diff --git a/change_detection/notebooks/Haario Bardenet ACMC/2dim Gaussian distribution/baseline.ipynb b/change_detection/notebooks/Haario Bardenet ACMC/2dim Gaussian distribution/baseline.ipynb new file mode 100644 index 0000000..a3fd9fe --- /dev/null +++ b/change_detection/notebooks/Haario Bardenet ACMC/2dim Gaussian distribution/baseline.ipynb @@ -0,0 +1,421 @@ +{ + "metadata": { + "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" + }, + "orig_nbformat": 2, + "kernelspec": { + "name": "python3", + "display_name": "Python 3", + "language": "python" + } + }, + "nbformat": 4, + "nbformat_minor": 2, + "cells": [ + { + "source": [ + "# Baseline for Haario Bardenet ACMC on a 2 dimensional Gaussian distribution" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "source": [ + "## Hyperparameters I: Marginal $\\hat{R} < 1.01$ and an effective sample size per parameter $>200$ per chain." + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "source": [ + "### Infer posterior" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import pints\n", + "import pints.toy\n", + "\n", + "# Define pdf \n", + "# (prior is only used to sample starting positions for chains)\n", + "normal_log_pdf = pints.toy.GaussianLogPDF(mean=[0, 0], sigma=[1, 1])\n", + "log_prior = pints.ComposedLogPrior(\n", + " pints.GaussianLogPrior(mean=0, sd=3),\n", + " pints.GaussianLogPrior(mean=0, sd=3))\n", + "\n", + "# Set up hyperparameters\n", + "initial_parameters = log_prior.sample(n=10)\n", + "n_chains = 10\n", + "n_iterations = 15000\n", + "method = pints.HaarioBardenetACMC\n", + "is_run_parallel = True\n", + "\n", + "# Set up problem\n", + "sampler = pints.MCMCController(\n", + " log_pdf=normal_log_pdf,\n", + " x0=initial_parameters,\n", + " chains=n_chains,\n", + " method=method)\n", + "sampler.set_max_iterations(n_iterations)\n", + "sampler.set_parallel(is_run_parallel)\n", + "sampler.set_log_to_screen(False)\n", + "\n", + "# Sample\n", + "chains = sampler.run()" + ] + }, + { + "source": [ + "### Visualise traces" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "param mean std. 2.5% 25% 50% 75% 97.5% rhat ess\n------- ------ ------ ------ ----- ----- ----- ------- ------ --------\nparam 1 -0.01 1.00 -1.98 -0.68 -0.01 0.66 1.98 1.00 13248.96\nparam 2 -0.01 1.01 -1.98 -0.69 -0.02 0.67 1.95 1.00 13332.37\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": "
