{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Inference: Metropolis-Adjusted Langevin Algorithm (MALA)\n", "\n", "This example shows you how to perform Bayesian inference on a Normal distribution and a time-series problem, using MALA for MCMC." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we create a simple normal distribution" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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oB7h/g3Jo243Y/eMBTidkcv+nd1i0mvbDj3eQkVHKMysWmEXstXo9D3y7gW0n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\n07KD/PjTAZo28eHdt+/Hw8PRaO1lFRSx9thZVh2J4HpuPvX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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import pints\n", "import pints.toy\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# Create log pdf\n", "log_pdf = pints.toy.GaussianLogPDF([2, 4], [[1, 0], [0, 3]])\n", "\n", "# Contour plot of pdf\n", "levels = np.linspace(-3,12,20)\n", "num_points = 100\n", "x = np.linspace(-1, 5, num_points)\n", "y = np.linspace(-0, 8, num_points)\n", "X, Y = np.meshgrid(x, y)\n", "Z = np.zeros(X.shape)\n", "Z = np.exp([[log_pdf([i, j]) for i in x] for j in y])\n", "plt.contour(X, Y, Z)\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we set up and run a sampling routine using MALA MCMC" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Running...\n", "Using Metropolis-Adjusted Langevin Algorithm (MALA)\n", "Generating 3 chains.\n", "Running in sequential mode.\n", "Iter. Eval. Accept. Accept. Accept. Time m:s\n", "0 3 0 0 0 0:00.0\n", "1 6 0 0.5 0.5 0:00.0\n", "2 9 0 0.667 0.667 0:00.0\n", "3 12 0.25 0.5 0.75 0:00.0\n", "100 303 0.723 0.673 0.832 0:00.3\n", "200 603 0.751 0.741 0.796 0:00.5\n", "300 903 0.767 0.751 0.797 0:00.8\n", "400 1203 0.736 0.743 0.771 0:01.1\n", "500 1503 0.750499 0.748503 0.752495 0:01.4\n", "600 1803 0.757 0.76 0.747 0:01.6\n", "700 2103 0.753 0.755 0.743224 0:01.9\n", "800 2403 0.75 0.757 0.735 0:02.2\n", "900 2703 0.75 0.757 0.73 0:02.4\n", "1000 3003 0.751 0.756 0.733 0:02.7\n", "1100 3303 0.751 0.752 0.736 0:03.0\n", "1200 3603 0.749 0.746045 0.729 0:03.2\n", "1300 3903 0.743 0.745 0.73 0:03.5\n", "1400 4203 0.747 0.747 0.726 0:03.8\n", "1500 4503 0.744 0.749 0.729 0:04.0\n", "1600 4803 0.747 0.751 0.723 0:04.3\n", "1700 5103 0.743 0.748 0.718 0:04.6\n", "1800 5403 0.745 0.751 0.723487 0:04.8\n", "1900 5703 0.742767 0.75 0.725 0:05.1\n", "2000 6000 0.7435 0.7485 0.7285 0:05.4\n", "Halting: Maximum number of iterations (2000) reached.\n", "Done!