{ "cells": [ { "cell_type": "markdown", "id": "4572ab74", "metadata": {}, "source": [ "# rf403_weightedevts\n", "'DATA AND CATEGORIES' RooFit tutorial macro #403\n", "\n", "Using weights in unbinned datasets\n", "\n", "\n", "\n", "\n", "**Author:** Clemens Lange, Wouter Verkerke (C version) \n", "This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Tuesday, May 19, 2026 at 08:31 PM." ] }, { "cell_type": "code", "execution_count": 1, "id": "2995278b", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:40.023031Z", "iopub.status.busy": "2026-05-19T20:31:40.022900Z", "iopub.status.idle": "2026-05-19T20:31:41.014220Z", "shell.execute_reply": "2026-05-19T20:31:41.013490Z" } }, "outputs": [], "source": [ "import ROOT" ] }, { "cell_type": "markdown", "id": "874a1c37", "metadata": {}, "source": [ "Create observable and unweighted dataset\n", "-------------------------------------------" ] }, { "cell_type": "markdown", "id": "2e166c50", "metadata": {}, "source": [ "Declare observable" ] }, { "cell_type": "code", "execution_count": 2, "id": "1e4dadff", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:41.026481Z", "iopub.status.busy": "2026-05-19T20:31:41.026334Z", "iopub.status.idle": "2026-05-19T20:31:41.189973Z", "shell.execute_reply": "2026-05-19T20:31:41.189186Z" } }, "outputs": [], "source": [ "x = ROOT.RooRealVar(\"x\", \"x\", -10, 10)\n", "x.setBins(40)" ] }, { "cell_type": "markdown", "id": "19592469", "metadata": {}, "source": [ "Construction a uniform pdf" ] }, { "cell_type": "code", "execution_count": 3, "id": "834ce35e", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:41.192389Z", "iopub.status.busy": "2026-05-19T20:31:41.192255Z", "iopub.status.idle": "2026-05-19T20:31:41.316364Z", "shell.execute_reply": "2026-05-19T20:31:41.315718Z" } }, "outputs": [], "source": [ "p0 = ROOT.RooPolynomial(\"px\", \"px\", x)" ] }, { "cell_type": "markdown", "id": "aa9c090b", "metadata": {}, "source": [ "Sample 1000 events from pdf" ] }, { "cell_type": "code", "execution_count": 4, "id": "d3666764", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:41.318505Z", "iopub.status.busy": "2026-05-19T20:31:41.318376Z", "iopub.status.idle": "2026-05-19T20:31:41.504515Z", "shell.execute_reply": "2026-05-19T20:31:41.503712Z" } }, "outputs": [], "source": [ "data = p0.generate(x, 1000)" ] }, { "cell_type": "markdown", "id": "c0a9d95d", "metadata": {}, "source": [ "Calculate weight and make dataset weighted\n", "--------------------------------------------------" ] }, { "cell_type": "markdown", "id": "68a069ca", "metadata": {}, "source": [ "Construct formula to calculate (fake) weight for events" ] }, { "cell_type": "code", "execution_count": 5, "id": "4f2e6964", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:41.506350Z", "iopub.status.busy": "2026-05-19T20:31:41.506224Z", "iopub.status.idle": "2026-05-19T20:31:41.686920Z", "shell.execute_reply": "2026-05-19T20:31:41.686209Z" } }, "outputs": [], "source": [ "wFunc = ROOT.RooFormulaVar(\"w\", \"event weight\", \"(x*x+10)\", [x])" ] }, { "cell_type": "markdown", "id": "0a04ac3e", "metadata": {}, "source": [ "Add column with variable w to previously generated dataset" ] }, { "cell_type": "code", "execution_count": 6, "id": "722bd641", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:41.688730Z", "iopub.status.busy": "2026-05-19T20:31:41.688592Z", "iopub.status.idle": "2026-05-19T20:31:41.820809Z", "shell.execute_reply": "2026-05-19T20:31:41.812845Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data.addColumn(wFunc)" ] }, { "cell_type": "markdown", "id": "a88d0297", "metadata": {}, "source": [ "Dataset