", + "image/svg+xml": "\n\n\n\n \n \n \n \n 2021-02-09T16:50:36.486912\n image/svg+xml\n \n \n Matplotlib v3.3.4, https://matplotlib.org/\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n 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\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n", + "image/png": 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\n" + }, + "metadata": { + "needs_background": "light" + } + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import pints.plot\n", + "\n", + "# Set warmup iterations\n", + "warmup = 1000\n", + "\n", + "# Show summary\n", + "print(pints.MCMCSummary(chains=chains[:, warmup:]))\n", + "\n", + "# Plot traces\n", + "fig = pints.plot.trace(chains[:, warmup:])\n", + "plt.show()" + ] + }, + { + "source": [ + "### Visualise $\\hat{R}$ and ESS over length of chains" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": "
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8DviXqPYPCDaoklSW33QgkUS0tQbtSiYiUiKSJpNwd8NFZna+u/+ul2IqLTsbu9cuIlKE0qrN5e6/M7OzgI8D/aLab8pVYCVjYF0wtBWvXUSkRKS7mmshcCHBFrsGzAQ+ksO4SsfkG6CqunNbVXXQLiJSItJdzfVJd78U2O7uPwBOAT6au7BKyNhZcM4CGDgCsOD7OQs0XyIiJSXdEvSRGeQWMxsObAWG5SakEjR2lpKHiJS0dJPJo2ZWA8wHXgQcuCtXQYmISHFJdwL+5vDm78zsUaCfu+/MXVgiIlJM0t5p0cw+CYyMPMbMcPd7cxSXiIgUkbSSiZndBxwDrAH2h80OKJmIiEjaPZN64Dgvhz1+RUSk29JNJuuAI4FNOYylqD28uon5S9fz7o5WhtdUM3vqaGaMr813WCIivSJVocdHCIazBgCvmtnzwN8jx919em7DKw4Pr27i+gdfprUtGAFs2tHK9Q++DKCEIiJlIVXP5Ke9EkWRm790fUciiWht28/8peuVTESkLCS9At7d/yfeF/AMQSXhhMzsbjPbbGbrEhw3M1tgZhvMbK2ZTYg6dpmZvRl+XRbV3tfM7jSzN8zsdTM7v3v/3Nx4d0drt9q1v4mIlJqkycTMDjWz683sl2Y2JUwA3wD+AqS6pPseYFqS42cAx4ZfVwJ3hK95GHAjcDJwEnCjmQ0KH/M9YLO7fxQ4DvifFDH0iuE11em3R/Y32bkR8AP7myihiEgRS1Wb6z5gNPAycAXwFEGRxxnufm6yB7r708C2JKecC9zrgeeAGjMbRrCHyjJ33+bu24FlHEhK/wTcEj5/u7tvSRF/r5g9dTTVVZWd2qqrKpk9dXTXk5PtbyIiUqRSzZkc7e7HA5jZXQSruY5y9z1ZeO1aILo2e2PYFrc9LOcCcLOZnQ68BXzD3d+P9+RmdiVBj4ejjjoqC+EmFpkXSWs1l/Y3EZESlCqZtEVuuPt+M2vMUiLpiT4E8zR/dPdvmdm3CBYIXBLvZHe/E7gToL6+PufXx8wYX5veZLv2NxGREpRqmOsTZrYr/PoAGBu5bWa7MnztJmBE1P26sC1R+1agBXgwbP8tMIFio/1NRKQEpVrNVenuh4ZfA9y9T9TtQzN87SXApeGk/kRgp7tvApYCU8xsUDjxPgVYGl59/whwevj4ycCrGcbQ+7S/iYiUoLQLPXaXmT1A8MY/xMwaCVZoVQG4+0LgceBMYANBj+PL4bFtZnYz8EL4VDe5e2Qi/7vAfWb2c6A58piio/1NRKTEWDmU26qvr/eGhoZeez2VVhGRUmBmq9y9Pp1zc9YzKVcqrSIi5SjdPeAlTclKq4iIlColkyzrdmkVEZESoGSSZYlKq1SYMWrOY5w670keXt3Uy1GJiOSWkkmWxSutArDfHefAHIoSioiUEiWTLJsxvpZbzjue2ppqDKg063JOlzkUVREWkSKn1Vw5EF1aZdScx+Ke0zGHEqkiHCn+GKkiDLoWRUSKhnomOZayPL2qCItICVAyybGU5elVRVhESoCGuXIsZXl6VREWkRKgZNILkpann3xD5zkTUBVhESk6GubKN1URFpESoJ5JIVAVYREpckomeaCqwiJSapRMepmqCotIKdKcSS9TVWERKUVKJr1MVYVFpBQpmfSylFfEi4gUISWTXpbyinhQ4UcRKTqagO9lKa+IV+FHESlC5u75jiHn6uvrvaGhId9hpOe2MQnKq4yAb67r/XhEpGyZ2Sp3r0/nXA1zFRoVfhSRIpTTZGJmd5vZZjOL+5HaAgvMbIOZrTWzCVHHLjOzN8Ovy+I8dkmi5y1