\n" ] } ], "source": [ "# Choose starting points for 3 mcmc chains\n", "xs = [\n", " [2, 1],\n", " [3, 3],\n", " [5, 4],\n", "]\n", "\n", "# Create mcmc routine\n", "mcmc = pints.MCMCController(log_pdf, 3, xs, method=pints.MALAMCMC)\n", "\n", "# Add stopping criterion\n", "mcmc.set_max_iterations(2000)\n", "\n", "# Set up modest logging\n", "mcmc.set_log_to_screen(True)\n", "mcmc.set_log_interval(100)\n", "\n", "# # Update step sizes used by individual samplers (which is then scaled by sigma0)\n", "for sampler in mcmc.samplers():\n", " sampler.set_epsilon([1.5, 1.5])\n", "\n", "# Run!\n", "print('Running...')\n", "full_chains = mcmc.run()\n", "print('Done!')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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KgI6RIKLCXLo12Is9R9XHZc7XmXdkNyz5B85w7yDWwjqjR5YuDfYM7mG5qMoc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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Show traces and histograms\n", "import pints.plot\n", "pints.plot.trace(full_chains)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "R-hat:\n", "[1.0011357940509646, 1.0017031271797681]\n", "0.0103631865061\n", "0.00530188143198\n", "0.00250108715373\n" ] }, { "data": { "image/png": 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GZqn1L4Tb5XiB0FovBy7e8HRn4Oe0z38GuuRoKJHvnbqcZHQEITyOp4xiKqa1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\nS8GRQga9nq1rlrLg+89IiYum3aD7GPTUVBzdlJu7lJLwk4c4vmUNZw7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WnJfevKp7hvaa\n83xpPQeMlW+Vqq4gVFQAe+uq9ayUN07fi1iW2X6IPUYm614mA1sLSla92GDsxOe6MUyzXqK0KB04\nvVJ1p1IVhIoKkJBeNct91yaO320+w5VUxma9TaSsmC1fqzKzDSPwEnE8tm+m0kOi9zRLi1RsVAWh\nogI4VYBSGyevJprN0C2tc7OBuMHv1p/hLpJ5POt1Tkm/OxVRpVQIPtRP4LEOtWDHZ6b8k/cqxUrC\n8t8KFZUKgJWm4n9ZS0JHcZY5NjMAGJf1Niekmu9gSSQaGDlTSZzbMwNSb8Kwb8CqYvu+VAWhogLY\naquQDyL4VxbbfEKE9OQJ3WuEyzqWlkgFlKqvw78FR0/Y9QXEhsF988G17LtAlhWqglBRAWLSqoAP\nIisV/n0djv3OPmNrXtQ9TyJOlpZKxUSu+TCQEZrn+fzyPLJmdOI93WP88EnFdF5XoccmFZXSU8uh\nctfMIfIwzO2tlNDoOZXHda+ryqECs9YYxPCsT7ksPfnBZib8fh9EVbz2N+oKQkUFSKwA5b5rE89P\n1t/gSAZxOHPRWJcDxuagH1CwrTo5CnZ/BYd+BicvmLAK/Hpj3KQmwVV0Lsk6jM76iEe1G3k/cg3M\n7gYtR0O3F6FOG0uLB6gKQkUFACdrraVFwFMk0ERcJQU7GnKDkVb70AgJX3wDfr3BpzN4NAZrO0iM\nhLBtELoeDDpo/7jSg8DO1dKXoVICjGj41TCEFYk9eMZqLeNPrsP51DKOGRux0tCdD19/HVy9LSaf\nqiBUVICMCtAQ4rRsQP+sr3Jeu5BKZ00I89rHK8rg7D+3HuBQEwLHQ9fn1KqslZxEnPhcP5ZZ+pHc\nr93FA9odfGi9EL5ZCB5NoH4XqBsItZpBzabgWOuu+CxUBaGigpn2hRbAeJtLMAlHNhs7wAhTHkTK\nTWXloEsDl3r4fXEK4x4N7DkLnL37AquUOUk48othCL8YhuAnrrFteDqE71YeDo7+ljMuVdpyRXoS\nIT25LGtzWdbmivQkXHqxa/ojZdaHQlUQKipAWpbB0iIUjZOn8mPCSMVzaqqUHRdlXeg2TPFJSKk8\nHMSEQmwYS9duxVtE4ytu0ENzEnuRlXvg9FfBpZ5imnKuA85eyoqjFKgKQkUFsK5KeRAqVQ8hwM1H\n+Wncnw9X5vVLSDxJwFfcoIEmCh9xE++4GOrFx+DJRTxFAo4is3TTykpa5lgIEQ1ctqAINYEYC85f\nGlSZC6aBlHe/UJEQYhIwyfTSHwgth2ks+X+39Geuul67ublL/BmvtArC0gghgqWUHSwtR0lQZa6e\nWPI9tPT/r7pee1nNra6rVVRUVFTMoioIFRUVFRWzqAqi9My1tAClQJW5emLJ99DS/7/qeu1lMrfq\ng1BRUVFRMYu6glBRUVFRMYuqIFRUVFRUzKIqCJUKixAVsEC+iko1QlUQJUAI4S+E6CqEsBZCWL78\nZxEIIRoLIToIIWwtLUtxEUJ0F0I8AiCllKqSqPwIIRwtLYMlqArXrZbaKCZCiNHAp8BV00+wEGKB\nlDLJspKZRwgxHEXeWOCGEOJ9KeU5C4tVIEIIDeAAzFFeCkcp5WyTktBIKS1fbrUSIoQIBDIBpJQh\nFpi/P9BbCPGJlDL9Ls/dCbAG9FLKA3d5botddx4ZagHWUsprebYJWYLIJHUFUQyEENbAQ8ATUsp+\nwGrAB3hdCOFiUeHMIIQIAr4CHpVS9gHigWmWlapwpJRGKWUKsBCYDwQJIV7O3mdR4SopQoghwFrg\nWeBvIcTjFpj/f8BmCyiHQcAaYBjwpxDieSHEXWmxZ8nrziPD/cA6YLUQ4mMhRA8o+apcVRDFxwVo\nYvp7JfAPYAOMq6BmkM+llEdNf78P1KgkpiY9ivJdCHQSQswQQnwmFNTPazEwvVdOwAvAc1LKF4An\ngbeFEJPvkgz+KN+TGVLKnUIITyGErxAioJznFabP+VjgRSnlW8Bo4B5gshDCvpznt8h13yaDBzAF\neAoYAQjgHpMVBHUFUcZIKXXADGC0EKKH6Yl2D3AM6G5R4cxzAFgBYPKV2AINUJRc9geoorIauCGl\n3AoEA5MBF6mgriSKgem9SkF5/1yEENZSyv3AGOANIcSjd0GMZGAm0Nm0ov0DeAfYKoR4prwmNV17\nJhACtBZCOEkpj6HcMIcCE8trbhMWue7byP7OZ0gpbwDfAFeArkKILiU5kaogis9uYBPwiBCip5TS\nIKX8A6gLVIwGsiZMsmX7RgSQAMRJKaOFEOOB6eX9JHUHpAP+QoinUJTD50B9IcTTlhWrUnID6AfY\nA0gpg4FHgBeEEA3Lc2KT3fs7IAXYAayWUj6JYvKZXtIbVSk4AXgAjYQQVlLK08BU4BUhRLl9XyvA\ndSOlvAksB54QQtSVUsaiKCpQlGSxURVEMZFSZgCLgePAm0KISaYnsdrAdYsKVwhSSr3paTJCCPEZ\n8Aowy1K20aIwfcEigHeBV6SUH6Gs3v61qGCViGyTp5RyForjf7YQwtW0ktiDcvMstxIKeeaPAGYB\nI6WUP5gcpMHAn0C5dGjKM/d6lJv0S0CAaSVxGNiA8tBUlnN6CyFssl9b4rrNsN30e4xJScSgKK4+\nQoiaxT2JWmqjhJg+CN2Ap4EM4Ls8tv4Kh+kLY42y5LYG+kkpz1tWqsIRQvgAnqYvNGoUU9GYbN81\nUMxKRimlIc++JSgrs/0okYuvAL2klJFlOH9jwA04ZXqYyrvPSkqpN/09DngDGCGlvFJGc48A/KSU\n35le53xehBBfAM4o39UI4FWgm5QyvIzmHgR8AIyXUl4UQmiz3/vyvu4C5Mk7/zCgF4q5aS7QAkVh\nDjY9NBZ9PlVBlA6Tbb/S2MWFEI8Bh0xL7UpBSUPyqivCTAg2cEsIthBiIrnm0A/K8nMgbgupBj6R\nUp667UZtg+Iofh94qKzmF0IMBL4ApkopN+fZnvdG2QdoDTQFfpRSlkmv1jxzu6GYkl4yM6ZcrjvP\n+TsDdkCalPKQaZu1yW+KEKId0BcYCehQ3qcjxT6/+v2rHqg326qJUEKwfwe+l1LuFULcB3RByX34\nUkqZeNt4W5MTt6zmDwJ+AcZKKY8KIWYBdlLKfM5gIURX4HoZPr0HoUQMjZBSHhRCuKLcrGOAzOyn\n9zzjrW7fdgdz9wdmo9z8z6GElE6XUu4yM7ZMrzvPeYcA36OYkzyBWCnlE6Z9t/yfTWaldCllaknm\nUH0Q1QRVOVRpCgrBHgtKwpjpSRIgK//hd0yhIdVCiI5CiIFSyn1lfJOMRXkqrmOKzFsF/AT8iuKM\nz557mGl8Wdr/tcAE04rAEaVVbEvTnML0u7MQon85XHe2BeNR4CMp5SRgAkpwxzKAbOUglMoEtlLK\nmJIqB1AVhIpKpaaIEOyepmi1bsA10/iyflAoKqTaG2iG4hgvU6SUoSjRQd+gBI/8AQxHcUQPEkLU\nAxoCR0zjy+zapZQbpZT/mcxoCSgriPeFEK2klNK0svMDysWkazKfHc3zOklK2R2oLYSYAzmlPnqj\n9KcuFaqJSUWlkiOEsENJhGsN/J5t5hBC7EDJ/g+7S3JYodjDV0sp+wkhHgbaovg8kstx3hZAHynl\nj3m2bQBeMimRu4IQ4iOUYID/SSmN5WHWFUI0laaSOab3dxowNNvxbTIlzUaJAjyLUmqj1KtGtRaT\nikolR0qZIYRYjBK6+qYQohmKD6IWSqjn3ZJDD6QIIbJDqgcCj5encjDNewbIcTyb/DC1gMQCDyof\njgMvA1+iRJKVtXIYDiwVQqyRUo6RUv5uil7bK4ToJqW8IqWMEULoAVfT/HdkUlRNTHcJIYRBCHFM\nCHFKCPG3EMLB0jIBCCHeKoNzPCCEOC2EMAohOpSFXColQ0oZD8xDiarpC/QBHpZSRt0tGYSCDdAD\nGA+MkVKWuWmpiPknAh+j+Adu3K25AaSUy1FMed5lfW6Tueh5lIzwDCHEn6Y53wUWAGuFEE8LId5G\niVQrk/+7amK6SwghUqSUTqa/FwOHpZQzinlsTsheecpVgmNukUcI0RwwolRifc2UFKRiISwdgm2p\nkGqTc7gXSqmWs3d77vIOBBFC1AWSUMx4swGdlDI7EGEU4AW0B76VUp4qiznVFYRl2A00BhBCrBJC\nHDY9gU/KHiCESBFCfCSEOIBSQ+U9IcQh0wpkbp5IiR1CiG+EELuEECGmqI0VQojzQojpec73sBDi\noGkVM0cIoRVCfA7Ym7YtLmicOXnyXoyUMuRu2npVCkcqpVYsmZ+z0BL5NlJhx91WDtlz34U5rkkp\nU6SSFf00YJO9kkAJtf1XSvlkWSkHUBXEXcfkyBsCnDRtmiilbA90AF4UuYX0HFGyUjtLpTzCTCll\nRyllAEptneF5TpslpeyJ8lSxGngOCAAeE0J4mJ7wH0LJIA1ECfcbL6WchhIbHSilHF/QuALkUVEx\nixpSXf5Ipb7S0yjmplCU732ZWxlUJ/Xdw14Iccz0926UngegKIVRpr99UOLZY1H+2cvzHN9HCPE6\nSm2dGijhc2tN+9aYfp8ETksprwMIIS6aztkdZel5yLTwsAdumpGxXyHjbpdHRUXFgpgc0idQHjgH\nyDIsnZKNqiDuHummp/IchBC9gf5AVyllmiks0c60O0PmlgqwQyn+1UFKGSGE+CDPODB1DEPxA+TN\nkjWi/I8FyrL/zSJkLGxcjjwqKiqWRwjhjlKddaCU8mRR40uDamKyLK5AvEk5NEMpkWCObGUQI5RG\nMPeXcJ6twP1CCE8AIUQNIUQD0z6dKamnqHEqKioVCFPk2ojyjBRTFYRl2QBYmZaJH6NU28yHKVNz\nHooJaRVwqCSTmOLE3wE2mebaDNQx7Z4LnBBCLC5iXIEIIUYJISJRnNfrhBAbSyKfiopK6ZC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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Discard warm up\n", "chains = full_chains[:, 1000:]\n", "\n", "# Check convergence using rhat criterion\n", "print('R-hat:')\n", "print(pints.rhat_all_params(chains))\n", "\n", "# Check Kullback-Leibler divergence of chains\n", "print(log_pdf.kl_divergence(chains[0]))\n", "print(log_pdf.kl_divergence(chains[1]))\n", "print(log_pdf.kl_divergence(chains[2]))\n", "\n", "# Look at distribution in chain 0\n", "pints.plot.pairwise(chains[0], kde=True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## MAMA MCMC on a time-series problem\n", "\n", "We now try the same method on a time-series problem\n", "\n", "First, we try it in 1d, using a wrapper around the LogisticModel to make it one-dimensional." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import pints.toy as toy\n", "\n", "# Create a wrapper around the logistic model, turning it into a 1d model\n", "class Model(pints.ForwardModel):\n", " def __init__(self):\n", " self.model = toy.LogisticModel()\n", " def simulate(self, x, times):\n", " return self.model.simulate([x[0], 500], times)\n", " def simulateS1(self, x, times):\n", " values, gradient = self.model.simulateS1([x[0], 500], times)\n", " gradient = gradient[:, 0]\n", " return values, gradient\n", " def n_parameters(self):\n", " return 1\n", "\n", "# Load a forward model\n", "model = Model()\n", " \n", "# Create some toy data\n", "real_parameters = np.array([0.015])\n", "times = np.linspace(0, 1000, 50)\n", "org_values = model.simulate(real_parameters, times)\n", "\n", "# Add noise\n", "np.random.seed(1)\n", "noise = 10\n", "values = org_values + np.random.normal(0, noise, org_values.shape)\n", "\n", "plt.figure()\n", "plt.plot(times, values)\n", "plt.plot(times, org_values)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Now running MALA MCMC" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Running...