{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# ChiSquare test/distribution for general fits:\n", "\n", "This Python program/notebook illustrates the use of ChiSquare as a goodness-of-fit measure, how this distribution comes about, and that it actually works, here with three different examples! The first example is the linear fit, while the two others are more complicated (oscillatory graph fit and exponential fit of a histogram). However, they have one thing in common, namely the number of degrees of freedom!\n", "\n", "## References:\n", "* Barlow: Chapter 6\n", "* Cowan: Chapter 2.7, Chapter 7\n", "* Bevington: Chapter 6\n", "\n", "## Author(s), contact(s), and dates:\n", "* Author: Troels C. Petersen (NBI)\n", "* Email: petersen@nbi.dk\n", "* Date: 12th of November 2018" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "lines_to_next_cell": 2 }, "outputs": [], "source": [ "import numpy as np # Matlab like syntax for linear algebra and functions\n", "import matplotlib.pyplot as plt # Plots and figures like you know them from Matlab\n", "import seaborn as sns # Make the plots nicer to look at\n", "from iminuit import Minuit # The actual fitting tool, better than scipy's\n", "from probfit import BinnedLH, Chi2Regression, Extended # Helper tool for fitting\n", "import sys # Module to see files and folders in directories\n", "from scipy import stats" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "sys.path.append('../../External_Functions')\n", "from ExternalFunctions import nice_string_output, add_text_to_ax # useful functions to print fit results on figure" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "Make sure you've read the relevant references and that you understand not only what\n", "the ChiSquare is, but also that it follows the ChiSquare distribution, and that the\n", "probability of obtaining such a ChiSquare or worse can be calculated from it.\n", "\n", "The program generates a certain number of datasets in three different ways, from\n", "which the Chi2 of the fit is recorded.\n", "***\n", "\n", "## Program settings:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "save_plots = False" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "r = np.random # Random generator\n", "r.seed(42) # Set a random seed (but a fixed one - more on that later.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generate and fit LINEAR data:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "Nexp = 1000\n", "NpointsLin = 17" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "alpha0 = 3.6\n", "alpha1 = 0.3\n", "sigmay = 0.4" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "array_Chi2_Lin = np.zeros(Nexp)\n", "array_Prob_Lin = np.zeros(Nexp)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "lines_to_next_cell": 2 }, "outputs": [], "source": [ "# Loop over number of experiments to generate data and subsequent Chi2 values:\n", "for iexp in range( Nexp ) : \n", "\n", " # Generate points:\n", " xLin = np.arange(NpointsLin)+1\n", " exLin = np.zeros_like(xLin)\n", " yLin = alpha0 + alpha1 * xLin + r.normal(0, sigmay, NpointsLin)\n", " eyLin = sigmay*np.ones_like(xLin)\n", "\n", " def fit_function_Lin(x, alpha0, alpha1):\n", " return alpha0 + alpha1*x\n", " \n", " chi2_object = Chi2Regression(fit_function_Lin, xLin, yLin, eyLin) \n", " minuitLin = Minuit(chi2_object, pedantic=False, alpha0=1, alpha1=1, print_level=0) \n", " minuitLin.migrad(); # perform the actual fit\n", " Chi2Lin = minuitLin.fval # the chi2 value\n", " \n", " NvarLin = 2 # Number of variables (alpha0 and alpha1)\n", " NdofLin = NpointsLin - NvarLin # Number of degrees of freedom\n", " \n", " #from scipy import stats\n", " ProbLin = stats.chi2.sf(Chi2Lin, NdofLin) # The chi2 probability given N_DOF degrees of freedom\n", " \n", " array_Chi2_Lin[iexp] = Chi2Lin\n", " array_Prob_Lin[iexp] = ProbLin" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to inspect the fits, we plot the last one produced:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figLin, axLin = plt.subplots(figsize=(16, 8))\n", "axLin.errorbar(xLin, yLin, eyLin, fmt='ro', ecolor='k', elinewidth=1, capsize=2, capthick=1)\n", "axLin.plot(xLin, fit_function_Lin(xLin, *minuitLin.args), '-r')\n", "\n", "d = {'Intercept':[minuitLin.values['alpha0'], minuitLin.errors['alpha0']],\n", " 'Slope': [minuitLin.values['alpha1'], minuitLin.errors['alpha1']],\n", " 'Chi2': Chi2Lin,\n", " 'ndf': NdofLin,\n", " 'Prob': ProbLin,\n", " }\n", "\n", "text = nice_string_output(d, extra_spacing=2, decimals=3)\n", "add_text_to_ax(0.04, 