examples/plotting/mcmc-autocorrelation.ipynb

{
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  {
   "cell_type": "markdown",
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   "source": [
    "# Inference plots - Autocorrelation plot\n",
    "\n",
    "This example builds on [adaptive covariance MCMC](https://pints.readthedocs.io/en/latest/mcmc_samplers/adaptive_covariance_mc.html), and shows you how to plot the autocorrelation of the MCMC samples.\n",
    "\n",
    "Inference plots:\n",
    "* [Predicted time series](mcmc-predicted-time-series.ipynb)\n",
    "* [Trace plots](mcmc-trace-plots.ipynb)\n",
    "* [Pairwise scatterplots](mcmc-pairwise-scatterplots.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setting up an MCMC routine\n",
    "\n",
    "See the adaptive covariance MCMC example for details."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pints\n",
    "import pints.toy as toy\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 = [0.015, 500]  # growth rate, carrying capacity\n",
    "times = np.linspace(0, 1000, 100)\n",
    "org_values = model.simulate(real_parameters, times)\n",
    "\n",
    "# Add noise\n",
    "noise = 50\n",
    "values = org_values + np.random.normal(0, noise, org_values.shape)\n",
    "real_parameters = np.array(real_parameters + [noise])\n",
    "\n",
    "# Get properties of the noise sample\n",
    "noise_sample_mean = np.mean(values - org_values)\n",
    "noise_sample_std = np.std(values - org_values)\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 (adds an extra parameter!)\n",
    "log_likelihood = pints.GaussianLogLikelihood(problem)\n",
    "\n",
    "# Create a uniform log-prior over both the parameters and the new noise variable\n",
    "log_prior = pints.UniformLogPrior(\n",
    "    [0.01, 400, noise*0.1],\n",
    "    [0.02, 600, noise*100]\n",
    "    )\n",
    "\n",
    "# Create a posterior log-likelihood (log(likelihood * prior))\n",
    "log_posterior = pints.LogPosterior(log_likelihood, log_prior)\n",
    "\n",
    "# Perform sampling using MCMC, with a single chain\n",
    "x0 = real_parameters * 1.1\n",
    "mcmc = pints.MCMCController(log_posterior, 1, [x0])\n",
    "mcmc.set_max_iterations(6000)\n",
    "mcmc.set_log_to_screen(False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Autocorrelation\n",
    "\n",
    "The [autocorrelation](https://en.wikipedia.org/wiki/Autocorrelation) in a Markov chain indicates how much each sample in the chain differs from the next. Checking for (lack of) autocorrelation is an easy way to check if your MCMC routine is converging. It can easily be plotted using pints.plot's autocorrelation method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Running...\nDone!\n"
    }
   ],
   "source": [
    "print('Running...')\n",
    "chains = mcmc.run()\n",
    "print('Done!')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Select chain 0 and discard warm-up\n",
    "chain = chains[0]\n",
    "chain = chain[3000:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "import pints.plot\n",
    "pints.plot.autocorrelation(chain, parameter_names=['growth rate', 'carrying capacity', 'noise'], max_lags=10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.5-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}