{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Writing a custom LogPrior\n", "\n", "This example shows you how to write a custom [LogPrior](http://pints.readthedocs.io/en/latest/log_pdfs.html#pints.LogPrior) class to use in your inference problems.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Most priors in Pints are defined over just 1 parameter, and then combined into a multivariate prior using the [ComposedLogPrior](http://pints.readthedocs.io/en/latest/log_priors.html#pints.ComposedLogPrior) class.\n", "But sometimes you might want to define a prior over multiple variables at once. In such a case, it may make sense to create a custom LogPrior class." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example, we'll implement a uniform 2d logprior that defines a circle in the parameter space such that points within the circle have probability c = 1/A and points outside it have probability 0." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before we begin, let's define a toy problem, like in the basic MCMC example:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from __future__ import print_function\n", "import pints\n", "import pints.toy\n", "import pints.plot\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# Load a forward model\n", "model = pints.toy.LogisticModel()\n", "\n", "# Create some toy data\n", "real_parameters = np.array([1, 500])\n", "times = np.linspace(0, 1000, 1000)\n", "org_values = model.simulate(real_parameters, times)\n", "\n", "# Add noise\n", "noise = 0.10\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 (adds an extra parameter!)\n", "log_likelihood = pints.KnownNoiseLogLikelihood(problem, noise)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's add our prior.\n", "\n", "First, we take a look at the [LogPrior](http://pints.readthedocs.io/en/latest/log_pdfs.html#pints.LogPrior) class, as well as the [LogPDF](http://pints.readthedocs.io/en/latest/log_pdfs.html#pints.LogPDF) class which it extends.\n", "\n", "From this we learn that:\n", "\n", "1. We need to provide a method `n_parameters()` that returns the dimension of the parameter space our prior is defined on.\n", "2. Objects of our prior class should be [callable](https://docs.python.org/3/reference/datamodel.html#object.__call__): they should have a `__call__` method that takes a parameter vector as input and returns a scalar.\n", "3. If we like, we can implement an optional `sample()` method.\n", "\n", "Leaving aside the `sample()` method, we can implement our prior like this:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class CircularLogPrior(pints.LogPrior):\n", " def __init__(self, center, radius):\n", " # Store center\n", " self._center = np.array(center)\n", " # Set circle radius\n", " self._r = float(radius)\n", " # Calculate c \n", " A = np.pi * self._r * self._r\n", " self._c = np.log(1 / A)\n", " \n", " def n_parameters(self):\n", " return 2\n", " \n", " def __call__(self, parameters):\n", " # Get coordinates relative to center\n", " p = np.array(parameters) - self._center\n", " \n", " # Calculate the radius\n", " r = np.sqrt(p[0]*p[0] + p[1]*p[1])\n", " \n", " # Return\n", " return self._c if r < self._r else -float('inf')\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can test our prior with a few values:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-1.14472988585\n", "-inf\n", "-1.14472988585\n", "-inf\n", "-1.14472988585\n" ] } ], "source": [ "p = CircularLogPrior([0, 0], 1)\n", "print(p([0, 0])) # c\n", "print(p([1, 1])) # -inf\n", "print(p([-0.5, -0.5])) # c\n", "print(p([-1.0, 0])) # -inf\n", "print(p([0.9, 0])) # c" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can try using it in an inference routine:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Running...\n", "Done!\n", "R-hat:\n", "[1.0000189021071446, 1.0019107390010724]\n" ] }, { "data": { "image/png": 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AcSxXr7utahtVzQCTQMtxjj1hn65r4L8H/lC0+UMi8raIPCUiF1IFEblZRLaI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\n9tdYvbdf9Pzu+Sx7YRktNQMr1smEcETbEWx6a9PAf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udH7K78Nn8LnnZO768exgh9UirTfdubvsTt7IfAE+vR2u+HedH9rVe0NK+act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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Create a log-prior\n", "log_prior = CircularLogPrior(center=real_parameters, radius=0.001)\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 + np.array([0.0005, -0.0005]),\n", " real_parameters + np.array([-0.0005, -0.0005]),\n", " real_parameters + np.array([-0.0005, 0.0005]),\n", "]\n", "\n", "# Create mcmc routine\n", "mcmc = pints.MCMCSampling(log_posterior, 3, xs, method=pints.AdaptiveCovarianceMCMC)\n", "\n", "# Add stopping criterion\n", "mcmc.set_max_iterations(4000)\n", "\n", "# Start adapting after 1000 iterations\n", "mcmc.set_initial_phase_iterations(1000)\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", "# Show traces and histograms\n", "pints.plot.trace(chains)\n", "\n", "# Discard warm up\n", "chains = chains[:, 2000:, :]\n", "\n", "# Check convergence using rhat criterion\n", "print('R-hat:')\n", "print(pints.rhat_all_params(chains))\n", "\n", "# Look at distribution in chain 0\n", "pints.plot.pairwise(chains[0], kde=True)\n", "\n", "# Show graphs\n", "plt.show()" ] } ], "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": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 2 }