{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "755f9c39", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iminuit version: 2.16.0\n" ] } ], "source": [ "# Example of Bayesian parameter estimation using iminuit to find\n", "# posterior mode (MAP) estimators and MCMC for intervals.\n", "# pdf is a mixture of Gaussian (signal) and exponential (background),\n", "# truncated in [xMin,xMax].\n", "# G. Cowan / RHUL Physics / December 2022\n", "\n", "import numpy as np\n", "import scipy.stats as stats\n", "from scipy.stats import truncexpon\n", "from scipy.stats import truncnorm\n", "from scipy.stats import chi2\n", "from scipy.special import logsumexp\n", "from scipy.signal import correlate\n", "import iminuit\n", "from iminuit import Minuit\n", "import matplotlib.pyplot as plt\n", "plt.rcParams[\"font.size\"] = 12\n", "print(\"iminuit version:\", iminuit.__version__) # need 2.x" ] }, { "cell_type": "code", "execution_count": 2, "id": "e8d6985c", "metadata": {}, "outputs": [], "source": [ "# Define pdf\n", "np.random.seed(seed=1234567) # fix random seed\n", "theta = 0.2 # fraction of signal\n", "mu = 10. # mean of Gaussian\n", "sigma = 2. # std. dev. of Gaussian\n", "xi = 5. # mean of exponential\n", "xMin = 0.\n", "xMax = 20.\n", "\n", "def f(x, par):\n", " theta = par[0]\n", " mu = par[1]\n", " sigma = par[2]\n", " xi = par[3]\n", " fs = stats.truncnorm.pdf(x, a=(xMin-mu)/sigma, b=(xMax-mu)/sigma, loc=mu, scale=sigma)\n", " fb = stats.truncexpon.pdf(x, b=(xMax-xMin)/xi, loc=xMin, scale=xi)\n", " return theta*fs + (1-theta)*fb" ] }, { "cell_type": "code", "execution_count": 3, "id": "ddba61c0", "metadata": {}, "outputs": [], "source": [ "# Generate data\n", "numVal = 400\n", "xData = np.empty([numVal])\n", "for i in range (numVal):\n", " r = np.random.uniform();\n", " if r < theta:\n", " xData[i] = stats.truncnorm.rvs(a=(xMin-mu)/sigma, b=(xMax-mu)/sigma, loc=mu, scale=sigma)\n", " else:\n", " xData[i] = stats.truncexpon.rvs(b=(xMax-xMin)/xi, loc=xMin, scale=xi)" ] }, { "cell_type": "code", "execution_count": 4, "id": "b5098d7d", "metadata": {}, "outputs": [], "source": [ "# Specify parameters, initial values, limits, etc.\n", "parin = np.array([theta, mu, sigma, xi]) # initial values (here = true values)\n", "parname = [r'theta', r'mu', r'sigma', r'xi']\n", "parname_latex = [r'$\\theta$', r'$\\mu$', r'$\\sigma$', r'$\\xi$']\n", "parstep = np.array([0.1, 1., 1., 1.]) # initial step sizes for iminuit\n", "parfix = [False, False, False, False] # change these to fix/free parameters\n", "numFreePar = sum(1 for i in parfix if parfix[i] == False)\n", "parlim = [(0.,1.), (None, None), (0., None), (0., None)] # set limits" ] }, { "cell_type": "code", "execution_count": 5, "id": "0fe51134", "metadata": {}, "outputs": [], "source": [ "# Negative log-likelihood\n", "def negLogL(par):\n", " fx = f(xData, par)\n", " return -np.sum(np.log(fx))\n", "\n", "# Prior pdf\n", "def prior(par):\n", " theta = par[0]\n", " mu = par[1]\n", " sigma = par[2]\n", " xi = par[3]\n", " pi_theta = 1. if theta >= 0. and theta <= 1. else 0.\n", " pi_mu = 1. if mu >= 0. else 0.\n", " pi_sigma = 1. if sigma > 0. else 0.\n", " pi_xi = 1. if xi > 0. else 0.