{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Inference plots - Pairwise scatterplots with KDE\n", "\n", "This example builds on the [adaptive covariance MCMC example](https://github.com/pints-team/pints/blob/master/examples/sampling-adaptive-covariance-mcmc.ipynb), and shows you a different way to plot the results.\n", "The plot shown here is similar to the [pairwise scatterplots example](https://github.com/pints-team/pints/blob/master/examples/plot-mcmc-pairwise-scatterplots.ipynb), but instead of using histogram plots, we use [kernel density estimation (KDE)](https://docs.scipy.org/doc/scipy-0.19.1/reference/generated/scipy.stats.gaussian_kde.html) to represent the pairwise probability distributions of each parameter.\n", "\n", "Inference plots:\n", "* [Predicted time series](https://github.com/pints-team/pints/blob/master/examples/plot-mcmc-predicted-time-series.ipynb)\n", "* [Trace plots](https://github.com/pints-team/pints/blob/master/examples/plot-mcmc-trace-plots.ipynb)\n", "* [Autocorrelation](https://github.com/pints-team/pints/blob/master/examples/plot-mcmc-autocorrelation.ipynb)\n", "* [Pairwise scatterplots](https://github.com/pints-team/pints/blob/master/examples/plot-mcmc-pairwise-scatterplots.ipynb)\n", "* __Pairwise scatterplots with KDE__" ] }, { "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": [ "from __future__ import print_function\n", "import pints\n", "import pints.toy as toy\n", "import numpy as np\n", "import scipy.stats as stats\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]\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": [ "## Plotting one variable: histogram + KDE\n", "\n", "We now run the MCMC routine and plot the histogram for a single parameter. In addition, we can use SciPy's [Kernel-Density Estimation (KDE) method](https://docs.scipy.org/doc/scipy-0.19.1/reference/generated/scipy.stats.gaussian_kde.html) to obtain a smooth estimate of the probability distribution." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Running...\n", "Done!\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": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/chonlei/anaconda3/envs/matplotlib_build/lib/python3.7/site-packages/matplotlib/axes/_axes.py:6521: MatplotlibDeprecationWarning: \n", "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n", " alternative=\"'density'\", removal=\"3.1\")\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def plot_kde_1d(x, ax):\n", " \"\"\" Creates a 1d histogram and an estimate of the PDF using KDE. \"\"\"\n", " xmin = np.min(x)\n", " xmax = np.max(x)\n", " x1 = np.linspace(xmin, xmax, 100)\n", " x2 = np.linspace(xmin, xmax, 50)\n", " kernel = stats.gaussian_kde(x)\n", " f = kernel(x1)\n", " hist = ax.hist(x, bins=x2, normed=True)\n", " ax.plot(x1, f)\n", "\n", "fig, ax = plt.subplots(1, 1)\n", "ax.set_xlabel('Parameter 1')\n", "ax.set_ylabel('Probability density')\n", "plot_kde_1d(chain[:, 0], ax)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plotting two variables with KDE\n", "\n", "We can use KDE again to get very nice plots of 2d distributions." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def plot_kde_2d(x, y, ax):\n", " # Get minimum and maximum values\n", " xmin, xmax = np.min(x), np.max(x)\n", " ymin, ymax = np.min(y), np.max(y)\n", " \n", " # Plot values\n", " values = np.vstack([x, y])\n", " ax.set_xlim(xmin, xmax)\n", " ax.set_ylim(ymin, ymax)\n", " ax.imshow(np.rot90(values), cmap=plt.cm.Blues, extent=[xmin, xmax, ymin, ymax])\n", "\n", " # Create grid\n", " xx, yy = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]\n", " positions = np.vstack([xx.ravel(), yy.ravel()])\n", "\n", " # Get kernel density estimate and plot contours\n", " kernel = stats.gaussian_kde(values)\n", " f = np.reshape(kernel(positions).T, xx.shape)\n", " ax.contourf(xx, yy, f, cmap='Blues')\n", " ax.contour(xx, yy, f, colors='k')\n", " \n", " # Fix aspect ratio\n", " ax.set_aspect((xmax - xmin) / (ymax - ymin))\n", "\n", "fig, ax = plt.subplots(1, 1)\n", "ax.set_xlabel('parameter 1')\n", "ax.set_ylabel('parameter 2')\n", "plot_kde_2d(chain[:, 0], chain[:, 1], ax)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A matrix of scatterplots with KDE\n", "\n", "Using these functions, we can now create a matrix of scatterplots with KDE." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "n_param = log_likelihood.n_parameters()\n", "fig_size = (12, 12)\n", "\n", "fig, axes = plt.subplots(n_param, n_param, figsize=fig_size)\n", "for i in range(n_param):\n", " for j in range(n_param):\n", " \n", " # Create subplot\n", " if i == j:\n", " # Plot the diagonal\n", " plot_kde_1d(chain[:, i], ax=axes[i, j])\n", " axes[i, j].axvline(real_parameters[i], c='g', label='True value')\n", " axes[i, j].legend()\n", " elif i < j:\n", " # Upper triangle: No plot\n", " axes[i, j].axis('off')\n", " else:\n", " # Lower triangle: Pairwise plot\n", " plot_kde_2d(chain[:, j], chain[:, i], ax=axes[i, j])\n", " axes[i, j].axhline(real_parameters[i], c='g')\n", " axes[i, j].axvline(real_parameters[j], c='g')\n", " \n", " # Adjust the tick labels\n", " if i < n_param - 1:\n", " # Only show x tick labels for the last row\n", " axes[i, j].set_xticklabels([])\n", " else:\n", " # Rotation the x tick labels to fit in the plot\n", " for tl in axes[i, j].get_xticklabels():\n", " tl.set_rotation(45)\n", " if j > 0:\n", " # Only show y tick labels for the first column\n", " axes[i, j].set_yticklabels([])\n", "\n", " # Add labels to the subplots at the edges\n", " axes[i, 0].set_ylabel('parameter %d' % (i + 1))\n", " axes[-1, i].set_xlabel('parameter %d' % (i + 1))\n", "\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": "3.7.2" } }, "nbformat": 4, "nbformat_minor": 2 }