d is now a dataset with two observable (x,w) with 1000 entries" ] }, { "cell_type": "code", "execution_count": 7, "id": "a659aa8d", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:41.833079Z", "iopub.status.busy": "2026-05-19T20:31:41.832942Z", "iopub.status.idle": "2026-05-19T20:31:41.941285Z", "shell.execute_reply": "2026-05-19T20:31:41.940643Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "RooDataSet::pxData[x,w] = 1000 entries\n" ] } ], "source": [ "data.Print()" ] }, { "cell_type": "markdown", "id": "707ff348", "metadata": {}, "source": [ "Create a new dataset wdata where w is interpreted as event weight rather than\n", "as observable" ] }, { "cell_type": "code", "execution_count": 8, "id": "d8f7b35b", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:41.942897Z", "iopub.status.busy": "2026-05-19T20:31:41.942775Z", "iopub.status.idle": "2026-05-19T20:31:42.129664Z", "shell.execute_reply": "2026-05-19T20:31:42.129063Z" } }, "outputs": [], "source": [ "wdata = ROOT.RooDataSet(data.GetName(), data.GetTitle(), data.get(), Import=data, WeightVar=\"w\")" ] }, { "cell_type": "markdown", "id": "8f20612a", "metadata": {}, "source": [ "Dataset d is now a dataset with one observable (x) with 1000 entries and\n", "a sum of weights of ~430K" ] }, { "cell_type": "code", "execution_count": 9, "id": "9b7ad2b7", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:42.135530Z", "iopub.status.busy": "2026-05-19T20:31:42.135403Z", "iopub.status.idle": "2026-05-19T20:31:42.239890Z", "shell.execute_reply": "2026-05-19T20:31:42.239261Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "RooDataSet::pxData[x,weight:w] = 1000 entries (43238.9 weighted)\n" ] } ], "source": [ "wdata.Print()" ] }, { "cell_type": "markdown", "id": "ed87d27c", "metadata": {}, "source": [ "Unbinned ML fit to weighted data\n", "---------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "e150ec4f", "metadata": {}, "source": [ "Construction quadratic polynomial pdf for fitting" ] }, { "cell_type": "code", "execution_count": 10, "id": "aa4670e0", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:42.241511Z", "iopub.status.busy": "2026-05-19T20:31:42.241388Z", "iopub.status.idle": "2026-05-19T20:31:42.358754Z", "shell.execute_reply": "2026-05-19T20:31:42.358157Z" } }, "outputs": [], "source": [ "a0 = ROOT.RooRealVar(\"a0\", \"a0\", 1)\n", "a1 = ROOT.RooRealVar(\"a1\", \"a1\", 0, -1, 1)\n", "a2 = ROOT.RooRealVar(\"a2\", \"a2\", 1, 0, 10)\n", "p2 = ROOT.RooPolynomial(\"p2\", \"p2\", x, [a0, a1, a2], 0)" ] }, { "cell_type": "markdown", "id": "fcb8fcd2", "metadata": {}, "source": [ "Fit quadratic polynomial to weighted data" ] }, { "cell_type": "markdown", "id": "812f999f", "metadata": {}, "source": [ "NOTE: A plain Maximum likelihood fit to weighted data does in general\n", " NOT result in correct error estimates, individual\n", " event weights represent Poisson statistics themselves.\n", "\n", "Fit with 'wrong' errors" ] }, { "cell_type": "code", "execution_count": 11, "id": "ad197445", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:42.360757Z", "iopub.status.busy": "2026-05-19T20:31:42.360635Z", "iopub.status.idle": "2026-05-19T20:31:42.562354Z", "shell.execute_reply": "2026-05-19T20:31:42.561674Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Fitting -- RooAbsPdf::fitTo(p2_over_p2_Int[x]) fixing normalization set for coefficient determination to observables in data\n", "[#1] INFO:Fitting -- using generic CPU library compiled with no vectorizations\n", "[#1] INFO:Fitting -- Creation of NLL object took 755.084 μs\n", "[#0] WARNING:InputArguments -- RooAbsPdf::fitTo(p2): WARNING: a likelihood fit is requested of what appears to be weighted data.