diff --git a/change_detection/notebooks/Haario Bardenet ACMC/2dim Gaussian distribution/accept_regardless_of_score.ipynb b/change_detection/notebooks/Haario Bardenet ACMC/2dim Gaussian distribution/accept_regardless_of_score.ipynb new file mode 100644 index 0000000..c361a38 --- /dev/null +++ b/change_detection/notebooks/Haario Bardenet ACMC/2dim Gaussian distribution/accept_regardless_of_score.ipynb @@ -0,0 +1,520 @@ +{ + "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": [ + "# Break Haario Bardenet ACMC on a 2 dimensional Gaussian distribution by accepting proposal with some probability regardless of score\n", + "\n", + "In this notebook, we deliberately break The Haario Bardenet ACMC sampler by causing it to incorrectly accept proposals with a certain probability. The sampler is used on the 1D Gaussian distribution." + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "source": [ + "## Define broken sampler" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "class BrokenHaarioBardenetACMC(pints.HaarioBardenetACMC):\n", + " \"\"\"Broken version of Metropolis Hastings.\n", + "\n", + " At each MH step, with probability given by error_freq, it will always\n", + " accept the proposal.\n", + " \"\"\"\n", + " def __init__(self, x0, sigma0=None):\n", + " super().__init__(x0, sigma0)\n", + " self.error_freq = 0.0\n", + "\n", + " def set_error_freq(self, error_freq):\n", + " self.error_freq = error_freq\n", + "\n", + " def tell(self, fx):\n", + " if self.error_freq == 0.0 or random.random() > self.error_freq:\n", + " # Run MH step correctly\n", + " return super().tell(fx)\n", + " else:\n", + " # Always accept it even if it is bad\n", + " self._acceptance = ((self._iterations * self._acceptance + 1) /\n", + " (self._iterations + 1))\n", + " self._iterations += 1\n", + " self._current = self._proposed\n", + " self._current_log_pdf = fx\n", + " self._proposed = None\n", + " return self._current" + ] + }, + { + "source": [ + "## Changepoint detection with hyperparameters I (marginal Rhat criterion)\n", + "\n", + "We desire marginal $\\hat{R}$s of <1.01 and ESS per chain to be greater >200 for each chain. The corresponing hyperparameters were found in the baseline notebook to be\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": [], + "cell_type": "markdown", + "metadata": {} + }, + { + "source": [ + "### Compute Kullback-Leibler divergence for 15 unbroken and 15 broken posteriors" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#TODO\n", + "def get_klds(num_runs, start_breaking, error_freq):\n", + " \"\"\"Run MCMC multiple times, break at some point, and get the KL divs.\n", + " \n", + " It uses the BrokenMH sampler and the 1D Gaussian distribution.