{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lotka-Volterra toy model\n", "\n", "The [LotkaVolterraModel](http://pints.readthedocs.io/en/latest/toy/lotka_volterra_model.html) describes the relationship between two interacting species, where one preys on the other. A good description of its history and interpretation can be found on [Wikipedia](https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equations).\n", "\n", "The model has 2 states $x$ and $y$, where $x$ represents a population of prey, and $y$ represents a population of predators.\n", "It is described by the ODEs:\n", "\n", "$$ \\frac{dx}{dt} = ax - bxy $$\n", "\n", "and\n", "\n", "$$ \\frac{dy}{dt} = -cy + dxy $$\n", "\n", "where $a, b, c$, and $d$ are the four model parameters." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Outputs: 2\n", "Parameters: 4\n" ] } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pints\n", "import pints.toy\n", "\n", "model = pints.toy.LotkaVolterraModel()\n", "\n", "print('Outputs: ' + str(model.n_outputs()))\n", "print('Parameters: ' + str(model.n_parameters()))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can get some suggested parameters and plot some data!" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[3 2 3 2]\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "times = model.suggested_times()\n", "parameters = model.suggested_parameters()\n", "print(parameters)\n", "\n", "plt.figure()\n", "plt.xlabel('Time')\n", "plt.ylabel('Population size')\n", "plt.plot(times, model.simulate(parameters, times))\n", "plt.legend(['prey', 'predators'])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this set-up, the first state represents the prey, and the second the predators.\n", "When there is no prey, the predators begin to die out, which allows the prey population to recover.\n", "\n", "To show the cyclical nature more clearly, these two populations are often plotted against each other:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "values = model.simulate(parameters, times)\n", "\n", "plt.figure()\n", "plt.xlim(0, 10)\n", "plt.ylim(0, 10)\n", "plt.xlabel('Prey')\n", "plt.ylabel('Predators')\n", "plt.plot(values[:, 0], values[:, 1])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can explore the model further by varying the initial conditions:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.xlim(0, 8)\n", "plt.ylim(0, 8)\n", "plt.xlabel('Prey')\n", "plt.ylabel('Predators')\n", "\n", "for x in [1.5, 1.6, 2, 2.5, 3, 4, 5]:\n", " model.set_initial_conditions([x, x])\n", " values = model.simulate(parameters, times)\n", " plt.plot(values[:, 0], values[:, 1])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To see how sensitive the system is to different parameters, we can set up and run an MCMC routine:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "model.set_initial_conditions([2, 2])\n", "values = model.simulate(parameters, times)\n", "sigma = 0.05\n", "noisy_values = values + np.random.normal(0, sigma, values.shape)\n", "\n", "plt.figure()\n", "plt.xlabel('Time')\n", "plt.ylabel('Population size')\n", "plt.plot(times, noisy_values)\n", "plt.plot(times, values)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Running\n", "Using Adaptive covariance MCMC\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 0:00.0\n", "2 9 0 0.667 0 0:00.0\n", "3 12 0.25 0.5 0 0:00.0\n", "20 63 0.381 0.524 0.286 0:00.1\n", "40 123 0.439 0.415 0.415 0:00.2\n", "60 183 0.377 0.344 0.377 0:00.2\n", "80 243 0.321 0.333 0.296 0:00.3\n", "100 303 0.257 0.297 0.238 0:00.3\n", "120 363 0.214876 0.273 0.198 0:00.4\n", "140 423 0.184 0.234 0.17 0:00.5\n", "160 483 0.161 0.205 0.149 0:00.5\n", "180 543 0.144 0.188 0.133 0:00.6\n", "Initial phase completed.