qiQo8qvCjiBSwXPdM7gGmJTl+BnBs+HUlcAeAmR0G3AicDJwE3GhmgyIPMrPzgN25CTnPJt8QFHqMpsKPIlLgcppM3P1pYFuSU84F7vXAc0CNmQ0DpgLL3H2bu28HlhEmJTPrD3wL+GEuY88bFX4UkSKU79VctUD0bHNj2JaoHeBm4GdAS7InNrMrCXo7HHXUUVkKt5eo8KOIFJmimoA3s3HAMe7+UKpz3f1Od6939/qhQ4fmPjgRkTKW755JEzAi6n5d2NYEnB7TvgI4Bag3s3cIYj/czFa4e/S5RU9VhUWk2OS7Z7IEuDRc1TUR2Onum4ClwBQzGxROvE8Blrr7He4+3N1HApOAN0oxkVz/4Ms07WjFOVBV+OHVTfkOTUQkoZz2TMzsAYIexhAzayRYoVUF4O4LgceBM4ENBHMgXw6PbTOzm4EXwqe6yd2TTeSXjGRVhdU7EZFCldNk4u4XpzjuwNcTHLsbuDvJY98BxmQSXyFSVWERKUb5HuaSGKoqLCLFSMmkwMSrKlxVYbTs3ceoOY9x6rwnC3b+5OHVTZw678mCj1NEsi/fq7kkRmxV4YHVVXy4dx/bW9qANLb5XbsYlt8U1PIaWBdcOd8L16xoO2KR8qZkUgDiLQVeOeezAJw670k+9fen+E7fxQy3LbzrQ7h13yzmL+3b9U06jfL1uVp2rIUDIuVNySTPUn2ir9+1jFuq7uJg2wtAnW1hXtVdzNkFo+bEJITlNx1IJBFtrUH72Fk57T1o4YBIedOcSZ4l+0QPcH3f33YkkoiDbS/f6bO463UoKcrXp3qtTGjhgEh5UzLJs1Sf6I9gS9zjw21rx+2OhJCifH0uew9pbUcsIiVLw1x5NrymmqY4b+aRT/Q2sC7uzovv+mAAplc8y3f6LGZ46xZ27BnAAKui0tsOnBhVvj7Va3VX7PzL+SfU8tTrzSoDI1KG1DPJs5Sf6OPsb9Lifbl13yymVzzLvKq7qKvYQoVBDR+wv72dv1fVEK98fTZ7D/HKvvxuVROzp47m7XlndVpAoKXCIqVPPZM8i10K3OUTfWRZb7jct6X6SG748HyWtH+SZ/te02U+pa/t5722Ko6cu6P7r0Xy1V7RxyrM2O/e6fmjV29pqbBIeTGPeUMoRfX19d7Q0JDvMLIm8qb+TOsXqLCux9vdqPjBjh49b3QCgOCCyf79+rC9pQ0DUv21GPD2vLM4dd6TcYfUamuqO3otIlLYzGyVu9enc66GuYrQjMqVrDzoGixOIgHYxOAeDS3FW+3V1u4dF0ym87EjMv+ipcIi5UXDXMUm6sLEeLmkxfvyk7ZZnZYNQ+Khpeihq0z7qNHzL9me7BeRwqaeSbGJd2Ei4A5NPoQ5bVewpH1SR3uy60hiJ9F7otIMIxi+uuW84zuSlpYKi5QX9UyKTYILE82MSXsWdEkK0yue5Tsti2m/cQubbSgffmQyx+xYCTsbmcgQPr9/JkuYFPc5U6muquyUQKKlM9kvIqVDyaTYJLjuhIF1DO/XeWgpsnQ4suLrSJrxd35NZHzsSJqZV3UXtNGpNwPBKZEik237vVO7E/REUiWHGeNrlTxEyoSSSbGZfEPnYo7QcWHi7P2jO63G+k6fxV2WDsdO2kdKsyzZGyST6RXP8s99f8uRbIFD63jhmKu57tVjs9K70N72IqVLyaTYxFx3El1mfkZ4SscbtsUvxRIrUpplesWz/KTqLqoJE9DOjZz48o2sjLrwsad03YlIadN1JiXsvbn/wJE0pz6PoZyy53b+1O/a+OcPHAHfXJdRLLruRKT46DoTAWDjhNm0et9ObV0+O1RVc+R5P+bteWcFQ1vxJKpG3A267kSktCmZlLATp3+FdSf8kPcYSrsb7zGUv4y8KOhpRGp3feKLwZDZ3BqwBH8OiaoRd4NK1IuUNs2ZlLgTp38Fpn8FgCNjD8buzOj7Y8/oVHU4E7Onju5SqkXXnYiUjpz1TMzsbjPbbGZxB9stsMDMNpjZWjObEHXsMjN7M/y6LGw72MweM7PXzewVM5uXq9jLRoILILFK4lUdzsSM8bXcct7x1NZUd1zkeP4Jtcxful5VhUVKQC57JvcAvwTuTXD8DODY8Otk4A7gZDM7DLgRqCe4pGGVmS0B/g781N2fMrO+wHIzO8Pdf5/Df0NpSzQX4u0QqTq8djHcNqbLyrGeiL7uRKu7REpLznom7v40sC3JKecC93rgOaDGzIYBU4Fl7r7N3bcDy4Bp7t7i7k+Fz70XeBHIfDC/nKXYmbFjGGznRsCD749cE7RnKJdbCItI78vnBHwtEH0pd2PYlqi9g5nVAOcAyxM9uZldaWYNZtbQ3Jx6eWxZirPxVqc5knjDYG2tQXuGtLpLpLQU3WouM+sDPAAscPe/JDrP3e9093p3rx86dGjvBVhMxs4K5kSiV3dFz5EkGgbLwlJhre4SKS35XM3VBIyIul8XtjUBp8e0r4i6fyfwprv/PLfhlYmxsxLPgSSpA5apeKu7qiqMlr37GDXnMQZWV2EGO1rairv0ytrFcasViJSafPZMlgCXhqu6JgI73X0TsBSYYmaDzGwQMCVsw8x+CAwErstTzOUl1TBYBmJXd9VUV4HB9pY2HNjR2tZxOzI5X7CrvSKLFObWBN8jc0q5mHNK9FoieZazcipm9gBBD2MI8D7BCq0qAHdfaGZGsNprGtACfNndG8LH/hPwz+FT/cjd/8PM6gjmUl4nWNkF8Et3vytVLOVaTiUreumTdaJyK9EKpvRK9M+kehDs3Q37owpqVlUHw4XLb0rQs+tGeZp0X0u9HcmB7pRTUW0uKQij5jyW1gZdBvkd9oq90DORgSPCuaVE/ypLnZy781oZ1k4Tiac7yURXwEtBSLTNb6xE2xFnVN4+tvd17BR487/j98YSXegZK16PJPZfEhn2gvgJJe3XynxBhEim1DOR9OVwyCv2IsZ0VJrR7h53E69ku0B2ks6n/4oqOGgAtG4ncU8jA1YZXCgam8jSfa3ox2uCX7JIw1wxlEyyIN6bbpbH66N7F9GrudL5C51e8Szf6bOY4baFd30It+6bxWN+Gu3uyXsqt41JoxdRTMK9MAeOUGKRjCmZxFAyyYJEb7q9MF6fanI+dntigBbvy5y2Kzq2I76g7x+56ZDfcXDre50/wc+tIePeRlTPxXEszintbmy2IWntL5Pua2EV8YtzRsQmey1Tlm5SMomhZJIFCd90rXMdr3TnHroh1RDYs32voa6i614s+7yCCtrZ7v0ZYHvoa/s6x42HQ0TpD611FkyiR29t/OxB11AbZ4fLxvagtxSb9Lr7Wp1+hukkwkiyj9ezjE5MSi4Sh5JJDCWTLEjUM4mM18dbthorg2GxF5b8GyNenM/h3swmhvCH/eOYXLGG4bYFo+ve9jkXvknHJrpUvaQDw3FbacfoY+1pv1YXaQ/RWepeDHRNLln6MCC9L6MFKVGUTGIomWRBustUU+nJsFic13bPcgJJNAlePYj9ez6g0ts6Tt1rB/Hjyq+xaPdJVJixP+b/UHTCeNcHc+u+WR3DbbHnxSaeLv+uZAk4W7+TdOmalqIQryef9oKUGEomMZRMsiR6GCudT7pxRQ2L5fy1Mo/r4dVNPPvQv3Idv06ZHHoiNvEsbw96XHUVW9PrDXT8nDbSMXSXS+muHNP8TK+L9EYSzS/25KJfJZMYSiY50NOJ60Q9gOg3nIw+cac5pBMrqscUPUQQr+eRjsrwcT15e48sec7oeplcJxXo3FNJdaW+5me6SjHH+FbNqRzy1+Uc7s1stqE8fdTXuH3z+I6hq2sPX82n/nYHh3sz79kQlu8fz2dsNcNtC9u9P2ZQw+6O1Y2PtE/i7XlndStEJZMYSiY5kIsltR1vOMm2wUkiyWTzXq9kN9XUsDt4qaihpH2V/fihfZVFu0+Ke81Kd0UPKcQud+7uc/d0eCIrc1xpB3lY95+rHJNLioTr0GklYOyQ59+9kg/Dv+F4i0qSDf22eF9urbqKud//QbdCVjKJoWSSA+msDor+pJXroaoky2DfYwg/3juzY2gqemjpPRvM/H0X8tC+UzN6+XR7E7ETo5/52FCeer05aS+oJ899Wf/n+b4vpM/+PWn9jLKaXHoim8mlEIfY1i5m339d3fn30ctaqodx8Hdf79ZjlExiKJnkSHf+02bjeo50hsjiSLfuV0/1uPcQI504E71WvEnXL/RZyew+v+FI38pmG8LGCbM5cfpXEj95smGXXpm3ipIsuSSLM50httjzoecr2FIthw/v+86Nca8/6l1pzldGP0LJpDMlkwKQ6bBYBiuJ0qlInEp07yC6N5HNopPpxhlvIjWdx2aU9Hp75VgX4exTT4bUMpEqEaWIJXboKq96sJJSySSGkkkByOTNKMPSID2p+xUtWz2PVLoTZ6R6ciSxpZssMyrj32nlWArRb8L5HkIrErFzHt1d/p70/B5+GFMyiaFkUiC6OzyRxesaUi2bjFZVYfTv1ycvuzxmYyVZKrGJKFEPK9H8Tv2uZczr+yuqO7YVIvWcRyHNzxSIAxPqH3ZaFh5ZJv6Uj2dy5WqO9K3ssv70tz30ibreaR+V7OZgDvXdbLYhfPiRyRyzY2X84bsefhhTMomhZFIkemHiNN6n/3wmj2Qy7VF1V/TPIdXKs+kVz/LdqmARg/Xkd1XGycUdmsLlutHXK6X8O8zDwgIlkxhKJhItW6UmekN0rN35n1qThSXO6arNws/wQLmcLey0QzjEY2upJdZleCeql/T3qkOxvR+mvYQ208oKqYaqIqV1Vh36+ZzNvWWTkkkMJRMpBd2doO9pIuqJ2E/VsW+Uye7H6wVFbykAna8Lijc89LnKNQwjWLUWfXFfhRln2TNxqwwMt61s90PCi/u6DjVt90NSXsuRaqgq9v7PuYhJX7iq4JJGIkomMZRMpBSkM+yVaLFANla05Uu6tc5647Vjk0M6sfS4okEBUDKJoWQipSLZRY/J3qx6e/5FAr21EjBXtAe8SImaMb62R29MkcckSkTxhpoSDV3lo4cTqXHWm3NBiSTbLrpQF3P0BiUTkTKRKhGluzChN3o5yd6Ue7J8OlkCSPS68c6N7WkU02KOXMvpMJeZ3Q2cDWx29zFxjhtwO3Am0AJ8yd1fDI9dBnw/PPWH7r4obD8BuAeoBh4HrvUU/wgNc4lkV6YFLGP19BN9T+aRYmM3I+HrlnuyKJg5EzP7FLAbuDdBMjkTuJogmZwM3O7uJ5vZYUADUE/Qu10FnODu283seeAa4M8EyWSBu/8+WRxKJiK5lWouJ9X9TN6kezqPJKkVzJyJuz9tZiOTnHIuQaJx4DkzqzGzYcDpwDJ33wZgZsuAaWa2AjjU3Z8L2+8FZgBJk4mI5FZP53KK/bXlgIo8v34tEF3opzFsS9beGKe9CzO70swazKyhubk5q0GLiEhn+U4mOePud7p7vbvXDx06NN/hiIiUtHwnkyZgRNT9urAtWXtdnHYREcmjfCeTJcClFpgI7HT3TcBSYIqZDTKzQcAUYGl4bJeZTQxXgl0K/FfeohcRESDHE/Bm9gDBZPoQM2sEbgSqANx9IcFqrDOBDQRLg78cHttmZjcDL4RPdVNkMh64igNLg3+PJt9FRPKuLMqpmFkz8NcePnwIsCWL4WRTocZWqHFB4cZWqHFB4cZWqHFB4cbW3bg+4u5pTTqXRTLJhJk1pLvOurcVamyFGhcUbmyFGhcUbmyFGhcUbmy5jCvfcyYiIlIClExERCRjSiap3ZnvAJIo1NgKNS4o3NgKNS4o3NgKNS4o3NhyFpfmTEREJGPqmYiISMaUTEREJGNll0zMbISZPWVmr5rZK2Z2bdh+mJktM7M3w++DwnYzswVmtsHM1prZhKjnuiw8/81w/5VMY+tnZs+b2UthbD8I20eZ2Z/DGH5jZn3D9oPC+xvC4yOjnuv6sH29mU3NNLbwOSvNbLWZPVpgcb1jZi+b2RozawjbCuH3WWNm/2lmr5vZa2Z2SoHENTr8WUW+dpnZdQUS2zfDv/11ZvZA+H+iUP7Org3jesXMrgvb8vIzM7O7zWyzma2LastaLGZ2Qvh/akP4WEsZlLuX1RcwDJgQ3h4AvAEcB9wKzAnb5wA/CW+fSXCVvQETgT+H7YcBfwm/DwpvD8owNgP6h7erCPZsmQgsBi4K2xcCXwtvXwUsDG9fBPwmvH0c8BJwEDAKeAuozMLP7lvA/wMeDe8XSlzvAENi2grh97kIuCK83ReoKYS4YmKsBN4DPpLv2AgqgL8NVEf9fX2pEP7OgDHAOuBggsohfwD+IV8/M+BTwARgXS7+5oHnw3MtfOwZKWPK1h9lsX4R1Pb6PLAeGBa2DQPWh7f/Dbg46vz14fGLgX+Lau90XhbiOhh4kWDTsC1An7D9FII6ZRDUMDslvN0nPM+A64Hro56r47wM4qkDlgOfBR4NXyfvcYXP8w5dk0lef5/AQII3RiukuOLEOQVYWQixcWDricPCv5tHgamF8HcGzAR+FXX//wDfyefPDBhJ52SSlVjCY69HtXc6L9FX2Q1zRQu7xeMJegBHeFBIEoJPakeEt7u750qmMVWa2RpgM7CM4FPVDnffF+d1OmIIj+8EBucotp8T/OdpD+8PLpC4INiN87/NbJWZXRm25fv3OQpoBv7DgqHBu8zskAKIK9ZFwAPh7bzG5u5NwE+BvwGbCP5uVlEYf2frgNPMbLCZHUzwaX8EhfX7zFYsae8bFa1sk4mZ9Qd+B1zn7ruij3mQjvOyZtrd97v7OIKewEnAx/IRRzQzOxvY7O6r8h1LApPcfQJwBvB1C7aL7pCn32cfgmGIO9x9PPAhwdBDvuPqEM49TAd+G3ssH7GFY/znEiTi4cAhwLTejCERd38N+Anw38ATwBpgf8w5ef19RstHLGWZTMysiiCR3O/uD4bN71uwZTDh981he3f3XMkKd98BPEXQra8xs0iF5+jX6YghPD4Q2JqD2E4FppvZO8CvCYa6bi+AuICOT7S4+2bgIYIknO/fZyPQ6O5/Du//J0FyyXdc0c4AXnT398P7+Y7tc8Db7t7s7m3AgwR/e4Xyd/Yrdz/B3T8FbCeYb833zyxatmLp0b5RZZdMwlUJvwJec/d/iTq0BIisZriMA/ukdGvPlQxjG2pmNeHtaoK5nNcIksoFCWKLxHwB8GT4iWQJcFG42mUUcCzBhFqPuPv17l7n7iMJhkWedPf/le+4AMzsEDMbELlN8HtYR55/n+7+HrDRzEaHTZOBV/MdV4yLOTDEFYkhn7H9DZhoZgeH/08jP7O8/50BmNnh4fejgPMIFqPk+2cWLSuxeE/3jcpkUqoYv4BJBN2/tQRd1TUE45+DCSaY3yRYqXFYeL4B/5dg7uJloD7quf6JYC+WDcCXsxDbWGB1GNs64Iaw/WiC/wwbCIYkDgrb+4X3N4THj456ru+FMa8njZUY3YjxdA6s5sp7XGEML4VfrwDfC9sL4fc5DmgIf58PE6yYyXtc4XMeQvApfmBUW95jA34AvB7+/d9HsCIr739n4XM+Q5DcXgIm5/NnRvAhYBPQRtALvjybsQD14e/gLeCXxCwkifelcioiIpKxshvmEhGR7FMyERGRjCmZiIhIxpRMREQkY0omIiKSMSUTKXtmdqSZ/drM3gpLsjxuZh81s9MtrJDcjee6ycw+143zu/0aaT7vDDM7Lur+CjOrz/briET0SX