\n", + "\n", + " Parameters\n", + " ----------\n", + " num_runs : int\n", + " Total number of runs\n", + " start_breaking : int\n", + " Which run to break the MCMC algorithm\n", + " error_freq : float\n", + " Error probability per MH step once the algorithm is broken\n", + "\n", + " Returns\n", + " -------\n", + " list\n", + " List of kl divergences from samples to posterior for each run\n", + " \"\"\"\n", + " posterior = NormalDist(np.array([1.0]), np.array([0.1**2]))\n", + " x0 = [np.array([1.0])]\n", + "\n", + " klds = []\n", + " for run in range(num_runs):\n", + " mcmc = pints.MCMCController(posterior, 1, x0, method=BrokenMH)\n", + " mcmc.set_max_iterations(1000)\n", + " if run >= start_breaking:\n", + " for s in mcmc.samplers():\n", + " s.set_error_freq(error_freq)\n", + "\n", + " mcmc.set_log_to_screen(False)\n", + " chains = mcmc.run()\n", + " kld = posterior.kl_divergence(chains[0])\n", + " klds.append(kld)\n", + "\n", + " return klds" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "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", + "n_chains = 3\n", + "initial_parameters = log_prior.sample(n=n_chains)\n", + "n_iterations = 4000\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": 4, + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "param mean std. 2.5% 25% 50% 75% 97.5% rhat ess\n------- ------ ------ ------ ----- ----- ----- ------- ------ ------\nparam 1 -0.03 1.02 -2.08 -0.68 0.00 0.65 2.02 1.00 858.70\nparam 2 -0.00 0.99 -1.87 -0.71 -0.02 0.67 1.93 1.00 960.10\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": "
", + "image/svg+xml": "\n\n\n\n \n \n \n \n 2021-02-09T18:33:30.200827\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 \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \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": "
", + "image/svg+xml": "\n\n\n\n \n \n \n \n 2021-02-09T16:50:44.477111\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", + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZMAAAEGCAYAAACgt3iRAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAAsdklEQVR4nO3de3jU9Zn38fedECQKEgRUSLCga+lapIBRsWJrSwt4QqqC2udR29XLtrYe2qu0uO2jVNtKpV0r7bOyrnVFLx9bulUXD5WlKKvSWg2CiAcUqy2JKOEsJpRA7ueP32/CZDKnZGYyp8/runJl5vv7zcxNEuae7+F3f83dERERyURFvgMQEZHip2QiIiIZUzIREZGMKZmIiEjGlExERCRjffIdQG8YMmSIjxw5Mt9hiIgUlVWrVm1x96HpnFsWyWTkyJE0NDTkOwwRkaJiZn9N91wNc4mISMaUTEREJGNKJiIikrGymDMRkcLV1tZGY2Mje/bsyXcoZatfv37U1dVRVVXV4+dQMhGRvGpsbGTAgAGMHDkSM8t3OGXH3dm6dSuNjY2MGjWqx8+jYa50rV0Mt42BuTXB97WL8x2RSEnYs2cPgwcPViLJEzNj8ODBGfcM1TNJx9rF8Mg10NYa3N+5MbgPMHZW/uISKRFKJPmVjZ+/eibpWH7TgUQS0dYatIuIiJJJWnY2dq9dRIpKZWUl48aNY8yYMcycOZOWlpZ8h8SKFSv44x//mPHzTJs2jZqaGs4+++wsRJWYkkk6BtZ1r11Eikp1dTVr1qxh3bp19O3bl4ULF6b1uH379uUspp4kk3jxzJ49m/vuuy9bYSWkZJKOyTdAVXXntqrqoF1EetXDq5s4dd6TjJrzGKfOe5KHVzdl9flPO+00NmzYwCOPPMLJJ5/M+PHj+dznPsf7778PwNy5c7nkkks49dRTueSSS3jnnXc47bTTmDBhAhMmTOhIACtWrODTn/405557LkcffTRz5szh/vvv56STTuL444/nrbfeAqC5uZnzzz+fE088kRNPPJGVK1fyzjvvsHDhQm677TbGjRvHM888E/e8ePHEmjx5MgMGDMjqzygeTcCnIzLJvvymYGhrYF2QSDT5LtKrHl7dxPUPvkxr234Amna0cv2DLwMwY3xtxs+/b98+fv/73zNt2jQmTZrEc889h5lx1113ceutt/Kzn/0MgFdffZVnn32W6upqWlpaWLZsGf369ePNN9/k4osv7qgF+NJLL/Haa69x2GGHcfTRR3PFFVfw/PPPc/vtt/OLX/yCn//851x77bV885vfZNKkSfztb39j6tSpvPbaa3z1q1+lf//+fPvb3wbgi1/8YtzzYuPJFyWTdI2dpeQhkmfzl67vSCQRrW37mb90fUbJpLW1lXHjxgFBz+Tyyy9n/fr1XHjhhWzatIm9e/d2ugZj+vTpHW/cbW1tfOMb32DNmjVUVlbyxhtvdJx34oknMmzYMACOOeYYpkyZAsDxxx/PU089BcAf/vAHXn311Y7H7Nq1i927d3eJMdl50fHki5KJiBSNd3e0dqs9XZE5k2hXX3013/rWt5g+fTorVqxg7ty5HccOOeSQjtu33XYbRxxxBC+99BLt7e3069ev49hBBx3UcbuioqLjfkVFRcf8Rnt7O88991ynx8WT7LzoePJFcyYiUjSG18T/9J2oPRM7d+6ktjbo7SxatCjpecOGDaOiooL77ruP/fv3Jzw3nilTpvCLX/yi434kqQ0YMIAPPvgg5XmFQslERIrG7Kmjqa6q7NRWXVXJ7Kmjs/5ac+fOZebMmZxwwgkMGTIk4XlXXXUVixYt4hOf+ASvv/56t3sJCxYsoKGhgbFjx3Lcccd1rCQ755xzeOihhzom4BOdl8ppp53GzJkzWb58OXV1dSxdurRb8aXL3D0nT1xI6uvrXZtjiRSm1157jX/8x39M+/yHVzcxf+l63t3RyvCaamZPHZ2VyfdyF+/3YGar3L0+ncdrzkREisqM8bVKHgVIw1wiIpIxJRMREcmYkomIiGRMyURERDKmCfg0aQWJiEhiOeuZmNndZrbZzNYlOG5mtsDMNpjZWjObEHXsCTPbYWaPxjzmfjNbb2brwufv+YbF3RCpB9S0oxXnQD2gbBeYE5H8KNUS9GvWrOGUU07h4x//OGPHjuU3v/lNlqLrKpfDXPcA05IcPwM4Nvy6Ergj6th8oGv5S7gf+BhwPFANXJGNQFNJVg9IRIpfqZagP/jgg7n33nt55ZVXeOKJJ7juuuvYsWNHFqM8IGfJxN2fBrYlOeVc4F4PPAfUmNmw8LHLgQ9iH+Duj4fnO/A80CsbiuSqHpCI9MDaxXDbGJhbE3xfuzirT19KJeg/+tGPcuyxxwIwfPhwDj/8cJqbm7P684rI55xJLbAx6n5j2LYp1QPD4a1LgGuTnHMlQY+Ho446KqNAh9dU0xQnceSiHpCIJLF2MTxyzYFttHduDO5DVqp6l3IJ+ueff569e/dyzDHHZPxziqdYJ+D/FXja3Z9JdIK73wncCUE5lUxebPbU0Z32UIDc1QMSkSSW33QgkUS0tQbtGSSTUi9Bv2nTJi655BIWLVpERUVuBqTymUyagBFR9+vCtqTM7EZgKPCVHMXVRWTVllZzieTZzsbutaeplEvQ79q1i7POOosf/ehHTJw4MelrZCKf15ksAS4NV3VNBHa6e9IhLjO7ApgKXOzu7b0RZMSM8bWsnPNZ3p53FivnfFaJRCQfBiaYJk3UnoFSKEG/d+9evvCFL3DppZdywQUXdCuu7srl0uAHgD8Bo82s0cwuN7OvmtlXw1MeB/4CbAD+Hbgq6rHPAL8FJoePnRoeWggcAfzJzNaYmTZhFyknk2+AqpjhnKrqoD3LSqEE/eLFi3n66ae55557GDduHOPGjcvZPigqQS8iedXdEvSsXRzMkexsDHokk2/QltpZoBL0IlJexs5S8ihAqs0lIiIZUzIRkbwrh+H2QpaNn7+SiYjkVb9+/di6dasSSp64O1u3bk25NDkVzZmISF7V1dXR2NiYszIfklq/fv2oq8tsebWSiYjkVVVVVaery6U4aZhLREQypmQiIiIZUzJJJMdlrkVESonmTOLJcZlrEZFSo55JPMnKXIuISBdKJnF4gnLWidpFRMqdkkkc7xO/QmiidhGRcqdkEscte2fS4n07tbV4X27ZOzNPEYmIFDYlkzgaDv08c9quoLF9CO1uNLYPYU7bFTQc+vl8hyYiUpC0miuOYM/3vSzZO6mjrbqqklu057uISFxKJnFoz3cRke5RMklgxvhaJQ8RkTRpzkRERDKmZNJTKrciItJBw1w9oXIrIiKdqGfSEyq3IiLSSc6SiZndbWabzWxdguNmZgvMbIOZrTWzCVHHnjCzHWb2aMxjRpnZn8PH/MbM+nZ95l6QqKyKyq2