\n", "200 603 0.129 0.174 0.119403 0:00.7\n", "220 663 0.127 0.172 0.122 0:00.7\n", "240 723 0.133 0.191 0.129 0:00.8\n", "260 783 0.176 0.192 0.161 0:00.9\n", "280 843 0.196 0.199 0.185 0:00.9\n", "300 903 0.216 0.229 0.203 0:01.0\n", "320 963 0.227 0.252 0.218 0:01.1\n", "340 1023 0.246 0.264 0.228739 0:01.1\n", "360 1083 0.252 0.258 0.241 0:01.2\n", "380 1143 0.255 0.268 0.244 0:01.3\n", "400 1203 0.257 0.267 0.254 0:01.3\n", "420 1263 0.261 0.263658 0.259 0:01.4\n", "440 1323 0.263 0.260771 0.254 0:01.4\n", "460 1383 0.271 0.262 0.249 0:01.5\n", "480 1443 0.262 0.258 0.247 0:01.6\n", "500 1503 0.257485 0.265 0.243513 0:01.6\n", "520 1563 0.255 0.263 0.251 0:01.7\n", "540 1623 0.253 0.266 0.253 0:01.7\n", "560 1683 0.254902 0.267 0.253 0:01.8\n", "580 1743 0.258 0.272 0.251 0:01.9\n", "600 1803 0.256 0.263 0.245 0:01.9\n", "620 1863 0.252818 0.259 0.245 0:02.0\n", "640 1923 0.253 0.254 0.245 0:02.1\n", "660 1983 0.251 0.248 0.245 0:02.1\n", "680 2043 0.253 0.248 0.244 0:02.2\n", "700 2103 0.251 0.243 0.243 0:02.2\n", "720 2163 0.247 0.245 0.239 0:02.3\n", "740 2223 0.245614 0.244 0.235 0:02.4\n", "760 2283 0.243 0.244 0.23 0:02.4\n", "780 2343 0.242 0.239 0.224 0:02.5\n", "800 2403 0.241 0.24 0.22 0:02.6\n", "820 2463 0.242 0.24 0.218 0:02.6\n", "840 2523 0.237 0.235434 0.21522 0:02.7\n", "860 2583 0.233 0.233 0.213 0:02.8\n", "880 2643 0.238 0.238 0.211 0:02.9\n", "900 2703 0.235 0.238 0.211 0:02.9\n", "920 2763 0.236 0.24 0.212 0:03.0\n", "940 2823 0.238 0.24017 0.214 0:03.1\n", "960 2883 0.234 0.24 0.219 0:03.1\n", "980 2943 0.234 0.243629 0.218 0:03.2\n", "1000 3003 0.231 0.243 0.219 0:03.3\n", "1020 3063 0.233 0.24 0.224 0:03.4\n", "1040 3123 0.233 0.24 0.221902 0:03.4\n", "1060 3183 0.236 0.24 0.221 0:03.5\n", "1080 3243 0.237 0.239593 0.221 0:03.6\n", "1100 3303 0.238 0.242 0.222 0:03.6\n", "1120 3363 0.238 0.243 0.224 0:03.7\n", "1140 3423 0.237511 0.245 0.223 0:03.7\n", "1160 3483 0.235 0.246 0.221 0:03.8\n", "1180 3543 0.233 0.249 0.223 0:03.9\n", "1200 3603 0.234 0.246 0.22398 0:03.9\n", "1220 3663 0.237 0.244 0.221 0:04.1\n", "1240 3723 0.233 0.242 0.218 0:04.1\n", "1260 3783 0.234 0.239 0.219 0:04.2\n", "1280 3843 0.233 0.24 0.219 0:04.3\n", "1300 3903 0.23 0.239 0.223 0:04.3\n", "1320 3963 0.23 0.238 0.221 0:04.4\n", "1340 4023 0.233 0.239 0.223 0:04.5\n", "1360 4083 0.231 0.238795 0.226 0:04.5\n", "1380 4143 0.232 0.237 0.226 0:04.6\n", "1400 4203 0.23 0.238 0.226 0:04.7\n", "1420 4263 0.229 0.24 0.228 0:04.7\n", "1440 4323 0.232 0.243 0.229 0:04.8\n", "1460 4383 0.231 0.247091 0.229 0:04.9\n", "1480 4443 0.231 0.246 0.229 0:05.0\n", "1500 4503 0.232 0.245 0.229 0:05.1\n", "1520 4563 0.229 0.246 0.227 0:05.2\n", "1540 4623 0.229721 0.245 0.227 0:05.2\n", "1560 4683 0.233 0.243 0.228 0:05.3\n", "1580 4743 0.231 0.242 0.227704 0:05.4\n", "1600 4803 0.232 0.242 0.229 