{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "4b20235e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iminuit version: 2.11.2\n" ] } ], "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\n", "print(\"iminuit version:\", iminuit.__version__) # need 2.x" ] }, { "cell_type": "code", "execution_count": 2, "id": "de8ff1c6", "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.\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, \n", " 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\n", " \n", "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)\n", "\n", "# 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": 3, "id": "8f9d03ee", "metadata": {}, "outputs": [], "source": [ "# Initialize Minuit and set up fit:\n", "parin = 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, parin, 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": 4, "id": "b99ab1e5", "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": 5, "id": "45d93ce4", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "CL = 0.3934693402873665\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "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$' + f'{sigmaMLE[3]:.4f}')\n", "plt.xlim(xMin, xMax)\n", "plt.ylim(yMin, yMax)\n", "plt.show()\n", "\n", "# Make scan of lnL (for theta, if free)\n", "if not(m.fixed['theta']):\n", " plt.figure()\n", " m.draw_mnprofile('theta')\n", " plt.show()\n", " \n", "# Make a contour plot of lnL = lnLmax - 1/2 (here for theta and xi).\n", "# The tangents to this contour give the standard deviations.\n", "CL = stats.chi2.cdf(1.,2) # Q_alpha = 1, npar = 2\n", "print('CL = ', CL)\n", "if not(m.fixed['theta'] | m.fixed['xi']):\n", " fig, ax = plt.subplots(1,1)\n", " con = m.mncontour('theta', 'xi', cl=CL, size=200)\n", " con = np.vstack([con, con[0]]) # close contour\n", " plt.plot(MLE[0], MLE[3], marker='o', linestyle='None', color='black', label=r'$(\\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$')\n", " plt.show()\n", "\n", "# Confidence region from lnL = lnLmax - Q/2 (here for theta and xi)\n", "# where Q is the chi2 quantile of CL = 1-alpha = 0.683 and 0.95 for 2 dof.\n", "if not(m.fixed['theta'] | m.fixed['xi']):\n", " fig, ax = plt.subplots(1,1)\n", " m.draw_mncontour('theta', 'xi', cl=[0.683, 0.95], size=200);\n", " plt.plot(MLE[0], MLE[3], marker='o', linestyle='None', color='black', label=r'$(\\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, "id": "e57747df", "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 }