2KSOkKL8p6CFjk7heFbZ/gQF2jbnH3G7IYXiZmEBRKfDXPcUiZUM9Eyt1ngDZ3XxhpcPeX3P2Z8G5/O7Anyf1h8sHMbjCzFyzY3+LOqPZ7zOyC8PY7ZvYDM3vRgr0hktZZC6/mv9uCPW1Wm9m5YfuXzOxBM3vCgn0nbo16zOVm9kb4mH83s1+a2ScJam7Nt2C/kmPC02eG571hZqdl6ecnAiiZiIwhqEybyHjgOoI9Mo4mqBUF8Et3P9HdxwDVwNkJHr/FgyKUdwDfThHL9whKgpxEkOTmhyViILia/kLgeOBCCzZ5G05QCn1iGNfHANz9jwQlNGa7+zh3fyt8jj7hc18H3JgiFpFuUTIRSe55d29093aC0jsjw/bPWLC738sEhS8/nuDxkUKiq6Iem8gUYI4FWxCsICgXclR4bLm773T3PQRDVx8hKGj5P+6+zYPCiF2q/2YQi0i3aM5Eyt0rHCg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\n" + }, + "metadata": { + "needs_background": "light" + } + } + ], + "source": [ + "import numpy as np\n", + "\n", + "# Define chain lengths for Rhat evaluation\n", + "warmup = 1000\n", + "chain_lengths = np.arange(start=2000, stop=10000, step=100)\n", + "\n", + "# Compute rhat\n", + "n_parameters = 2\n", + "n_lengths = len(chain_lengths)\n", + "rhats = np.empty(shape=(n_lengths, n_parameters))\n", + "ess = np.empty(shape=(n_chains, n_lengths, n_parameters))\n", + "for length_id, chain_length in enumerate(chain_lengths):\n", + " # Get relevant chain samples\n", + " cleaned_chains = chains[:, warmup:chain_length]\n", + "\n", + " # Compute rhat and ess\n", + " rhats[length_id] = pints.rhat(cleaned_chains)\n", + " for chain_id, chain in enumerate(cleaned_chains):\n", + " ess[chain_id, length_id] = pints.effective_sample_size(chain)\n", + "\n", + "# Plot evolution of rhat\n", + "plt.scatter(x=chain_lengths, y=rhats[:, 0], label='Parameter 1')\n", + "plt.scatter(x=chain_lengths, y=rhats[:, 1], label='Parameter 2')\n", + "plt.xlabel('Chain length')\n", + "plt.ylabel('Rhat')\n", + "plt.legend()\n", + "plt.show()\n", + "\n", + "# Plot evolution of ess\n", + "median_ess = np.median(ess, axis=0)\n", + "plt.scatter(x=chain_lengths, y=median_ess[:, 0], label='Parameter 1')\n", + "plt.scatter(x=chain_lengths, y=median_ess[:, 1], label='Parameter 2')\n", + "plt.xlabel('Chain length')\n", + "plt.ylabel('Median ESS across chains')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "source": [ + "### Reduce the number of chains\n", + "\n", + "The desired ESS is reached after 3000 iterations (plus initial 1000 iterations warmup). The Rhat is well below 1.01, so we may use fewer chains." + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": "