0.95, text, axLin, fontsize=20)\n", "figLin.tight_layout()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "if (save_plots) : \n", " figLin.savefig(\"Chi2Dist_LinearFit.pdf\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generate and fit OSCILLATING data:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "NpointsOsc = 19\n", "mean = 1.6\n", "amp = 3.3\n", "omega = 0.7\n", "phase = 0.3\n", "sigmay = 0.5" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "lines_to_next_cell": 2 }, "outputs": [], "source": [ "# Again we record the resulting Chi2 values and probabilities:\n", "array_Chi2_Osc = np.zeros(Nexp)\n", "array_Prob_Osc = np.zeros(Nexp)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "lines_to_next_cell": 2 }, "outputs": [], "source": [ "# Loop over number of experiments to generate data and subsequent Chi2 values:\n", "for iexp in range( Nexp ) : \n", "\n", " # Generate points:\n", " xOsc = np.arange(NpointsOsc)+1\n", " exOsc = np.zeros_like(xLin)\n", " yOsc = mean + amp*np.cos(omega*xOsc + phase) + r.normal(0, sigmay, NpointsOsc)\n", " eyOsc = sigmay*np.ones_like(xOsc)\n", "\n", " # Fit points:\n", " def fit_function_Osc(x, mean, amp, omega, phase):\n", " return mean + amp*np.cos(omega*x + phase)\n", " \n", " chi2_object = Chi2Regression(fit_function_Osc, xOsc, yOsc, eyOsc) \n", " minuitOsc = Minuit(chi2_object, pedantic=False, mean=mean, amp=amp, omega=omega, phase=phase, print_level=0) \n", " # minuitOsc = Minuit(chi2_object, pedantic=False, mean=0.0, amp=0.0, omega=0.0, phase=0.0, print_level=0) \n", " minuitOsc.migrad(); # Perform the actual fit\n", " Chi2Osc = minuitOsc.fval # Get the chi2 value\n", " \n", " NvarOsc = 4 # Number of variables (alpha0 and alpha1)\n", " NdofOsc = NpointsOsc - NvarOsc # Number of degrees of freedom\n", " \n", " ProbOsc = stats.chi2.sf(Chi2Osc, NdofOsc) # The chi2 probability given N degrees of freedom, Ndof\n", " \n", " array_Chi2_Osc[iexp] = Chi2Osc\n", " array_Prob_Osc[iexp] = ProbOsc" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figOsc, axOsc = plt.subplots(figsize=(16, 8))\n", "axOsc.errorbar(xOsc, yOsc, eyOsc, fmt='ro', ecolor='k', elinewidth=1, capsize=2, capthick=1)\n", "xaxis = np.linspace(min(xOsc), max(xOsc), 1000)\n", "axOsc.plot(xaxis, fit_function_Osc(xaxis, *minuitOsc.args), '-r')\n", "\n", "d = {'Mean': [minuitOsc.values['mean'], minuitOsc.errors['mean']],\n", " 'Amplitude':[minuitOsc.values['amp'], minuitOsc.errors['amp']],\n", " 'Omega': [minuitOsc.values['omega'], minuitOsc.errors['omega']],\n", " 'Phase': [minuitOsc.values['phase'], minuitOsc.errors['phase']],\n", " 'Chi2': Chi2Osc,\n", " 'ndf': NdofOsc,\n", " 'Prob': ProbOsc,\n", " }\n", "\n", "text = nice_string_output(d, extra_spacing=2, decimals=3)\n", "add_text_to_ax(0.08, 0.95, text, axOsc, fontsize=16)\n", "figOsc.tight_layout()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "if (save_plots) : \n", " figOsc.savefig(\"Chi2Dist_OscillationFit.pdf\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generate and fit EXPONENTIAL binned data:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "NpointsExp = 1000 # Put this number of points (exponentially distributed) in each histogram.\n", "NbinsExp = 17 # Decide on the number of bins (for a reason!)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "tau = 3.14 # I'm just picking a random lifetime..." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "array_Chi2_Exp = np.zeros(Nexp)\n", "array_Prob_Exp = np.zeros(Nexp)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "# Define an exponential PDF (i.e. normalised):\n", "def fit_function_Exp(x, tau):\n", " return 1.0 / tau * np.exp(- x / tau)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "lines_to_next_cell": 2 }, "outputs": [], "source": [ "# Define an exponential fit function, which includes a normalisation:\n", "def fit_function_Exp_Ext(x, tau, N):\n", " return N * fit_function_Exp(x, tau)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "lines_to_next_cell": 2 }, "outputs": [], "source": [ "# Loop over number of experiments to generate data and subsequent Chi2 values:\n", "for iexp in range( Nexp ) : \n", " \n", " dataExp = r.exponential(tau, NpointsExp)\n", "\n", " yExp, xExp_edges = np.histogram(dataExp, bins=NbinsExp, range=(0, NbinsExp))\n", " xExp = (xExp_edges[1:] + xExp_edges[:-1])/2\n", " syExp = np.sqrt(yExp)\n", " \n", " Chi2_object = Chi2Regression(fit_function_Exp_Ext, xExp[yExp>0], yExp[yExp>0], syExp[yExp>0])\n", " minuitExp = Minuit(Chi2_object, pedantic=False, tau = tau, N=NpointsExp, print_level=0) \n", " minuitExp.migrad(); # perform