ISJnKZc/kHmBakuNnAMeGX1cCd0Qdmw9cEucxPwFuc/d/ALYDl2cl0u4amGB7y0TtIiIlLmfJxN2fBrYlOeVc4F4PPAfUmNmw8LHLgQ+iTzYzAz4L/GfYtAiYke240zL5Bqiq7txWVR20i4iUoXzOmdQCG6PuN4ZtiQwGdrj7vnTON7MrzazBzBqam5szDraTsbPgnAUwcARgwfdzFmjyXUTKVsmu5nL3O4E7Aerr6z3rLzB2lpKHiEgonz2TJmBE1P26sC2RrQRDYX3SPF9ERHpJPpPJEuDScFXXRGCnu29KdLK7O/AUcEHYdBnwX7kPU0REUsnZMJeZPQCcDgwxs0bgRqAKwN0XAo8DZwIbgBbgy1GPfQb4GNA/fOzl7r4U+C7wazP7IbAa+FWu4hcRkfTlLJm4+8Upjjvw9QTHTkvQ/hfgpMyjExGRbNIV8CIikjElExERyZiSiYiIZEzJREREMqZkki3a30REyljJXgHfq7S/iYiUOfVMskH7m4hImVMyyQbtbyIiZU7JJBu0v4mIlDklk2zQ/iYiUuaUTLJB+5uISJnTaq5s0f4mIlLG1DMREZGMKZmIiEjGNMzVQw+vbmL+0vW8u6OV4TXVzJ46mhnjk21hLyJSupRMeuDh1U1c/+DLtLbtB6BpRyvXP/gyQJBQ1i4OLljc2RgsD558g+ZTRKSkKZn0wPyl6zsSSURr237mL13PjMqVKq0iImVHcyY98O6O1sTtKq0iImVIyaQHhtdUJ25XaRURKUNKJj0we+poqqsqO7VVV1Uye+polVYRkbKkZNIDM8bXcst5x1NbU40BtTXV3HLe8cHku0qriEgZyukEvJndDZwNbHb3MXGOG3A7cCbQAnzJ3V8Mj10GfD889Yfuvihsvxj4Z8CBd4H/7e5bcvnviGfG+Nr4S4Ejk+xazSUiZcTcPXdPbvYpYDdwb4JkciZwNUEyORm43d1PNrPDgAagniBprAJOAD4gSCDHufsWM7sVaHH3ucniqK+v94aGhuz9w0REyoCZrXL3+nTOzekwl7s/DWxLcsq5BInG3f05oMbMhgFTgWXuvs3dtwPLgGmAhV+HhL2aQwmSi4iI5FG+rzOpBTZG3W8M2+K2u3ubmX0NeBn4EHgT+HovxSoiIgkU1QS8mVUBXwPGA8OBtcD1Cc690swazKyhubm5F6MUESk/+U4mTcCIqPt1YVui9nEA7v6WB5M9i4FPxntid7/T3evdvX7o0KE5CF1ERCLynUyWAJdaYCKw0903AUuBKWY2yMwGAVPCtibgODOLZIfPA6/lI3ARETkg10uDHwBOB4aYWSNwI1AF4O4LgccJVnJtIFga/OXw2DYzuxl4IXyqm9x9W/icPwCeNrM24K/Al3L5bxARkdRyujS4UGhpsIhI9xXM0mARESkPSiYiIpIxJRMREcmYkomIiGRMyURERDKWVjIxs4PSaRMRkfKUbs/kT2m2STxrF8NtY2BuTfB97eJ8RyQiklVJL1o0syMJii5Wm9l4goq9EFTrPTjHsZWGtYvhkWsO7Au/c2NwH7THiYiUjFRXwE8luMK8DviXqPYPCDaoklSW33QgkUS0tQbtSiYiUiKSJpNwd8NFZna+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/2YQi0i3aM5Eyt0rHCgiGM/fo27vB/qYWT/gXwlqHG00s7kEb/zJHr+f1P/fDDjf3dd3ajQ7OV4cKZ4r01hEukU9Eyl3TwIH2YFNtTCzsSnmFCKJY4sF++IkS0bdsRS4Omr+ZXyK818APh1Wfe0DnB917AOCbalFeoWSiZQ1DyqdfgH4XLg0+BXgFoKd6hI9Zgfw7wRVVZcSvKlnw81AFbA2jOPmZCd7sI/Ljwkq5q4k2L54Z3j418DscCL/mPjPIJI9qhosUsTMrL+77w57Jg8Bd7v7Q/mOS8qPeiYixW1uOGG/DnibYN8UkV6nnomIiGRMPRMREcmYkomIiGRMyURERDKmZCIiIhlTMhERkYz9f7eYcczyYeGSAAAAAElFTkSuQmCC\n" + }, + "metadata": { + "needs_background": "light" + } + }, + { + "output_type": "display_data", + "data": { + "text/plain": "
", + "image/svg+xml": "\n\n\n\n \n \n \n \n 2021-02-09T16:50:44.812842\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", + "image/png": "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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": "