\n", " piArr = np.array([pi_theta, pi_mu, pi_sigma, pi_xi])\n", " pi = np.product(piArr[np.array(parfix) == False]) # exclude fixed par\n", " return pi\n", " \n", "# Negative log of posterior pdf\n", "def negLogPost(par):\n", " return negLogL(par) - np.log(prior(par))" ] }, { "cell_type": "code", "execution_count": 6, "id": "8d71330a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "par index, name, MAP estimate, standard deviation:\n", " 0 theta = 0.197936 +/- 0.081565\n", " 1 mu = 9.309286 +/- 0.785313\n", " 2 sigma = 2.347174 +/- 0.719711\n", " 3 xi = 5.054644 +/- 0.755291\n" ] } ], "source": [ "# Find maximum of posterior and its covariance\n", "m = Minuit(negLogPost, parin, name=parname)\n", "m.errors = parstep\n", "m.fixed = parfix\n", "m.limits = parlim\n", "m.migrad() # minimize -logPost\n", "MAP = m.values # posterior mode\n", "sigmaMAP = m.errors # standard deviations\n", "cov = m.covariance # covariance matrix\n", "rho = m.covariance.correlation() # correlation coeffs.\n", " \n", "print(r\"par index, name, MAP estimate, standard deviation:\")\n", "for i in range(m.npar):\n", " if not m.fixed[i]:\n", " print(\"{:4d}\".format(i), \"{:<10s}\".format(m.parameters[i]), \" = \",\n", " \"{:.6f}\".format(MAP[i]), \" +/- \", \"{:.6f}\".format(sigmaMAP[i]))" ] }, { "cell_type": "code", "execution_count": 7, "id": "41126c03", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plot fitted pdf (MAP estimators)\n", "yMin = 0.\n", "yMax = f(0., MAP)*1.1\n", "fig = plt.figure(figsize=(8,6))\n", "xCurve = np.linspace(xMin, xMax, 100)\n", "yCurve = f(xCurve, MAP)\n", "plt.plot(xCurve, yCurve, color='dodgerblue')\n", "plt.xlabel(r'$x$')\n", "plt.ylabel(r'$f(x)$')\n", "y_fitval = 0.8\n", "delta_y_fitval = 0.08\n", "plt.figtext(0.6, y_fitval, 'MAP Estimators')\n", "for i in range(len(parin)):\n", " y_fitval -= delta_y_fitval\n", " if not parfix[i]:\n", " plt.figtext(0.6, y_fitval, parname_latex[i] + ' = ' + f'{MAP[i]:.4f}' + r'$\\pm$' + f'{sigmaMAP[i]:.4f}')\n", "\n", "# Add data as tick marks\n", "tick_height = 0.05*(yMax - yMin)\n", "xvals = [xData, xData]\n", "yvals = [np.zeros_like(xData), tick_height * np.ones_like(xData)]\n", "plt.plot(xvals, yvals, color='black', linewidth=1)\n", "plt.xlim(xMin, xMax)\n", "plt.ylim(yMin, yMax)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 8, "id": "2898ad75", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "posterior covariance = \n", "┌───────┬─────────────────────────────────┐\n", "│ │ theta mu sigma xi │\n", "├───────┼─────────────────────────────────┤\n", "│ theta │ 0.00675 -0.0236 0.0394 -0.0416 │\n", "│ mu │ -0.0236 0.617 -0.229 0.0273 │\n", "│ sigma │ 0.0394 -0.229 0.52 -0.249 │\n", "│ xi │ -0.0416 0.0273 -0.249 0.571 │\n", "└───────┴─────────────────────────────────┘\n", "proposal covariance = \n", "┌───────┬─────────────────────────────────┐\n", "│ │ theta mu sigma xi │\n", "├───────┼─────────────────────────────────┤\n", "│ theta │ 0.00956 -0.0334 0.0558 -0.0589 │\n", "│ mu │ -0.0334 0.873 -0.324 0.0387 │\n", "│ sigma │ 0.0558 -0.324 0.737 -0.352 │\n", "│ xi │ -0.0589 0.0387 -0.352 0.808 │\n", "└───────┴─────────────────────────────────┘\n" ] } ], "source": [ "# Set up MCMC\n", "# see J. Rosenthal, http://probability.ca/jeff/ftpdir/galinart.pdf\n", "scale_prop = 2.38**2/numFreePar # or adjust to minimize acf\n", "cov_prop = scale_prop*cov\n", "print('posterior covariance = ')\n", "print(cov)\n", "print('proposal covariance = ')\n", "print(cov_prop)" ] }, { "cell_type": "code", "execution_count": 9, "id": "e2ad849a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Start MCMC iterations: ...............................................................................................\n", " MCMC acceptance fraction = 0.2447\n" ] } ], "source": [ "# Iterate with Metropolis-Hastings algorithm\n", "chain = [np.array(MAP)] # start point is MAP estimate\n", "numIterate = 10000\n", "numBurn = 100\n", "numAccept = 0\n", "print(\"Start MCMC iterations: \", end=\"\")\n", "while len(chain) < numIterate:\n", " par = chain[-1]\n", " log_post = -negLogL(par) + np.log(prior(par))\n", " par_prop = np.random.multivariate_normal(par, cov_prop)\n", " if prior(par_prop) <= 0:\n", " chain.append(chain[-1]) # never accept if prob<=0.