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\n" + }, + "metadata": { + "needs_background": "light" + } + } + ], + "source": [ + "# Get relevant chain lengths\n", + "warmup = 1000\n", + "chain_length = 4000\n", + "cleaned_chains = chains[:, warmup:chain_length]\n", + "\n", + "# Define number of chains to explore\n", + "number_chains = np.arange(start=3, stop=n_chains+1)\n", + "\n", + "# Compute rhat\n", + "n_parameters = 2\n", + "rhats = np.empty(shape=(len(number_chains), n_parameters))\n", + "for _id, n in enumerate(number_chains):\n", + " # Compute rhat for chains\n", + " reduced_chains = cleaned_chains[:n]\n", + " rhats[_id] = pints.rhat(reduced_chains)\n", + " \n", + "# Plot evolution of rhat\n", + "plt.scatter(x=number_chains, y=rhats[:, 0], label='Parameter 1')\n", + "plt.scatter(x=number_chains, y=rhats[:, 1], label='Parameter 2')\n", + "plt.xlabel('Number chains')\n", + "plt.ylabel('Rhat')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "source": [ + "### Conclusion on hyperparameters\n", + "\n", + "We desire marginal $\\hat{R}$s of <1.01 and ESS per chain to be greater >200 for each chain. This suggests the following hyperparameters to satisfy these conditions\n", + "\n", + "1. Number of chains: 3\n", + "2. Number of iterations: 4000 (first 1000 iterations are warmup)\n", + "3. Other hyperparameters: Default" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "source": [ + "## Hyperparameters I: Multivariate $\\hat{R} < 1.01$ and an effective sample size per parameter $>200$ per chain." + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "def _within(chains):\n", + " # Get number of chains and number of parameters\n", + " n_chains, _, n_parameters = chains.shape\n", + "\n", + " # Compute unbiased within-chain covariance estimate\n", + " within_chain_cov = np.empty(shape=(n_chains, n_parameters, n_parameters))\n", + " for chain_id, chain in enumerate(chains):\n", + " within_chain_cov[chain_id] = np.cov(chain, ddof=1, rowvar=False)\n", + "\n", + " # Compute mean-within chain variance\n", + " w = np.mean(within_chain_cov, axis=0)\n", + "\n", + " return w\n", + "\n", + "def _between(chains):\n", + " # Get number of samples\n", + " n = chains.shape[1]\n", + "\n", + " # Compute within-chain mean\n", + " within_chain_means = np.mean(chains, axis=1)\n", + "\n", + " # Compute covariance across chains of within-chain means\n", + " between_chain_cov = np.cov(within_chain_means, ddof=1, rowvar=False)\n", + "\n", + " # Weight variance with number of samples per chain\n", + " b = n * between_chain_cov\n", + "\n", + " return b\n", + "\n", + "def multidimensional_rhat(chains):\n", + " # Get number of samples\n", + " n = chains.shape[1]\n", + "\n", + " # Split chains in half\n", + " n = n // 2 # new length of chains\n", + " if n < 1:\n", + " raise ValueError(\n", + " 'Number of samples per chain