{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iminuit version: 2.8.2\n" ] } ], "source": [ "# Example of simple combined fit using iminuit v 2.\n", "# Fit types available (choose below): LS = Least Squares, GVM = Gamma Variance Model\n", "# G. Cowan / RHUL Physics / March 2022\n", "\n", "import numpy as np\n", "import scipy.stats as stats\n", "from scipy.stats import chi2\n", "import iminuit\n", "from iminuit import Minuit\n", "import matplotlib.pyplot as plt\n", "plt.rcParams[\"font.size\"] = 14\n", "print(f\"iminuit version: {iminuit.__version__}\") # should be v 2.x" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Define the fit function and likelihood\n", "class NegLogL:\n", "\n", " def __init__(self, x, y, s, r, fitType):\n", " self.setData(x, y, s, r)\n", " self.fitType = fitType\n", " \n", " def setData(self, x, y, s, r):\n", " self.data = x, y, s, r\n", " \n", " def func(self, x, par): # fit function\n", " theta0 = par[0]\n", " theta1 = par[1]\n", " return theta0 + theta1*x\n", " \n", " def nll(self, par): # negative log-likelihood\n", " if self.fitType == 'LS':\n", " return self.nllLS(par)\n", " elif self.fitType == 'GVM':\n", " return self.nllGVM(par)\n", " else:\n", " print (\"fitType \", self.fitType, \" not supported\")\n", " return -1\n", "\n", " def nllLS(self, par): # ordinary least squares (r not used)\n", " x, y, s, r = self.data\n", " f = self.func(x, par)\n", " lnf = 0.5 * (y - f)**2 / s**2\n", " return np.sum(lnf)\n", "\n", " def nllGVM(self, par): # Gamma Variance Model (\"errors on errors\")\n", " x, y, s, r = self.data \n", " f = self.func(x, par)\n", " lnf = 0.5*(1. + 1./(2.*r**2))*np.log(1. + 2.*(r*(y-f))**2/s**2)\n", " return np.sum(lnf)\n", "\n", " def __call__(self, par):\n", " return self.nll(par)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# set values for two data sets and their combination\n", "x1 = np.array([1.0, 2.0, 3.0])\n", "y1 = np.array([2.9, 2.4, 2.3])\n", "s1 = np.array([0.7, 0.7, 0.7]) # std. dev. of meas.\n", "r1 = np.array([0.2, 0.2, 0.2]) # relative \"error on error\" (used only in GVM, not LS)\n", "\n", "x2 = np.array([7.0, 8.0, 9.0])\n", "y2 = np.array([5.2, 5.0, 3.9])\n", "s2 = np.array([0.7, 0.7, 0.7])\n", "r2 = np.array([0.2, 0.2, 0.2])\n", "\n", "x = np.concatenate((x1, x2), axis=0)\n", "y = np.concatenate((y1, y2), axis=0)\n", "s = np.concatenate((s1, s2), axis=0)\n", "r = np.concatenate((r1, r2), axis=0)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Initialize Minuit and set up fit:\n", "fitType = 'LS' # LS (least squares), GVM (Gamma Variance Model) \n", "negLogL = NegLogL(x, y, s, r, fitType) # instantiate function to be minimized\n", "parin = np.array([0., 0.]) # initial values\n", "parname = ['theta0', 'theta1']\n", "parstep = np.array([0.1, 0.1]) # initial setp sizes\n", "parfix = [False, False] # change these to fix/free parameters\n", "parlim = [(None, None), (None, 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": 5, "metadata": {}, "outputs": [], "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", "chi2min = 2.