", + "image/svg+xml": "\n\n\n\n \n \n \n \n 2021-02-09T16:50:45.164319\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", + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEICAYAAABI7RO5AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAAdZUlEQVR4nO3df7hVZZ338fcHOAoqCQg5yNFBHdQKEfEomj9ysgH8iWXYWKPk1DBN+auufEafmScZrbmczEfFnksuYxjAyqJSwzKJTKIfQ3pQRBRRKtNDTBAoaqAifJ8/1jq4gb3POQv23uusfT6v69rX2ftea6/zPUfcn3Pf91r3UkRgZmbWVb3yLsDMzIrFwWFmZpk4OMzMLBMHh5mZZeLgMDOzTBwcZmaWSc2CQ9JMSWslLa+wXZKmSVolaZmkMSXbJkt6Ln1MLmnfS9Kdkp6V9IykC2pVv5mZldenhseeBXwVmFNh+5nAiPQxFrgDGCtpEHAd0AIEsETSvIh4CfgXYG1EHCGpFzCoK4UMHjw4hg8fvgc/iplZz7NkyZI/RcSQndtrFhwRsUjS8A52mQjMieQKxMWSBkgaCpwOLIiIDQCSFgATgLuBvweOSo+/DfhTV2oZPnw4ra2tu/ujmJn1SJJ+X649zzmOYcCLJa/b0ray7ZIGpK9vkPSYpO9IOrAulZqZ2XZFmhzvAzQDv4qIMcB/A1+ptLOkKZJaJbWuW7euXjWamTW8PINjNXBwyevmtK1S+3pgE3BP2v4dYAwVRMSdEdESES1DhuwyRGdmZruplpPjnZkHXCbpWyST4xsjYo2k+cC/SxqY7jcOuDYiQtL9JHMgPwXOAJ7OoW4zq6ItW7bQ1tbG66+/nncpPVbfvn1pbm6mqampS/vXLDgk3U3yIT9YUhvJmVJNABExHXgAOAtYRdKTuDTdtkHSDcCj6aGub58oB/4ZuEvSrcC69veYWXG1tbXRv39/hg8fjqS8y+lxIoL169fT1tbGoYce2qX31PKsqos62R7AZypsmwnMLNP+e+C0qhRoubnv8dXcNH8lf3h5MwcN6MfV44/k/GOH5V2W5eT11193aORIEgcccABZ5oLzHKqyHui+x1dz7T1PsnnLVgBWv7yZa+95EsDh0YM5NPKV9fdfpLOqrAHcNH/l9tBot3nLVm6avzKniswsKweH1dUfXt6cqd2sHnr37s3o0aMZOXIkkyZNYtOmTXmXxMKFC/nVr361x8eZMGECAwYM4JxzzqlCVQkHh9XVQQP6ZWo3q4d+/fqxdOlSli9fzl577cX06dO79L633nqrZjXtTnCUq+fqq6/mrrvuqlZZgIPD6uzq8UfSr6n3Dm39mnpz9fgjc6rIiua+x1dz8o0/5dBrfsjJN/6U+x5fXdXjn3rqqaxatYr777+fsWPHcuyxx/KBD3yAP/7xjwBMnTqViy++mJNPPpmLL76Y559/nlNPPZUxY8YwZsyY7R/2Cxcu5H3vex8TJ07ksMMO45prruEb3/gGJ5xwAkcffTS/+c1vAFi3bh0XXHABxx9/PMcffzy//OUvef7555k+fTq33HILo0eP5uc//3nZ/crVs7MzzjiD/v37V/V35Mlxq6v2CXCfVWW7o9YnV7z11lv86Ec/YsKECZxyyiksXrwYScyYMYMvf/nL3HzzzQA8/fTT/OIXv6Bfv35s2rSJBQsW0LdvX5577jkuuuii7WvjPfHEE6xYsYJBgwZx2GGH8clPfpJHHnmE2267jdtvv51bb72VK6+8ks9+9rOccsopvPDCC4wfP54VK1bwqU99iv3224/Pf/7zAHz0ox8tu9/O9dSDg8Pq7vxjhzkobLd0dHLFnvyb2rx5M6NHjwaSHscnPvEJVq5cyUc+8hHWrFnDm2++ucM1Duedd972D+ktW7Zw2WWXsXTpUnr37s2zzz67fb/jjz+eoUOHAnD44Yczbtw4AI4++mgefvhhAH7yk5/w9NNvX8v8yiuv8Nprr+1SY0f7ldZTDw4OMyuMWp1c0T7HUeryyy/nc5/7HOeddx4LFy5k6tSp27ftu+++25/fcsstHHjggTzxxBNs27aNvn37bt+29957b3/eq1ev7a979eq1fT5i27ZtLF68eIf3ldPRfqX11IPnOMysMOp5csXGjRsZNizpxcyePbvD/YYOHUqvXr2466672Lp1a8V9yxk3bhy333779tftAda/f39effXVTvfLg4PDzAqjnidXTJ06lUmTJnHccccxePDgivt9+tOfZvbs2RxzzDE888wzmf/6nzZtGq2trYwaNYp3v/vd28/oOvfcc7n33nu3T45X2q8zp556KpMmTeKhhx6iubmZ+fPnZ6qvHCUrfzS2lpaW8I2czLqnFStW8K53vavL+3vJmtoo999B0pKIaNl5X89xmFmh+OSK/HmoyszMMnFwmJlZJg4OMzPLxMFhZmaZODjMzCwTB4eZ9XiNuqz60qVLOemkk3jPe97DqFGj+Pa3v12V2hwcZtbjNeqy6vvssw9z5szhqaee4sEHH+Sqq67i5Zdf3uPaHBxmVizL5sItI2HqgOTrsrlVPXwjLat+xBFHMGLECAAOOugg3vnOd2a6t3glvgDQzIpj2Vy4/wrYki5quPHF5DXAqAv3+PCNvKz6I488wptvvsnhhx++x78nB4eZFcdD178dGu22bE7a9yA4Gn1Z9TVr1nDxxRcze/ZsevXa84EmB4eZFcfGtmztXdTIy6q/8sornH322XzpS1/ixBNP7PB7dJXnOMysOPZvzta+BxphWfU333yTD37wg1xyySV8+MMfzlRXRxwcZlYcZ3wBmnYakmnql