\n", " While the estimated values of the parameters will always be calculated taking the weights into account,\n", " there are multiple ways to estimate the errors of the parameters. You are advised to make an\n", " explicit choice for the error calculation:\n", " - Either provide SumW2Error(true), to calculate a sum-of-weights-corrected HESSE error matrix\n", " (error will be proportional to the number of events in MC).\n", " - Or provide SumW2Error(false), to return errors from original HESSE error matrix\n", " (which will be proportional to the sum of the weights, i.e., a dataset with events).\n", " - Or provide AsymptoticError(true), to use the asymptotically correct expression\n", " (for details see https://arxiv.org/abs/1911.01303).\"\n", "[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_p2_over_p2_Int[x]_pxData) Summation contains a RooNLLVar, using its error level\n", "[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n" ] } ], "source": [ "r_ml_wgt = p2.fitTo(wdata, Save=True, PrintLevel=-1)" ] }, { "cell_type": "markdown", "id": "cd7926f3", "metadata": {}, "source": [ "A first order correction to estimated parameter errors in an\n", "(unbinned) ML fit can be obtained by calculating the\n", "covariance matrix as\n", "\n", " V' = V C-1 V\n", "\n", "where V is the covariance matrix calculated from a fit\n", "to -logL = - sum [ w_i log f(x_i) ] and C is the covariance\n", "matrix calculated from -logL' = -sum [ w_i^2 log f(x_i) ]\n", "(i.e. the weights are applied squared)\n", "\n", "A fit in self mode can be performed as follows:" ] }, { "cell_type": "code", "execution_count": 12, "id": "1cee1fde", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:42.564428Z", "iopub.status.busy": "2026-05-19T20:31:42.564300Z", "iopub.status.idle": "2026-05-19T20:31:42.682039Z", "shell.execute_reply": "2026-05-19T20:31:42.681461Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Fitting -- RooAbsPdf::fitTo(p2_over_p2_Int[x]) fixing normalization set for coefficient determination to observables in data\n", "[#1] INFO:Fitting -- Creation of NLL object took 152.79 μs\n", "[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_p2_over_p2_Int[x]_pxData) Summation contains a RooNLLVar, using its error level\n", "[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n", "[#1] INFO:Fitting -- RooAbsPdf::fitTo(p2) Calculating sum-of-weights-squared correction matrix for covariance matrix\n" ] } ], "source": [ "r_ml_wgt_corr = p2.fitTo(wdata, Save=True, SumW2Error=True, PrintLevel=-1)" ] }, { "cell_type": "markdown", "id": "952a9b71", "metadata": {}, "source": [ "Plot weighted data and fit result\n", "---------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "25e973cd", "metadata": {}, "source": [ "Construct plot frame" ] }, { "cell_type": "code", "execution_count": 13, "id": "58c41ca1", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:42.683899Z", "iopub.status.busy": "2026-05-19T20:31:42.683768Z", "iopub.status.idle": "2026-05-19T20:31:42.811932Z", "shell.execute_reply": "2026-05-19T20:31:42.811289Z" } }, "outputs": [], "source": [ "frame = x.frame(Title=\"Unbinned ML fit, chi^2 fit to weighted data\")" ] }, { "cell_type": "markdown", "id": "eda917d9", "metadata": {}, "source": [ "Plot data using sum-of-weights-squared error rather than Poisson errors" ] }, { "cell_type": "code", "execution_count": 