\n", " else:\n", " log_post_prop = -negLogL(par_prop) + np.log(prior(par_prop))\n", " alpha = np.exp(log_post_prop - log_post)\n", " u = np.random.uniform(0, 1)\n", " if u <= alpha:\n", " chain.append(par_prop)\n", " numAccept += 1\n", " else:\n", " chain.append(chain[-1])\n", " if len(chain)%(numIterate/100) == 0:\n", " print(\".\", end=\"\", flush=True)\n", "chain = np.array(chain)\n", "print('\\n MCMC acceptance fraction = ', numAccept/numIterate)" ] }, { "cell_type": "code", "execution_count": 10, "id": "c3db028b", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Show trace plots\n", "fig, axes = plt.subplots(sharex=True, nrows=4, figsize=(8,6))\n", "plt.xlim(0, numIterate)\n", "for i, (ax, label) in enumerate(zip(axes, parname_latex)):\n", " ax.plot(chain[:, i], color=\"dodgerblue\")\n", " ax.axvline(numBurn, color=\"orange\")\n", " ax.set_ylabel(label)\n", "axes[-1].set_xlabel(\"iteration number\")\n", "fig.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 11, "id": "93f7bc30", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Show marginal distributions\n", "fig, axes = plt.subplots(nrows=4, figsize=(8,6))\n", "for i, (ax, label, sim) in enumerate(zip(axes, parname_latex, np.array(MAP))):\n", " ax.hist(chain[numBurn:, i], bins=50, density=True, color=\"dodgerblue\")\n", " ax.set(xlabel=label, ylabel=\"pdf\")\n", " ax.axvline(sim, color=\"orange\")\n", "fig.tight_layout(pad=0.3)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 12, "id": "7d1d5c15", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Find autocorrelation and plot\n", "var = chain[numBurn:,].var(axis=0)\n", "x = chain[numBurn:,] - chain[numBurn:,].mean(axis=0)\n", "max_lag = 200\n", "N = len(x[:,0])\n", "acf = np.zeros(shape=[max_lag, len(chain[0])])\n", "for i in range(len(chain[0])):\n", " if var[i] > 0:\n", " acf[:,i] = np.correlate(x[:,i], x[:,i], mode='full')[N-1:N-1+max_lag]\n", " acf[:,i] /= (var[i]*N)\n", "\n", "fig, axes = plt.subplots(sharex=True, nrows=4, figsize=(8,6))\n", "for i, (ax, label) in enumerate(zip(axes, parname_latex)):\n", " ax.plot(acf[:,i], color=\"dodgerblue\")\n", " ax.set_ylabel('ACF[' + label + ']')\n", " ax.set_yticks([0., 0.5, 1.])\n", " ax.grid()\n", "axes[-1].set_xlabel(\"lag\")\n", "plt.xlim(0, max_lag)\n", "plt.subplots_adjust(left=0.15, bottom=0.1, right=0.9, top=0.9, wspace=0.4, hspace=0.4)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 13, "id": "3de762b6", "metadata": {}, "outputs": [], "source": [ "# Functions for computing intervals\n", "# input: values = numpy array with MCMC chain, e.g., chain[:,0]\n", "# CL = credibility level, e.g., 0.683\n", "\n", "# Central credible interval\n", "def cc_interval(values, CL):\n", " alpha = np.array([(1.-CL)/2., (1.+CL)/2.])\n", " return np.quantile(values, alpha)\n", "\n", "# Highest Probability Density (HPD) interval from MCMC chain\n", "def HPD_interval(values, CL):\n", " sorted = np.sort(np.copy(values))\n", " nPoints = len(values)\n", " nCovered = np.floor(0.683 * nPoints).astype(int)\n", " intWidth = sorted[nCovered:] - sorted[:nPoints-nCovered]\n", " minWidth = np.argmin(intWidth)\n", " hpdLo = sorted[minWidth]\n", " hpdHi = sorted[minWidth+nCovered]\n", " return np.array([hpdLo, hpdHi])" ] }, { "cell_type": "code", "execution_count": null, "id": "7134b40e", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.8" } }, "nbformat": 4, "nbformat_minor": 5 }