0:05.6\n", "1620 4863 0.231 0.244 0.23 0:05.6\n", "1640 4923 0.233 0.245582 0.23 0:05.7\n", "1660 4983 0.232 0.245 0.230584 0:05.8\n", "1680 5043 0.233 0.244 0.233 0:05.9\n", "1700 5103 0.236 0.242 0.233 0:06.0\n", "1720 5163 0.236 0.242882 0.233 0:06.1\n", "1740 5223 0.236 0.243 0.231 0:06.2\n", "1760 5283 0.236 0.241 0.229983 0:06.3\n", "1780 5343 0.236 0.242 0.232 0:06.4\n", "1800 5403 0.234 0.242643 0.232 0:06.4\n", "1820 5463 0.234 0.243 0.231 0:06.6\n", "1840 5523 0.234 0.242 0.232 0:06.7\n", "1860 5583 0.232 0.241 0.232 0:06.8\n", "1880 5643 0.23 0.242 0.232 0:06.8\n", "1900 5703 0.231 0.243 0.232 0:06.9\n", "1920 5763 0.231 0.242582 0.233 0:07.0\n", "1940 5823 0.229 0.244204 0.235 0:07.1\n", "1960 5883 0.229 0.243 0.234 0:07.1\n", "1980 5943 0.229 0.242 0.232 0:07.2\n", "2000 6003 0.228 0.242 0.231 0:07.3\n", "2020 6063 0.228 0.241 0.232 0:07.4\n", "2040 6123 0.227 0.243 0.23 0:07.4\n", "2060 6183 0.225 0.242 0.23 0:07.5\n", "2080 6243 0.226 0.241 0.231 0:07.6\n", "2100 6303 0.227 0.24 0.23 0:07.7\n", "2120 6363 0.227 0.239 0.229 0:07.8\n", "2140 6423 0.227 0.239 0.23 0:07.9\n", "2160 6483 0.228 0.24 0.23 0:07.9\n", "2180 6543 0.228 0.241 0.229 0:08.0\n", "2200 6603 0.228 0.242 0.229 0:08.0\n", "2220 6663 0.228 0.241 0.229 0:08.1\n", "2240 6723 0.227 0.241 0.227577 0:08.2\n", "2260 6783 0.227 0.24 0.227 0:08.3\n", "2280 6843 0.228 0.24 0.227 0:08.4\n", "2300 6903 0.227 0.239 0.228 0:08.5\n", "2320 6963 0.227 0.239 0.227 0:08.5\n", "2340 7023 0.228 0.239214 0.226399 0:08.6\n", "2360 7083 0.226 0.239 0.226 0:08.7\n", "2380 7143 0.226 0.24 0.227 0:08.8\n", "2400 7203 0.226 0.2399 0.226 0:08.9\n", "2420 7263 0.227 0.239 0.228005 0:09.0\n", "2440 7323 0.227 0.238 0.229 0:09.1\n", "2460 7383 0.227 0.238 0.229 0:09.2\n", "2480 7443 0.227 0.237 0.23 0:09.2\n", "2500 7503 0.227509 0.237 0.229 0:09.3\n", "2520 7563 0.226 0.236 0.227 0:09.4\n", "2540 7623 0.226 0.235734 0.227 0:09.4\n", "2560 7683 0.225 0.235 0.227 0:09.5\n", "2580 7743 0.224 0.235 0.227 0:09.6\n", "2600 7803 0.225298 0.235 0.229 0:09.6\n", "2620 7863 0.224 0.237 0.228 0:09.7\n", "2640 7923 0.225 0.236 0.228 0:09.8\n", "2660 7983 0.224 0.236 0.228 0:09.8\n", "2680 8043 0.224 0.234614 0.227527 0:09.9\n", "2700 8103 0.225472 0.234 0.226953 0:10.0\n", "2720 8163 0.225 0.233 0.227 0:10.1\n", "2740 8223 0.22583 0.234 0.228 0:10.2\n", "2760 8283 0.226 0.235 0.229 0:10.3\n", "2780 8343 0.227 0.234 0.228 0:10.3\n", "2800 8403 0.227 0.232774 0.228 0:10.4\n", "2820 8463 0.227 0.233 0.227 0:10.4\n", "2840 8523 0.228 0.232 0.228 0:10.5\n", "2860 8583 0.227 0.233 0.22964 0:10.6\n", "2880 8643 0.228 0.233 0.22874 0:10.6\n", "2900 8703 0.229 0.232 0.228 0:10.7\n", "2920 8763 0.229 0.233 0.228 0:10.7\n", "2940 8823 0.228 0.232 0.227 0:10.8\n", "2960 8883 0.227 0.231003 0.227 0:10.9\n", "2980 8943 0.226 0.23 0.228 0:10.9\n", "3000 9003 0.226 0.231 0.227 0:11.0\n", "3020 9063 0.225422 0.23 0.228 0:11.1\n", "3040 9123 0.225 0.231 0.228 0:11.1\n", "3060 9183 0.225 0.231 0.228 0:11.2\n", "3080 9243 0.224927 0.231 0.228 0:11.3\n", "3100 9303 0.224 0.231 0.227 0:11.3\n", "3120 9363 0.224 0.232 0.227 0:11.4\n", "3140 9423 0.224 0.231455 0.227 0:11.5\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "3160 9483 0.224 0.232 0.227 0:11.5\n", "3180 9543 0.224 0.231 0.226 0:11.6\n", "3200 9603 