14, "id": "26fb9d60", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:42.814042Z", "iopub.status.busy": "2026-05-19T20:31:42.813915Z", "iopub.status.idle": "2026-05-19T20:31:42.943425Z", "shell.execute_reply": "2026-05-19T20:31:42.942324Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "wdata.plotOn(frame, DataError=\"SumW2\")" ] }, { "cell_type": "markdown", "id": "aed273dc", "metadata": {}, "source": [ "Overlay result of 2nd order polynomial fit to weighted data" ] }, { "cell_type": "code", "execution_count": 15, "id": "f7b4a22c", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:42.945021Z", "iopub.status.busy": "2026-05-19T20:31:42.944895Z", "iopub.status.idle": "2026-05-19T20:31:43.080393Z", "shell.execute_reply": "2026-05-19T20:31:43.078859Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p2.plotOn(frame)" ] }, { "cell_type": "markdown", "id": "dfd62731", "metadata": {}, "source": [ "ML fit of pdf to equivalent unweighted dataset\n", "---------------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "e371dbf9", "metadata": {}, "source": [ "Construct a pdf with the same shape as p0 after weighting" ] }, { "cell_type": "code", "execution_count": 16, "id": "bc2a9aae", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:43.082057Z", "iopub.status.busy": "2026-05-19T20:31:43.081932Z", "iopub.status.idle": "2026-05-19T20:31:43.199136Z", "shell.execute_reply": "2026-05-19T20:31:43.198481Z" } }, "outputs": [], "source": [ "genPdf = ROOT.RooGenericPdf(\"genPdf\", \"x*x+10\", [x])" ] }, { "cell_type": "markdown", "id": "0d392c7c", "metadata": {}, "source": [ "Sample a dataset with the same number of events as data" ] }, { "cell_type": "code", "execution_count": 17, "id": "f4d07696", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:43.201155Z", "iopub.status.busy": "2026-05-19T20:31:43.201027Z", "iopub.status.idle": "2026-05-19T20:31:43.309747Z", "shell.execute_reply": "2026-05-19T20:31:43.308798Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:NumericIntegration -- RooRealIntegral::init(genPdf_Int[x]) using numeric integrator RooIntegrator1D to calculate Int(x)\n", "[#1] INFO:NumericIntegration -- RooRealIntegral::init(genPdf_Int[x]) using numeric integrator RooIntegrator1D to calculate Int(x)\n" ] } ], "source": [ "data2 = genPdf.generate(x, 1000)" ] }, { "cell_type": "markdown", "id": "77c79345", "metadata": {}, "source": [ "Sample a dataset with the same number of weights as data" ] }, { "cell_type": "code", "execution_count": 18, "id": "3b7f4c6c", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:43.311235Z", "iopub.status.busy": "2026-05-19T20:31:43.311112Z", "iopub.status.idle": "2026-05-19T20:31:43.434037Z", "shell.execute_reply": "2026-05-19T20:31:43.433642Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:NumericIntegration -- RooRealIntegral::init(genPdf_Int[x]) using numeric integrator RooIntegrator1D to calculate Int(x)\n", "[#1] INFO:NumericIntegration -- RooRealIntegral::init(genPdf_Int[x]) using numeric integrator RooIntegrator1D to calculate Int(x)\n" ] } ], "source": [ "data3 = genPdf.generate(x, 43000)" ] }, { "cell_type": "markdown", "id": "6ceeb527", "metadata": {}, "source": [ "Fit the 2nd order polynomial to both unweighted datasets and save the\n", "results for comparison" ] }, { "cell_type": "code", "execution_count": 19, "id": "7f7c94a6", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:43.439296Z", "iopub.status.busy": "2026-05-19T20:31:43.439163Z", "iopub.status.idle": "2026-05-19T20:31:43.565712Z", "shell.execute_reply": "2026-05-19T20:31:43.564725Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Fitting -- RooAbsPdf::fitTo(p2_over_p2_Int[x]) fixing normalization set for coefficient determination to observables in data\n", "[#1] INFO:Fitting -- Creation of NLL object