\n", "Using Metropolis-Adjusted Langevin Algorithm (MALA)\n", "Generating 3 chains.\n", "Running in sequential mode.\n", "Iter. Eval. Accept. Accept. Accept. Time m:s\n", "0 3 0 0 0 0:00.0\n", "1 6 0.5 0.5 0.5 0:00.0\n", "2 9 0.667 0.667 0.667 0:00.0\n", "3 12 0.75 0.75 0.75 0:00.0\n", "100 303 0.990099 0.990099 0.990099 0:00.3\n", "200 603 0.995 0.995 0.99 0:00.6\n", "300 903 0.993 0.993 0.99 0:00.9\n", "400 1203 0.995 0.993 0.993 0:01.2\n", "500 1503 0.992016 0.988024 0.99002 0:01.5\n", "600 1803 0.992 0.99 0.99 0:01.8\n", "700 2103 0.993 0.991 0.991 0:02.1\n", "800 2403 0.99 0.993 0.993 0:02.4\n", "900 2703 0.988 0.993 0.992 0:02.6\n", "1000 3003 0.988012 0.994006 0.993007 0:02.9\n", "1100 3303 0.988 0.995 0.993 0:03.2\n", "1200 3603 0.989 0.994 0.993 0:03.5\n", "1300 3903 0.99 0.995 0.992 0:03.8\n", "1400 4203 0.99 0.995 0.992 0:04.1\n", "1500 4503 0.99 0.995 0.991 0:04.4\n", "1600 4803 0.991 0.995 0.992 0:04.7\n", "1700 5103 0.991 0.995 0.991 0:05.0\n", "1800 5403 0.992 0.995 0.991116 0:05.3\n", "1900 5703 0.992 0.995 0.992 0:05.5\n", "2000 6000 0.992 0.9955 0.992 0:05.8\n", "Halting: Maximum number of iterations (2000) reached.\n", "Done!\n" ] } ], "source": [ "# Create an object with links to the model and time series\n", "problem = pints.SingleOutputProblem(model, times, values)\n", "\n", "# Create a log-likelihood function\n", "log_likelihood = pints.GaussianKnownSigmaLogLikelihood(problem, noise)\n", "\n", "# Create a uniform prior over the parameters\n", "log_prior = pints.UniformLogPrior(\n", " [0.01],\n", " [0.02]\n", ")\n", "\n", "log_posterior = pints.LogPosterior(log_likelihood, log_prior)\n", "\n", "# Choose starting points for mcmc chains\n", "xs = [\n", " real_parameters * 1.01,\n", " real_parameters * 0.9,\n", " real_parameters * 1.15,\n", "]\n", "\n", "# Create mcmc routine\n", "mcmc = pints.MCMCController(log_likelihood, len(xs), xs, method=pints.MALAMCMC)\n", "\n", "# Add stopping criterion\n", "mcmc.set_max_iterations(2000)\n", "\n", "# Set up modest logging\n", "mcmc.set_log_to_screen(True)\n", "mcmc.set_log_interval(100)\n", "\n", "# Run!\n", "print('Running...')\n", "chains = mcmc.run()\n", "print('Done!')" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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LhzP5q+t0s6+2C4MmuDwniWuyr+HdI38HCR83nHyxqLKr8rQEy+0LUu3oIyHK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\nM7OO5gTLzMzMzMysRTo+wZJ0rqRnJS2VdHWV50d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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Show trace and histogram\n", "pints.plot.trace(chains)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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ZAPPmzeP++++3b8vIyGDEiBG0bt2a5s2bs2TJEiB/7alOnTrRokULWrRowZYt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\nI0QJ4k6dpdvnu2kbuw08fPjzlqas7Tw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Show predicted time series for the first chain\n", "pints.plot.series(chains[0, 200:], problem, real_parameters)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2d Time series\n", "\n", "Finally, we try MALA MCMC on a 2d logistic model problem." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Running...\n", "Using Metropolis-Adjusted Langevin Algorithm (MALA)\n", "Generating 3 chains.\n", "Running in sequential mode.\n", "Iter. Eval. Accept. Accept. Accept. Time m:s\n", "0 3 0 0 0 0:00.0\n", "1 6 0.5 0.5 0.5 0:00.0\n", "2 9 0.333 0.667 0.667 0:00.0\n", "3 12 0.5 0.75 0.75 0:00.0\n", "100 303 0.970297 0.970297 0.980198 0:00.3\n", "200 603 0.975 0.98 0.99 0:00.6\n", "300 903 0.98 0.983 0.986711 0:00.9\n", "400 1203 0.975 0.985 0.985 0:01.2\n", "500 1503 0.976 0.984 0.986 0:01.5\n", "600 1803 0.975 0.987 0.985025 0:01.8\n", "700 2103 0.977 0.989 0.984 0:02.1\n", "800 2403 0.974 0.99 0.985 0:02.4\n", "900 2703 0.977 0.99 0.984 0:02.7\n", "1000 3003 0.979021 0.991009 0.983017 0:03.0\n", "1100 3303 0.98 0.992 0.981 0:03.3\n", "1200 3603 0.981 0.992 0.981 0:03.6\n", "1300 3903 0.982 0.991545 0.982 0:03.9\n", "1400 4203 0.983 0.991 0.982 0:04.2\n", "1500 4503 0.983 0.99 0.983 0:04.5\n", "1600 4803 0.984 0.989 0.983 0:04.9\n", "1700 5103 0.985 0.99 0.984 0:05.2\n", "1800 5403 0.985 0.991 0.984 0:05.5\n", "1900 5703 0.986 0.991 0.983 0:05.8\n", "2000 6003 0.986 0.99 0.983 0:06.1\n", "2100 6303 0.985 0.989 0.982 0:06.4\n", "2200 6603 0.985 0.989 0.982 0:06.7\n", "2300 6903 0.985 0.989 0.982 0:07.0\n", "2400 7203 0.985 0.99 0.982 0:07.3\n", "2500 7503 0.984 0.990004 0.981 0:07.6\n", "2600 7803 0.984 0.99 0.981 0:07.9\n", "2700 8103 0.984 0.99 0.981 0:08.2\n", "2800 8403 0.984 0.99 0.981 0:08.5\n", "2900 8703 0.984 0.991 0.981 0:08.8\n", "3000 9003 0.984 0.991 0.981 0:09.1\n", "3100 9303 0.984 0.99 0.981 0:09.4\n", "3200 9603 0.984 0.991 0.982 0:09.7\n", "3300 9903 0.985 0.991 0.982 0:10.0\n", "3400 10203 0.985 0.990885 0.983 0:10.3\n", "3500 10503 0.985 0.991 0.982862 0:10.6\n", "3600 10803 0.985 0.991 0.983 0:10.9\n", "3700 11103 0.985 0.991 0.982167 0:11.2\n", "3800 11403 0.986 0.991 0.982 0:11.5\n", "3900 11703 0.986 0.991 0.982 0:11.8\n", "4000 12000 0.986 0.99125 0.98225 0:12.1\n", "Halting: Maximum number of iterations (4000) reached.