*negLogL.nll(MLE)\n", "ndof = len(y) - m.nfit\n", "pval = chi2.sf(chi2min, ndof)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "par index, name, estimate, standard deviation:\n", " 0 theta0 = 2.099425 +/- 0.541178\n", " 1 theta1 = 0.303448 +/- 0.091915\n", "\n", "free par indices, covariance, correlation coeff.:\n", "0 0 0.292874 1.000000\n", "0 1 -0.042241 -0.849208\n", "1 0 -0.042241 -0.849208\n", "1 1 0.008448 1.000000\n", "\n", "minimized chi2 = 5.893150363593716\n", "degrees of freedom = 4\n", "p-value from chi2min = 0.20727123662782707\n" ] } ], "source": [ "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]))\n", " \n", "print()\n", "print(r\"minimized chi2 = \", chi2min)\n", "print(r\"degrees of freedom = \", ndof)\n", "print(r\"p-value from chi2min = \", pval)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot fitted curve with data\n", "xMin = 0.;\n", "xMax = 10.;\n", "yMin = 0.\n", "yMax = 8.\n", "fig = plt.figure(figsize=(8,6))\n", "xCurve = np.linspace(xMin, xMax, 100)\n", "yCurve = negLogL.func(xCurve, MLE)\n", "plt.plot(xCurve, yCurve, color='dodgerblue')\n", "plt.errorbar(x, y, yerr=s, xerr=0, color='black', fmt='o', label='data')\n", "plt.xlabel(r'$x$')\n", "plt.ylabel(r'$y$')\n", "plt.figtext(0.2, 0.72, r'$\\hat{\\theta}_0 = $' + f'{MLE[0]:.4f}' +\n", " r'$\\pm$' + f'{sigmaMLE[0]:.4f}')\n", "plt.figtext(0.2, 0.64, r'$\\hat{\\theta}_1 = $' + f'{MLE[1]:.4f}' +\n", " r'$\\pm$' + f'{sigmaMLE[1]:.4f}')\n", "plt.xlim(xMin, xMax)\n", "plt.ylim(yMin, yMax)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Make scan of lnL (for theta0, if free)\n", "if not(m.fixed['theta0']):\n", " plt.figure()\n", " m.draw_mnprofile('theta0')\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CL = 0.3934693402873665\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Make a contour plot of lnL = lnLmax - 1/2 (here for theta0 and theta1).\n", "# The tangents to the contour give the standard deviations of the MLEs.\n", "CL = stats.chi2.cdf(1., m.nfit) # Q_alpha = 1, number of fitted param = m.nfit\n", "print('CL = ', CL)\n", "if not(m.fixed['theta0'] | m.fixed['theta1']):\n", " fig, ax = plt.subplots(1,1)\n", " con = m.mncontour('theta0', 'theta1', cl=CL, size=200)\n", " con = np.vstack([con, con[0]]) # close contour\n", " plt.plot(MLE[0], MLE[1], marker='o', linestyle='None', color='dodgerblue', \n", " label=r'$(\\hat{\\theta}_0, \\hat{\\theta}_1)$')\n", " plt.plot(con[:,0], con[:,1], color='dodgerblue', linewidth=1)\n", " plt.xlabel(r'$\\theta_0$', labelpad=5)\n", " plt.ylabel(r'$\\theta_1$', labelpad=5)\n", " handles, labels = ax.get_legend_handles_labels()\n", " plt.legend(handles, labels, loc='upper right', fontsize=14, frameon=False)\n", " plt.figtext(0.4, 0.93, r'$\\ln L = \\ln L_{\\rm max} - 1/2$')\n", " plt.show() " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Confidence region from lnL = lnLmax - Q/2 (here for theta0 and theta1)\n", "# where Q is the chi2 quantile of CL = 1-alpha = 0.683 and 0.95 for 2 dof.\n", "if not(m.fixed['theta0'] | m.fixed['theta1']):\n", " fig, ax = plt.subplots(1,1)\n", " m.draw_mncontour('theta0', 'theta1', cl=[0.683, 0.95], size=200);\n", " plt.plot(MLE[0], MLE[1], marker='o', linestyle='None', color='black', \n", " label=r'$(\\hat{\\theta}_0, \\hat{\\theta}_1)$')\n", " plt.xlabel(r'$\\theta_0$', labelpad=10)\n", " plt.ylabel(r'$\\theta_1$', labelpad=10)\n", " plt.subplots_adjust(left=0.2, right=0.9, top=0.9, bottom=0.2)\n", " handles, labels = ax.get_legend_handles_labels()\n", " plt.legend(handles, labels, loc='upper right', fontsize=14, frameon=False)\n", " plt.figtext(0.3, 0.93, \n", " r'$\\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 }