took 155.05 μs\n", "[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_p2_over_p2_Int[x]_genPdfData) Summation contains a RooNLLVar, using its error level\n", "[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n", "[#1] INFO:Fitting -- RooAbsPdf::fitTo(p2_over_p2_Int[x]) fixing normalization set for coefficient determination to observables in data\n", "[#1] INFO:Fitting -- Creation of NLL object took 190.13 μs\n", "[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_p2_over_p2_Int[x]_genPdfData) Summation contains a RooNLLVar, using its error level\n", "[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n" ] } ], "source": [ "r_ml_unw10 = p2.fitTo(data2, Save=True, PrintLevel=-1)\n", "r_ml_unw43 = p2.fitTo(data3, Save=True, PrintLevel=-1)" ] }, { "cell_type": "markdown", "id": "805bcabc", "metadata": {}, "source": [ "Chis2 fit of pdf to binned weighted dataset\n", "---------------------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "86ed769b", "metadata": {}, "source": [ "Construct binned clone of unbinned weighted dataset" ] }, { "cell_type": "code", "execution_count": 20, "id": "1a18b88b", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:43.567352Z", "iopub.status.busy": "2026-05-19T20:31:43.567221Z", "iopub.status.idle": "2026-05-19T20:31:43.681746Z", "shell.execute_reply": "2026-05-19T20:31:43.680791Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "DataStore pxData_binned (Generated From px_binned)\n", " Contains 40 entries\n", " Observables: \n", " 1) x = 9.75 L(-10 - 10) B(40) \"x\"\n", "Binned Dataset pxData_binned (Generated From px_binned)\n", " Contains 40 bins with a total weight of 43238.9\n", " Observables: 1) x = 9.75 L(-10 - 10) B(40) \"x\"\n" ] } ], "source": [ "binnedData = wdata.binnedClone()\n", "binnedData.Print(\"v\")" ] }, { "cell_type": "markdown", "id": "24ad7f9a", "metadata": {}, "source": [ "Perform chi2 fit to binned weighted dataset using sum-of-weights errors\n", "\n", "NB: Within the usual approximations of a chi2 fit, chi2 fit to weighted\n", "data using sum-of-weights-squared errors does give correct error\n", "estimates" ] }, { "cell_type": "code", "execution_count": 21, "id": "cf69bcd0", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:43.683309Z", "iopub.status.busy": "2026-05-19T20:31:43.683179Z", "iopub.status.idle": "2026-05-19T20:31:43.824131Z", "shell.execute_reply": "2026-05-19T20:31:43.823454Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Fitting -- createChi2(p2) fixing normalization set for coefficient determination to observables in data\n" ] }, { "data": { "text/plain": [ "0" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n", "Minuit2Minimizer: Minimize with max-calls 1000 convergence for edm < 1 strategy 1\n", "Minuit2Minimizer : Valid minimum - status = 0\n", "FVAL = 31.3747451817532266\n", "Edm = 4.13511590231855403e-08\n", "Nfcn = 29\n", "a1\t = -0.009989\t +/- 0.0262975\t(limited)\n", "a2\t = 0.106373\t +/- 0.0101849\t(limited)\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Info in : MnSeedGenerator Computing seed using NumericalGradient calculator\n", "Info in : MnSeedGenerator Evaluated function and gradient in 44.259 μs\n", "Info in : MnSeedGenerator Initial state: FCN = 32.33995323 Edm = 0.8968537856 NCalls = 7\n", "Info in : MnSeedGenerator Initial state \n", " Minimum value : 32.33995323\n", " Edm : 0.8968537856\n", " Internal parameters:\t[ -0.00121057482 -1.372915994]\t\n", " Internal gradient :\t[ 27.17902731 -203.7916428]\t\n", " Internal covariance matrix:\n", "[[ 0.00060495515 0]\n", " [ 0 7.5618996e-05]]]\n", "Info in : VariableMetricBuilder