the actual fit\n", "\n", " Chi2Exp = minuitExp.fval\n", " \n", " NvarExp = 2 # Number of variables (alpha0 and alpha1)\n", " NdofExp = NbinsExp - NvarExp # Number of degrees of freedom\n", " \n", " ProbExp = stats.chi2.sf(Chi2Exp, NdofExp) # The chi2 probability given N_DOF degrees of freedom\n", " \n", " array_Chi2_Exp[iexp] = Chi2Exp\n", " array_Prob_Exp[iexp] = ProbExp" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figExp, axExp = plt.subplots(figsize=(16, 8))\n", "axExp.hist(dataExp, NbinsExp, range=(0, NbinsExp), histtype='step')\n", "x_axis = np.linspace(0, NbinsExp, 1000)\n", "axExp.plot(x_axis, fit_function_Exp_Ext(x_axis, *minuitExp.args), '-r') \n", "\n", "d = {'N events': [minuitExp.values['N'], minuitExp.errors['N']],\n", " 'Lifetime': [minuitExp.values['tau'], minuitExp.errors['tau']],\n", " 'Chi2': Chi2Exp,\n", " 'ndf': NdofExp,\n", " 'Prob': ProbExp,\n", " }\n", "\n", "text = nice_string_output(d, extra_spacing=2, decimals=3)\n", "add_text_to_ax(0.62, 0.95, text, axExp, fontsize=20)\n", "figExp.tight_layout()" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "lines_to_next_cell": 2 }, "outputs": [], "source": [ "if (save_plots) : \n", " figExp.savefig(\"Chi2Dist_ExponentialFit.pdf\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above histogram does not show us the uncertainty used in each bin, which the $\\chi^2$ needs for its calculation. We have discussed what error to use, and will surely be doing so more in the course, but below is code that gives a plot showing points and errors instead of a \"bare\" histogram. " ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Calculating points and errors:\n", "y, bin_edges = np.histogram(dataExp, bins=NbinsExp, range=(0, NbinsExp))\n", "x = 0.5*(bin_edges[:-1] + bin_edges[1:])\n", "sy = np.sqrt(y) # Note: Ask yourself (here on in question 4 below) where these errors come from?\n", "\n", "# Plotting the result of the above!\n", "fig, ax = plt.subplots(figsize=(16,8))\n", "hist1 = ax.errorbar(x, y, sy, fmt='.', label='Exponential distribution')\n", "\n", "# Plot the function we fitted on top? That is a simple exercise for you!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Considering repeated experiments/fits and resulting $\\chi^2$ distributions:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# If there have been more than one experiment, then make another white canvas:\n", "if (Nexp > 1) :\n", " \n", " xaxis = np.linspace(0, 50, 1000)\n", " yaxis = stats.chi2.pdf(xaxis, 15)\n", " \n", " array_Chi2 = [array_Chi2_Lin, array_Chi2_Osc, array_Chi2_Exp]\n", "\n", " fig2, ax2 = plt.subplots(ncols=3, figsize=(16, 6))\n", " for i in range(3):\n", " ax2[i].hist(array_Chi2[i], 50, range=(0, 50), histtype='step', density=True)\n", " ax2[i].plot(xaxis, yaxis)\n", " \n", " # Here, we \"just\" put in quick remarks (note the \"code\"-like way of defining format. Do you understand it?):\n", " string = f\"Entries {len(array_Chi2[i]):7d}\\n\"\n", " string += f\"Mean {array_Chi2[i].mean():10.3f}\\n\"\n", " string += f\"STD {array_Chi2[i].std(ddof=1):11.3f}\"\n", " ax2[i].text(0.6, 0.95, string, family='monospace', transform=ax2[i].transAxes, fontsize=10, verticalalignment='top')\n", " \n", " if (save_plots) : \n", " fig2.savefig(\"Chi2Dist_SeveralCases.pdf\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Questions:\n", " 1. Why have I chosen the three examples to have 17 points, 19 points and 17 bins?\n", " Hint: What is the number of degrees of freedom in each of the three cases?\n", "\n", " 2. In the example of the linear fit, what number of points lies outside +-1 sigma?\n", " Is that a reasonable number?\n", "\n", " 3. In the oscillatory case, try to drop the line were you set the parameters\n", " (line defining \"minuitOsc\"), and see how well the fit goes, when it does not\n", " have good starting values. How often does it get a good fit result?\n", "\n", " 4. In the exponential fit, where do the uncertainties come from? And is the fit\n", " reasonable?\n", "\n", "\n", "### Advanced questions:\n", " 5. Why does the last of the three Chi2 distributions not fit quite?\n", " Try to change the number of generated points to 100 instead of 1000,\n", " and/or change the lifetime to tau=2.1. Does this increase the mismatch\n", " of the Chi2 distribution. Does that give you a hint why?\n", " " ] } ], "metadata": { "executable": "/usr/bin/env python", "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": "3.6.7" }, "main_language": "python" }, "nbformat": 4, "nbformat_minor": 2 }