{ "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 2020" ] }, { "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", "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 Chi2Regression\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": 13, "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 (mean, amp, omega, phase)\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": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "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": 15, "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": 16, "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": 17, "metadata": {}, "outputs": [], "source": [ "tau = 3.14 # I'm just picking a random lifetime..." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "array_Chi2_Exp = np.zeros(Nexp)\n", "array_Prob_Exp = np.zeros(Nexp)" ] }, { "cell_type": "code", "execution_count": 19, "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": 20, "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": 21, "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 (N and tau)\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": 22, "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": 23, "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": 24, "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": 25, "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", " " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.7.6" }, "main_language": "python" }, "nbformat": 4, "nbformat_minor": 2 }