0.225 0.231 0.226 0:11.6\n", "3220 9663 0.226 0.231 0.226 0:11.7\n", "3240 9723 0.226 0.232 0.226 0:11.8\n", "3260 9783 0.225391 0.232 0.227 0:11.9\n", "3280 9843 0.226 0.232 0.227 0:12.0\n", "3300 9903 0.226 0.231445 0.227 0:12.1\n", "3320 9963 0.225 0.231 0.228 0:12.1\n", "3340 10023 0.224 0.232 0.228 0:12.2\n", "3360 10083 0.224 0.232 0.228801 0:12.3\n", "3380 10143 0.224 0.232 0.229 0:12.3\n", "3400 10203 0.224 0.233 0.229 0:12.4\n", "3420 10263 0.224 0.234 0.228 0:12.5\n", "3440 10323 0.224 0.233653 0.227 0:12.5\n", "3460 10383 0.223 0.235 0.227102 0:12.6\n", "3480 10443 0.223 0.235 0.227 0:12.6\n", "3500 10503 0.222 0.235647 0.228 0:12.7\n", "3520 10563 0.222096 0.235 0.228 0:12.8\n", "3540 10623 0.223 0.235 0.227 0:12.8\n", "3560 10683 0.223 0.233 0.227 0:12.9\n", "3580 10743 0.223 0.233 0.227 0:12.9\n", "3600 10803 0.224 0.234 0.227 0:13.0\n", "3620 10863 0.223 0.235 0.228 0:13.1\n", "3640 10923 0.223 0.235 0.229 0:13.1\n", "3660 10983 0.224 0.235 0.23 0:13.2\n", "3680 11043 0.223 0.236 0.23 0:13.3\n", "3700 11103 0.222 0.235612 0.23 0:13.4\n", "3720 11163 0.221 0.235 0.23 0:13.5\n", "3740 11223 0.221 0.235 0.23 0:13.6\n", "3760 11283 0.22 0.234778 0.23 0:13.6\n", "3780 11343 0.22 0.235123 0.23 0:13.7\n", "3800 11403 0.219 0.235 0.229 0:13.8\n", "3820 11463 0.219 0.234 0.23 0:13.9\n", "3840 11523 0.219 0.234 0.23 0:14.0\n", "3860 11583 0.219 0.234 0.23 0:14.0\n", "3880 11643 0.218 0.234 0.23 0:14.1\n", "3900 11703 0.218 0.233 0.23 0:14.2\n", "3920 11763 0.218 0.233 0.23 0:14.2\n", "3940 11823 0.218 0.232 0.23 0:14.3\n", "3960 11883 0.218 0.232517 0.229235 0:14.3\n", "3980 11943 0.218 0.232 0.229 0:14.4\n", "4000 12000 0.21875 0.232 0.2295 0:14.5\n", "Halting: Maximum number of iterations (4000) reached.\n", "Done!\n" ] } ], "source": [ "# Create an object with links to the model and time series\n", "problem = pints.MultiOutputProblem(model, times, noisy_values)\n", "\n", "# Create a log posterior\n", "log_prior = pints.UniformLogPrior([1, 1, 1, 1], [6, 6, 6, 6])\n", "log_likelihood = pints.GaussianKnownSigmaLogLikelihood(problem, sigma)\n", "log_posterior = pints.LogPosterior(log_likelihood, log_prior)\n", "\n", "# Run MCMC on the noisy data\n", "x0 = [[4, 1, 2, 3]]*3\n", "mcmc = pints.MCMCController(log_posterior, 3, x0)\n", "mcmc.set_max_iterations(4000)\n", "#mcmc.set_log_to_screen(False)\n", "\n", "print('Running')\n", "chains = mcmc.run()\n", "print('Done!')" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "R-hat:\n", "[1.078403673118607, 1.0477124994282836, 1.0651132349574168, 1.0629509070339487]\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Check convergence using rhat criterion\n", "print('R-hat:')\n", "print(pints.rhat_all_params(chains))\n", "\n", "import pints.plot\n", "pints.plot.trace(chains, ref_parameters=parameters)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also compare the predictions with these values to what we found:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Select first chain\n", "chain1 = chains[0]\n", "\n", "# Remove burn-in\n", "chain1 = chain1[2500:]\n", "\n", "# Plot some predictions with these samples\n", "pints.plot.series(chain1, problem)\n", "plt.show()" ] } ], "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": "3.6.7" } }, "nbformat": 4, "nbformat_minor": 2 }