(x_i, a, b) = [x_1 /a, ax_2 + ab(x_1^2 + a^2), x_3, ..., x_{npar}]$$\n", "\n", "We can construct a sum-of-squares function\n", "$$B_{sos}(x_i, a, b, \\mu_i, \\lambda) = B_f^{-1}(x_i-\\mu_i, a, b) \\cdot \\lambda \\cdot B_f^{-1}(x_i - \\mu_i, a, b)$$\n", "where $\\mu_i$ are the centers for our target distributions, $\\lambda$ is the target precision, and the banana parameters are $a$ and $b$. For this particular example we consider the problem where we have 2 unknown parameters with center $\\mu_i = 0$, and we have a target correlation of $\\rho = 0.9$ for the first two dimensions. We subsequently define the target precision matrix $\\lambda$\n", "\\begin{equation}\n", " \\lambda = \\sigma^{-1} = \\begin{bmatrix}\n", " 1 & \\rho & 0 & \\\\\n", " \\rho & 1 & \\\\\n", " 0 & & 1 \\\\\n", " & & & \\ddots \\\\\n", " & & & & 1\n", " \\end{bmatrix}^{-1}\n", "\\end{equation}\n", "\n", "Note, for a comparison between using MCMC algorithms in Matlab, Python, and R, see [here](https://prmiles.wordpress.ncsu.edu/files/2018/03/20180329_mcmc_banana_examples.pdf)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# import required packages\n", "import numpy as np\n", "from pymcmcstat.MCMC import MCMC\n", "from pymcmcstat.plotting.utilities import generate_ellipse\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We create a class to initialize model parameters" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "class Banana_Parameters:\n", " def __init__(self, rho=0.9, npar=12, a=1, b=1, mu=None):\n", " self.rho = rho\n", " self.a = a\n", " self.b = b\n", " self.sig = np.eye(npar)\n", " self.sig[0,1] = rho\n", " self.sig[1,0] = rho\n", " self.lam = np.linalg.inv(self.sig)\n", " self.npar = npar\n", " if mu is None:\n", " self.mu = np.zeros([npar, 1])\n", " \n", "npar = 6 # number of model parameters\n", "udobj = Banana_Parameters(npar=npar) # user defined object" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Initialize MCMC object\n", "- initialize data structure\n", "- assign model parameters\n", "- define simulation options" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# Initialize MCMC object\n", "mcstat = MCMC()\n", "mcstat.data.add_data_set(np.zeros(1), np.zeros(1),\n", " user_defined_object=udobj)\n", "# Add model parameters\n", "for ii in range(npar):\n", " mcstat.parameters.add_model_parameter(\n", " name=str('$x_{}$'.format(ii + 1)),\n", " theta0=0.0)\n", "# Define options\n", "mcstat.simulation_options.define_simulation_options(\n", " nsimu=4.0e3,\n", " qcov=np.eye(npar)*5,\n", " method='dram')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We define a series of functions to evaluation the sum-of-squares error" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Define model object\n", "def bananafunction(x, a, b):\n", " response = x\n", " response[:, 0] = a*x[:, 0]\n", " response[:, 1] = x[:, 1]*a**(-1) - b*((a*x[:, 0])**(2) + a**2)\n", " return response\n", "\n", "def bananainverse(x, a, b):\n", " response = x\n", " response[0] = x[0]*a**(-1)\n", " response[1] = x[1]*a + a*b*(x[0]**2 + a**2)\n", " return response\n", "\n", "def bananass(theta, data):\n", " udobj = data.user_defined_object[0]\n", " lam = udobj.lam\n", " mu = udobj.mu\n", " a = udobj.a\n", " b = udobj.b\n", " npar = udobj.npar\n", " x = np.array([theta])\n", " x = x.reshape(npar, 1)\n", " baninv = bananainverse(x - mu, a, b)\n", " stage1 = np.matmul(baninv.transpose(),lam)\n", " stage2 = np.matmul(stage1, baninv)\n", " \n", " return stage2\n", " \n", "mcstat.model_settings.define_model_settings(sos_function=bananass)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Run Simulation" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Sampling these parameters:\n", " name start [ min, max] N( mu, sigma^2)\n", " $x_1$: 0.00e+00 [ -inf, inf] N( 0.00e+00, inf)\n", " $x_2$: 0.00e+00 [ -inf, inf] N( 0.00e+00, inf)\n", " $x_3$: 0.00e+00 [ -inf, inf] N( 0.00e+00, inf)\n", " $x_4$: 0.00e+00 [ -inf, inf] N( 0.00e+00, inf)\n", " $x_5$: 0.00e+00 [ -inf, inf] N( 0.00e+00, inf)\n", " $x_6$: 0.00e+00 [ -inf, inf] N( 0.00e+00, inf)\n", " [-----------------100%-----------------] 4000 of 4000 complete in 1.0 sec" ] } ], "source": [ "mcstat.run_simulation()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Extract results and plot chain panel" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Extract results\n", "results = mcstat.simulation_results.results\n", "chain = results['chain']\n", "s2chain = results['s2chain']\n", "names = results['names'] # parameter names\n", "# plot chain panel\n", "mcstat.mcmcplot.plot_chain_panel(chain, names, figsizeinches=(6,6));\n", "plt.savefig('banana_chain_panel.eps',\n", " format='eps',\n", " bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Pairwise Correlation\n", "Here we plot the pairwise correlation as well as 50% and 95% critical regions. These critical regions have a shape resembling a banana, hence the name of the example." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# plot pairwise correlation\n", "mcstat.mcmcplot.plot_pairwise_correlation_panel(\n", " chain[:, 0:2], names[0:2], figsizeinches=(5, 5))\n", "# calculate contours for 50% and 95% critical regions\n", "c50 = 1.3863 # critical values from chisq(2) distribution\n", "c95 = 5.9915\n", "xe50, ye50 = generate_ellipse(udobj.mu, c50*udobj.sig[0:2, 0:2])\n", "xe95, ye95 = generate_ellipse(udobj.mu, c95*udobj.sig[0:2, 0:2])\n", "bxy50 = bananafunction(np.array([xe50, ye50]).T, udobj.a, udobj.b)\n", "bxy95 = bananafunction(np.array([xe95, ye95]).T, udobj.a, udobj.b)\n", "# add countours to pairwise plot\n", "plt.plot(bxy50[:,0], bxy50[:,1], 'k-', LineWidth=2)\n", "plt.plot(bxy95[:,0], bxy95[:,1], 'k-', LineWidth=2)\n", "plt.axis('equal')\n", "plt.title('2 first dimensions of the chain with 50% and 95% target contours');\n", "plt.savefig('banana_pairwise.png',\n", " format='png',\n", " dpi=500,\n", " bbox_inches='tight')" ] } ], "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": "3.6.8" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autoclose": false, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": true, "user_envs_cfg": false }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": true } }, "nbformat": 4, "nbformat_minor": 2 }