after warm-up and chain splitting is '\n", + " '%d. Method needs at least 1 sample per chain.' % n)\n", + " chains = np.vstack([chains[:, :n], chains[:, -n:]])\n", + "\n", + " # Compute mean within-chain covariance\n", + " w = _within(chains)\n", + "\n", + " # Compute mean between-chain convariance\n", + " b = _between(chains)\n", + "\n", + " # Compute Rhat\n", + " rhat = np.sqrt((n - 1.0) / n + np.linalg.det(b) / (np.linalg.det(w) * n))\n", + "\n", + " return rhat" + ] + }, + { + "source": [ + "### Visualise $\\hat{R}$ and ESS over number of iterations" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": "
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\n" 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\n" + }, + "metadata": { + "needs_background": "light" + } + } + ], + "source": [ + "import numpy as np\n", + "\n", + "# Define chain lengths for Rhat evaluation\n", + "warmup = 1000\n", + "chain_lengths = np.arange(start=2000, stop=15000, step=100)\n", + "\n", + "# Compute rhat\n", + "n_parameters = 2\n", + "n_lengths = len(chain_lengths)\n", + "rhats = np.empty(shape=n_lengths)\n", + "ess = np.empty(shape=(n_chains, n_lengths, n_parameters))\n", + "for length_id, chain_length in enumerate(chain_lengths):\n", + " # Get relevant chain samples\n", + " cleaned_chains = chains[:, warmup:chain_length]\n", + "\n", + " # Compute rhat and ess\n", + " rhats[length_id] = multidimensional_rhat(cleaned_chains)\n", + " for chain_id, chain in enumerate(cleaned_chains):\n", + " ess[chain_id, length_id] = pints.effective_sample_size(chain)\n", + "\n", + "# Plot evolution of rhat\n", + "plt.scatter(x=chain_lengths, y=rhats)\n", + "plt.xlabel('Chain length')\n", + "plt.ylabel('Rhat')\n", + "plt.show()\n", + "\n", + "# Plot evolution of ess\n", + "median_ess = np.median(ess, axis=0)\n", + "plt.scatter(x=chain_lengths, y=median_ess[:, 0], label='Parameter 1')\n", + "plt.scatter(x=chain_lengths, y=median_ess[:, 1], label='Parameter 2')\n", + "plt.xlabel('Chain length')\n", + "plt.ylabel('Median ESS across chains')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "source": [ + "### Conclusion on hyperparameters\n", + "\n", + "We desire a multivariate $\\hat{R}$s of <1.01 and ESS per chain to be greater >200 for each chain. This suggests the following hyperparameters to satisfy these conditions\n", + "\n", + "1. Number of chains: 10\n", + "2. Number of iterations: 10000 (first 1000 iterations are warmup)\n", + "3. Other hyperparameters: Default" + ], + "cell_type": "markdown", + "metadata": {} + } + ] +} \ No newline at end of file