{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Example of maximum-likelihood fit with iminuit version 2.\n", "# pdf is a mixture of Gaussian (signal) and exponential (background),\n", "# truncated in [xMin,xMax].\n", "# G. Cowan / RHUL Physics / December 2021\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", "import iminuit\n", "from iminuit import Minuit\n", "import matplotlib.pyplot as plt\n", "from matplotlib import container\n", "plt.rcParams[\"font.size\"] = 14" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# define pdf and generate data\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." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "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": 4, "metadata": {}, "outputs": [], "source": [ "numVal = 200\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": 5, "metadata": {}, "outputs": [], "source": [ "# Function to be minimized is negative log-likelihood\n", "def negLogL(par):\n", " pdf = f(xData, par)\n", " return -np.sum(np.log(pdf))" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# Initialize Minuit and set up fit:\n", "par = np.array([theta, mu, sigma, xi]) # initial values (here = true values)\n", "parname = ['theta', 'mu', 'sigma', 'xi']\n", "parstep = np.array([0.1, 1., 1., 1.]) # initial setp sizes\n", "parfix = [False, True, True, False] # change these to fix/free parameters\n", "parlim = [(0.,1), (None, None), (0., None), (0., None)] # set limits\n", "m = Minuit(negLogL, par, name=parname)\n", "m.errors = parstep\n", "m.fixed = parfix\n", "m.limits = parlim\n", "m.errordef = 0.5 # errors from lnL = lnLmax - 0.5" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "par index, name, estimate, standard deviation:\n", " 0 theta = 0.204551 +/- 0.052736\n", " 3 xi = 5.107878 +/- 0.644563\n", "\n", "free par indices, covariance, correlation coeff.:\n", "0 0 0.002797 1.000000\n", "0 3 -0.018131 -0.531774\n", "3 0 -0.018131 -0.531774\n", "3 3 0.415591 1.000000\n" ] } ], "source": [ "# Do the fit, get errors, extract results\n", "m.migrad() # minimize -logL\n", "MLE = m.values # max-likelihood estimates\n", "sigmaMLE = m.errors # standard deviations\n", "cov = m.covariance # covariance matrix\n", "rho = m.covariance.correlation() # correlation coeffs.\n", " \n", "print(r\"par index, name, 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(MLE[i]), \" +/- \", \"{:.6f}\".format(sigmaMLE[i]))\n", "\n", "print()\n", "print(r\"free par indices, covariance, correlation coeff.:\")\n", "for i in range(m.npar):\n", " if not(m.fixed[i]):\n", " for j in range(m.npar):\n", " if not(m.fixed[j]):\n", " print(i, j, \"{:.6f}\".format(cov[i,j]), \"{:.6f}\".format(rho[i,j]))" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot fitted pdf\n", "yMin = 0.\n", "yMax = f(0., MLE)*1.1\n", "fig = plt.figure(figsize=(8,6))\n", "xCurve = np.linspace(xMin, xMax, 100)\n", "yCurve = f(xCurve, MLE)\n", "plt.plot(xCurve, yCurve, color='dodgerblue')\n", "\n", "# Plot 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.xlabel(r'$x$')\n", "plt.ylabel(r'$f(x; \\theta)$')\n", "plt.figtext(0.6, 0.8, r'$\\hat{\\theta} = $' + f'{MLE[0]:.4f}' +\n", " r'$\\pm$' + f'{sigmaMLE[0]:.4f}')\n", "plt.figtext(0.6, 0.72, r'$\\hat{\\xi} = $' + f'{MLE[3]:.4f}' +\n", " r'$\\pm$' + f'{sigmaMLE[3]:.4f}')\n", "plt.xlim(xMin, xMax)\n", "plt.ylim(yMin, yMax)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Make scan of lnL (for theta, if free)\n", "if not(m.fixed['theta']):\n", " plt.figure()\n", " m.draw_mnprofile('theta')\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CL = 0.3934693402873665\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Make a contour plot of lnL = lnLmax - 1/2 (here for theta and xi).\n", "# The tangents to this contour give the standard deviations.\n", "CL = stats.chi2.cdf(1.,2) # Q_alpha = 1, npar = 2\n", "print('CL = ', CL)\n", "if not(m.fixed['theta'] | m.fixed['xi']):\n", " fig, ax = plt.subplots(1,1)\n", " con = m.mncontour('theta', 'xi', cl=CL, size=200)\n", " con = np.vstack([con, con[0]]) # close contour\n", " plt.plot(MLE[0], MLE[3], marker='o', linestyle='None', color='black', label=r'$(\\hat{\\theta}, \\hat{\\xi})$')\n", " plt.plot(con[:,0], con[:,1], color='black', linewidth=1)\n", " plt.xlabel(r'$\\theta$', labelpad=5)\n", " plt.ylabel(r'$\\xi$', labelpad=5)\n", " handles, labels = ax.get_legend_handles_labels()\n", " plt.legend(handles, labels, loc='upper right', fontsize=14, frameon=False)\n", " plt.figtext(0.4, 0.93, r'$\\ln L = \\ln L_{\\rm max} - 1/2$')\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Confidence region from lnL = lnLmax - Q/2 (here for theta and xi)\n", "# where Q is the chi2 quantile of CL = 1-alpha = 0.683 and 0.95 for 2 dof.\n", "if not(m.fixed['theta'] | m.fixed['xi']):\n", " fig, ax = plt.subplots(1,1)\n", " m.draw_mncontour('theta', 'xi', cl=[0.683, 0.95], size=200);\n", " plt.plot(MLE[0], MLE[3], marker='o', linestyle='None', color='black', label=r'$(\\hat{\\theta}, \\hat{\\xi})$')\n", " plt.xlabel(r'$\\theta$', labelpad=10)\n", " plt.ylabel(r'$\\xi$', labelpad=10)\n", " plt.subplots_adjust(left=0.2, right=0.9, top=0.9, bottom=0.2)\n", " handles, labels = ax.get_legend_handles_labels()\n", " plt.legend(handles, labels, loc='upper right', fontsize=14, frameon=False)\n", " plt.figtext(0.3, 0.93, r'$\\ln L = \\ln L_{\\rm max} - \\frac{1}{2} F^{-1}_{\\chi^2}(1-\\alpha;n)$')\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.12" } }, "nbformat": 4, "nbformat_minor": 4 }