\n", "Done!\n" ] } ], "source": [ "import pints\n", "import pints.toy as toy\n", "import pints.plot\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# Load a forward model\n", "model = toy.LogisticModel()\n", "\n", "# Create some toy data\n", "real_parameters = np.array([0.015, 500])\n", "org_values = model.simulate(real_parameters, times)\n", "\n", "# Add noise\n", "np.random.seed(1)\n", "noise = 10\n", "values = org_values + np.random.normal(0, noise, org_values.shape)\n", "\n", "# Create an object with links to the model and time series\n", "problem = pints.SingleOutputProblem(model, times, values)\n", "\n", "# Create a log-likelihood function\n", "log_likelihood = pints.GaussianKnownSigmaLogLikelihood(problem, noise)\n", "\n", "# Create a uniform prior over the parameters\n", "log_prior = pints.UniformLogPrior(\n", " [0.01, 400],\n", " [0.02, 600]\n", ")\n", "\n", "# Create a posterior log-likelihood (log(likelihood * prior))\n", "log_posterior = pints.LogPosterior(log_likelihood, log_prior)\n", "\n", "# Choose starting points for 3 mcmc chains\n", "xs = [\n", " real_parameters * 1.01,\n", " real_parameters * 0.9,\n", " real_parameters * 1.1,\n", "]\n", "\n", "# Create mcmc routine\n", "mcmc = pints.MCMCController(log_posterior, len(xs), xs, method=pints.MALAMCMC)\n", "\n", "# Add stopping criterion\n", "mcmc.set_max_iterations(4000)\n", "\n", "# Set up modest logging\n", "mcmc.set_log_to_screen(True)\n", "mcmc.set_log_interval(100)\n", "\n", "# Run!\n", "print('Running...')\n", "chains = mcmc.run()\n", "print('Done!')" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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yXnnlFebNm8f3v/99XnzxRR5++OH4sZubm1m8eDFr1qzB5XLxq1/9iqeffpoH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\n5eU4g/5s7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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Show traces and histograms\n", "pints.plot.trace(chains)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Chains have converged!" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "R-hat:\n", "[1.0035953753279669, 0.99995026418452926]\n" ] } ], "source": [ "# Discard warm up\n", "chains = chains[:, 1000:]\n", "\n", "# Check convergence using rhat criterion\n", "print('R-hat:')\n", "print(pints.rhat_all_params(chains))" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.14" } }, "nbformat": 4, "nbformat_minor": 2 }