7RXWSMsqz537lwWLVrErFmzGD16NKNHj67KfTy8rLqZ5Srrsuosm5vMaWxsS3oaZ3yhKhPjPZ2XVTezxjXqQgdFzjxUZWZmmTg4zCx3PWHIvDvL+vt3cJhZrvr27cv69esdHjmJCNavX9/p6cClajbHIWkmcA6wNiJGltku4DbgLGAT8PGIeCzdNhn413TXL0bE7LR9ITAUaL8CaFxErK3Vz2Bmtdfc3ExbW1tVlsKw3dO3b1+am7t+SnMtJ8dnAV8F5lTYfiYwIn2MBe4AxkoaBFwHtAABLJE0LyJeSt/3sYjwKVJmDaKpqWmHq7Kt+6vZUFVELAI2dLDLRGBOJBYDAyQNBcYDCyJiQxoWC4AJtarTzMyyyXOOYxjwYsnrtrStUnu7/5K0VNL/SYe7zMysjop2HcfHImK1pP7A94CLqTAUJmkKMAXgkEMOqV+FObjv8dXcNH8lf3h5MwcN6MfV44/k/GOHdf5GM7PdkGePYzVwcMnr5rStUjsR0f71VeCbwAmVDh4Rd0ZES0S0DBkypMqldx/3Pb6aa+95ktUvbyaA1S9v5tp7nuS+x1fnXZqZNag8g2MecIkSJwIbI2INMB8YJ2mgpIHAOGC+pD6SBgNIaiI5Y2t5XsV3FzfNX8nmLTsuqrZ5y1Zumr8yp4rMrNHV8nTcu4HTgcGS2kjOlGoCiIjpwAMkp+KuIjkd99J02wZJNwCPpoe6Pm3blyRAmoDewE+Ar9Wq/qL4w8ubM7Wbme2pmgVHRFzUyfYAPlNh20xg5k5tfwaOq1qBDeKgAf1YXSYkDhpQ+aYuZmZ7wleOF9zV44+kX1PvHdr6NfXm6vFH5lSRmTW6op1VZTtpP3vKZ1WZWb04OBrA+ccOc1CYWd14qMrMzDJxj8OsA7640mxXDg6zCtovrmy/Tqb94krA4WE9moeqzCrwxZVm5bnHUYGHKMwXV5qV5x5HGV7/yaDyRZS+uNJ6OgdHGR6iMPDFlWaVeKiqDA9RGPjiSrNKHBxleP0na+eLK8125aGqMjxEYWZWmXscZXiIwsysMgdHBR6iMDMrz0NVZmaWiYPDzMwycXCYmVkmDg4zM8vEk+NmDcRrrFk9ODjMGoSXgbd68VCVWYPwGmtWLw4OswbhNdasXhwcZg3Cy8BbvTg4zBqE11izevHkuFmD8BprVi8ODrMG4jXWrB48VGVmZpk4OMzMLBMHh5mZZVKz4JA0U9JaScsrbJekaZJWSVomaUzJtsmSnksfk8u8d16l45qZWW3VsscxC5jQwfYzgRHpYwpwB4CkQcB1wFjgBOA6SQPb3yTpQ8BrtSnZzMw6U7PgiIhFwIYOdpkIzInEYmCApKHAeGBBRGyIiJeABaQBJGk/4HPAF2tVt5mZdSzPOY5hwIslr9vStkrtADcANwObOju4pCmSWiW1rlu3rjoVm5lZcSbHJY0GDo+Ie7uyf0TcGREtEdEyZMiQ2hZnZtaD5Bkcq4GDS143p22V2k8CWiQ9D/wCOELSwrpUamZm2+V55fg84DJJ3yKZCN8YEWskzQf+vWRCfBxwbURs4O0J9OHADyLi9PqXbWbV4JtOFVfNgkPS3cDpwGBJbSRnSjUBRMR04AHgLGAVyZzFpem2DZJuAB5ND3V9Ghpm1iB806liU0TkXUPNtbS0RGtra95lmFnq5Bt/yuoy9wkZNqAfv7zm/TlUZOVIWhIRLTu3F2Zy3Mwah286VWwODjOrO990qtgcHGZWd77pVLH5fhxmVndFvOmUzwJ7m4PDzHJRpJtO+SywHXmoysysEzfNX7k9NNpt3rKVm+avzKmifDk4zMw64bPAduTgMDPrhM8C25GDw8ysEz4LbEeeHDcz60QRzwKrJQeHmVkXFOkssFrzUJWZmWXi4DAzs0y6FByS9u5Km5mZNb6u9jj+u4ttZmbW4DqcHJf0F8AwoJ+kYwGlm94B7FPj2szMrBvq7Kyq8cDHSe77/X9L2l8F/neNajIzsz1Q6wUZOwyOiJgNzJZ0QUR8r2rf1czMaqIeCzJ26TqOiPiepLOB9wB9S9qvr0oVZmZWFR0tyFit4OjqWVXTgY8Al5PMc0wC/rIqFZiZWdXUY0HGrp5V9d6IuAR4KSL+DTgJOKJqVZiZWVXUY0HGrgZHe1RtknQQsAUYWrUqzMysKuqxIGNX16r6gaQBwE3AY0AAM6pWhZmZVUU9FmRURGR7Q3LFeN+I2Fi1KmqspaUlWltb8y7DzKxQJC2JiJad27u8Oq6k9wLD298jiYiYU7UKzcysELoUHJLuAg4HlgLt53kF4OAwM+thutrjaAHeHVnHtczMrOF09ayq5cBf1LIQMzMrhs4WObyfZEiqP/C0pEeAN9q3R8R5tS3PzMy6m86Gqr5SlyrMzKwwOhyqioiflXsAPydZMbciSTMlrZW0vMJ2SZomaZWkZZLGlGybLOm59DG5pP1BSU9IekrSdEm9yx3bzMxqp8PgkPQOSddK+qqkcemH/WXAb4ELOzn2LGBCB9vPBEakjynAHen3HARcB4wFTgCukzQwfc+FEXEMMBIYQrJmlpmZ1VFnk+N3AUcCTwKfBB4m+bA+PyImdvTGiFgEbOhgl4nAnEgsBgZIGkpyD5AFEbEhIl4CFpAGUES8kr63D7AXyfyLmZnVUWdzHIdFxNEAkmYAa4BDIuL1KnzvYcCLJa/b0rZK7aR1zCfpifwI+G6lg0uaQtKT4ZBDDqlCuWZmBp33OLa0P4mIrUBblUJjt0XEeJIFFvcG3t/BfndGREtEtAwZMqRu9ZmZNbrOguMYSa+kj1eBUe3PJb3SyXs7sxo4uOR1c9pWqX27NLy+TzLcZWZmddTZWVW9I+Id6aN/RPQpef6OPfze84BL0gn3E4GNEbEGmA+MkzQwnRQfB8yXtF86B4KkPsDZwDN7WIOZmWXU5UUOs5J0N3A6MFhSG8mZUk0AETEdeAA4C1gFbAIuTbdtkHQD8Gh6qOvTtgOBeenqvL1IJuqn16p+MzMrL/Oy6kXkZdXNzLKrtKx6V9eqMjMzAxwcZmaWkYPDzMwycXCYmVkmDg4zM8vEwWFmZpk4OMzMLBMHh5mZZeLgMDOzTBwcZmaWiYPDzMwycXCYmVkmDg4zM8vEwWFmZpk4OMzMLBMHh5mZZeLgMDOzTBwcZmaWiYPDzMwycXCYmVkmDg4zM8vEwWFmZpk4OMzMLBMHh5mZZeLgMDOzTBwcZmaWiYPDzMwycXCYmVkmDg4zM8ukZsEhaaaktZKWV9guSdMkrZK0TNKYkm2TJT2XPianbftI+qGkZyQ9JenGWtVuZmaV1bLHMQuY0MH2M4ER6WMKcAeApEHAdcBY4ATgOkkD0/d8JSKOAo4FTpZ0Zm1KNzOzSmoWHBGxCNjQwS4TgTmRWAwMkDQUGA8siIgNEfESsACYEBGbIuLh9NhvAo8BzbWq38zMystzjmMY8GLJ67a0rVL7dpIGAOcCD9W2RDMz21nhJscl9QHuBqZFxG872G+KpFZJrevWratfgWZmDS7P4FgNHFzyujltq9Te7k7guYi4taODR8SdEdESES1DhgypTsVmZpZrcMwDLknPrjoR2BgRa4D5wDhJA9NJ8XFpG5K+COwPXJVTzWZmPV6fWh1Y0t3A6cBgSW0kZ0o1AUTEdOAB4CxgFbAJuDTdtkHSDcCj6aGuT9uagX8BngEekwTw1YiYUaufwczMdqWIyLuGmmtpaYnW1ta8yzAzKxRJSyKiZef2wk2Om5lZvhwcZmaWiYPDzMwycXCYmVkmDg4zM8vEwWFmZpk4OMzMLBMHh5mZZeLgMDOzTBwcZmaWiYPDzMwycXCYmVkmDg4zM8vEwWFmZpk4OMzMLBMHh5mZZeLgMDOzTBwcZo1k2Vy4ZSRMHZB8XTY374qsAdXsnuNmVmfL5sL9V8CWzcnrjS8mrwFGXZhfXdZw3OMwaxQPXf92aLTbsjlp747cOyos9zjMGsXGtmzteXLvqNDc4zBrFPs3Z2vPU9F6R7YDB0cjcJffAM74AjT127GtqV/S3t0UqXdku3BwFF17l3/ji0C83eV3ePQ8oy6Ec6fB/gcDSr6eO617Dv0UqXfUrkh/oNW4Vs9xFF1HXf7u+IFRNMvmJr/LjW3Jh9oZX+jev9dRF3bv+tqd8YUd5zig+/aOoFhzMnWo1T2OonOXv3bcm6udIvWOoFhzMnWo1T2Ootu/Of1gK9Nue8a9udoqSu8IivUHWh1qdY+j6Io0IdquKGPFRfqwsNoq0pxMHWp1cBRd0br8RRr+KdKHhdVWkf5Aq0OtHqpqBEXq8hdp+KdoE7hWO+3/NotwokQdaq1ZcEiaCZwDrI2IkWW2C7gNOAvYBHw8Ih5Lt00G/jXd9YsRMTtt/xJwCTAwIvarVe1WQ0Ua/inSh4XVXpH+QKtxrbXsccwCvgrMqbD9TGBE+hgL3AGMlTQIuA5oAQJYImleRLwE3J8e87ka1m21VLTJ/CJ9WJjVSc3mOCJiEbChg10mAnMisRgYIGkoMB5YEBEb0rBYAExIj7k4ItbUqmargyKNFZtZWXlOjg8DSv/0bEvbKrVbIyjaZL6Z7aJhJ8clTQGmABxyyCE5V2M78PCPWaHl2eNYDRxc8ro5bavUnklE3BkRLRHRMmTIkD0q1MzM3pZncMwDLlHiRGBjOn8xHxgnaaCkgcC4tM3MzLqBWp6OezdwOjBYUhvJmVJNABExHXiA5FTcVSSn416abtsg6Qbg0fRQ10fEhvSYXwY+CuyTHnNGREyt1c9gZma7UkTkXUPNtbS0RGtra95lmJkViqQlEdGyc7uXHDEzs0wcHGZmlomDw8zMMnFwVFKUpb/NzOqsYS8A3CNFuk2kmVmducdRTpFuE2lmVmcOjnKKtPS3mVmdOTjK8Z3fzMwqcnCU46W/zcwqcnCU46W/zcwq8llVlXjpbzOzstzjMDOzTBwcZmaWiYPDzMwycXCYmVkmDg4zM8ukR9zISdI64Pe7+fbBwJ+qWE4tFalWKFa9RaoVilVvkWqFYtW7p7X+ZUQM2bmxRwTHnpDUWu4OWN1RkWqFYtVbpFqhWPUWqVYoVr21qtVDVWZmlomDw8zMMnFwdO7OvAvIoEi1QrHqLVKtUKx6i1QrFKvemtTqOQ4zM8vEPQ4zM8vEwVGBpL6SHpH0hKSnJP1b3jV1RlJvSY9L+kHetXRG0vOSnpS0VFJr3vV0RNIASd+V9IykFZJOyrumciQdmf4+2x+vSLoq77o6Iumz6f9fyyXdLalv3jVVIunKtM6nuuPvVdJMSWslLS9pGyRpgaTn0q8Dq/G9HByVvQG8PyKOAUYDEySdmG9JnboSWJF3ERn8dUSMLsCpjbcBD0bEUcAxdNPfcUSsTH+fo4HjgE3AvflWVZmkYcAVQEtEjAR6A3+bb1XlSRoJ/ANwAsm/gXMk/VW+Ve1iFjBhp7ZrgIciYgTwUPp6jzk4KojEa+nLpvTRbSeEJDUDZwMz8q6lkUjaHzgN+E+AiHgzIl7OtaiuOQP4TUTs7oWv9dIH6CepD7AP8Iec66nkXcCvI2JTRLwF/Az4UM417SAiFgEbdmqeCMxOn88Gzq/G93JwdCAd+lkKrAUWRMSvcy6pI7cC/wvYlnMdXRXAjyUtkTQl72I6cCiwDvivdBhwhqR98y6qC/4WuDvvIjoSEauBrwAvAGuAjRHx43yrqmg5cKqkAyTtA5wFHJxzTV1xYESsSZ//D3BgNQ7q4OhARGxNu/3NwAlpd7XbkXQOsDYiluRdSwanRMQY4EzgM5JOy7ugCvoAY4A7IuJY4M9UqbtfK5L2As4DvpN3LR1Jx9snkoTzQcC+kv4u36rKi4gVwH8APwYeBJYCW/OsKatITqGtyqiJg6ML0qGJh9l1/LC7OBk4T9LzwLeA90v6er4ldSz9a5OIWEsyDn9CvhVV1Aa0lfQ2v0sSJN3ZmcBjEfHHvAvpxAeA30XEuojYAtwDvDfnmiqKiP+MiOMi4jTgJeDZvGvqgj9KGgqQfl1bjYM6OCqQNETSgPR5P+BvgGdyLaqCiLg2IpojYjjJEMVPI6Jb/uUGIGlfSf3bnwPjSIYCup2I+B/gRUlHpk1nAE/nWFJXXEQ3H6ZKvQCcKGkfSSL53XbLEw8AJL0z/XoIyfzGN/OtqEvmAZPT55OB71fjoL7neGVDgdmSepME7NyI6PanuRbEgcC9yWcFfYBvRsSD+ZbUocuBb6RDQL8FLs25norSIP4b4B/zrqUzEfFrSd8FHgPeAh6ne1+V/T1JBwBbgM90t5MkJN0NnA4MltQGXAfcCMyV9AmSFcIvrMr38pXjZmaWhYeqzMwsEweHmZll4uAwM7NMHBxmZpaJg8PMzDJxcFiPISkk3Vzy+vOSplbp2LMkfbgax+rge0yV9PmM73mg/Xoks2pxcFhP8gbwIUmD8y6kVLrAX01ExFnd7XoDKz4Hh/Ukb5FcYPbZnTfs3GOQ9Fr69XRJP5P0fUm/lXSjpI+l92p5UtLhJYf5gKRWSc+m64e1L5R5k6RHJS2T9I8lx/25pHmUuRJd0gRJj6X3g3moZNO7JS1Ma7miZP/70gUjnypdNFLJfU8GSxqe3kvka+k+P05XREDSFZKeTuv71m7+bq0H8ZXj1tP8P2CZpC9neM8xJMtqbyC5cnxGRJwg6UqSq8qvSvcbTrLm1uHAw+n9Gi4hWfX1eEl7A7+U1L4C7BhgZET8rvSbSRoCfA04LSJ+J2lQyeajgL8G+gMrJd2RrvP09xGxIQ2DRyV9LyLW7/RzjAAuioh/kDQXuAD4OsmijYdGxBse1rKucI/DepSIeAWYQ3IDoa56NCLWRMQbwG9IVkgFeJIkLNrNjYhtEfEcScAcRbIO1yXp8vy/Bg4g+QAHeGTn0EidCCxq3xYRpfdY+GFEvBERfyJZsK59mewrJD0BLCZZ7nsEu/pdRCxNny8pqX0ZyZIqf0fSKzPrkIPDeqJbgU8ApffVeIv0/wdJvYC9Sra9UfJ8W8nrbezYa995/Z4ABFzefme+iDi05J4Tf96N2ktr2Qr0kXQ6yUqzJ6V3rHwcKHcL1l3emz4/m6QnNoakt+KRCOuQg8N6nPQv+Lkk4dHueZLbrUJyL4um3Tj0JEm90nmPw4CVwHzgnyQ1AUg6ogs3gloMnCbp0PQ9gzrZf3/gpYjYJOkokh5Ll6QheXBEPAz8c3qs/br6fuuZ/JeF9VQ3A5eVvP4a8P10uOdBdq838ALwCPAO4FMR8bqkGSRDQo+lS4evo5Pbd0bEunSC+570g30tyYq3lTwIfErSCpKwWpyh5t7A15XcIlfANJ+FZZ3x6rhmZpaJh6rMzCwTB4eZmWXi4DAzs0wcHGZmlomDw8zMMnFwmJlZJg4OMzPLxMFhZmaZ/H8D59HgLOQWoQAAAABJRU5ErkJggg==\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": "
", + "image/svg+xml": "\n\n\n\n \n \n \n \n 2021-02-09T16:51:08.873001\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", + "image/png": "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\n" + }, + "metadata": { + "needs_background": "light" + } + }, + { + "output_type": "display_data", + "data": { + "text/plain": "
", + "image/svg+xml": "\n\n\n\n \n \n \n \n 2021-02-09T16:51:09.123447\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", + "image/png": "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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