Start iterating until Edm is < 0.002 with call limit = 1000\n", "Info in : VariableMetricBuilder 0 - FCN = 32.33995323 Edm = 0.8968537856 NCalls = 7\n", "Info in : VariableMetricBuilder 1 - FCN = 31.37772394 Edm = 0.002313012129 NCalls = 13\n", "Info in : VariableMetricBuilder 2 - FCN = 31.37474518 Edm = 3.566880604e-08 NCalls = 19\n", "Info in : MnHesse Done after 15.629 μs\n", "Info in : VariableMetricBuilder After Hessian\n", "Info in : VariableMetricBuilder 3 - FCN = 31.37474518 Edm = 4.135115902e-08 NCalls = 29\n", "Info in : VariableMetricBuilder Stop iterating after 63.432 μs\n", "Info in : Minuit2Minimizer::Hesse Using max-calls 1000\n", "Info in : MnHesse Done after 20.349 μs\n", "Info in : Minuit2Minimizer::Hesse Hesse is valid - matrix is accurate\n" ] } ], "source": [ "chi2 = p2.createChi2(binnedData, ROOT.RooFit.DataError(\"SumW2\"))\n", "m = ROOT.RooMinimizer(chi2)\n", "m.migrad()\n", "m.hesse()" ] }, { "cell_type": "markdown", "id": "377b5d93", "metadata": {}, "source": [ "Plot chi^2 fit result on frame as well" ] }, { "cell_type": "code", "execution_count": 22, "id": "9c72f576", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:43.826044Z", "iopub.status.busy": "2026-05-19T20:31:43.825911Z", "iopub.status.idle": "2026-05-19T20:31:43.945172Z", "shell.execute_reply": "2026-05-19T20:31:43.944510Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r_chi2_wgt = m.save()\n", "p2.plotOn(frame, LineStyle=\"--\", LineColor=\"r\")" ] }, { "cell_type": "markdown", "id": "17f7e8a9", "metadata": {}, "source": [ "Compare fit results of chi2, L fits to (un)weighted data\n", "------------------------------------------------------------" ] }, { "cell_type": "markdown", "id": "97408f8e", "metadata": {}, "source": [ "Note that ML fit on 1Kevt of weighted data is closer to result of ML fit on 43Kevt of unweighted data\n", "than to 1Kevt of unweighted data, the reference chi^2 fit with SumW2 error gives a result closer to\n", "that of an unbinned ML fit to 1Kevt of unweighted data." ] }, { "cell_type": "code", "execution_count": 23, "id": "e45f2a54", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:43.947403Z", "iopub.status.busy": "2026-05-19T20:31:43.947270Z", "iopub.status.idle": "2026-05-19T20:31:44.161615Z", "shell.execute_reply": "2026-05-19T20:31:44.160917Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "==> ML Fit results on 1K unweighted events\n", "==> ML Fit results on 43K unweighted events\n", "==> ML Fit results on 1K weighted events with a summed weight of 43K\n", "==> Corrected ML Fit results on 1K weighted events with a summed weight of 43K\n", "==> Chi2 Fit results on 1K weighted events with a summed weight of 43K\n", "\n", " RooFitResult: minimized FCN value: 2766.49, estimated distance to minimum: 0.000399952\n", " covariance matrix quality: Full, accurate covariance matrix\n", " Status : MINIMIZE=0 HESSE=0 \n", "\n", " Floating Parameter FinalValue +/- Error \n", " -------------------- --------------------------\n", " a1 8.9483e-03 +/- 2.70e-02\n", " a2 1.0177e-01 +/- 1.69e-02\n", "\n", "\n", " RooFitResult: minimized FCN value: 118892, estimated distance to minimum: 0.000206627\n", " covariance matrix quality: Full, accurate covariance matrix\n", " Status : MINIMIZE=0 HESSE=0 \n", "\n", " Floating Parameter FinalValue +/- Error \n", " -------------------- --------------------------\n", " a1 -1.2106e-03 +/- 4.02e-03\n", " a2 9.7573e-02 +/- 2.37e-03\n", "\n", "\n", " RooFitResult: minimized FCN value: 119682, estimated distance to minimum: 1.25398e-05\n", " covariance matrix quality: Full, accurate covariance matrix\n", " Status : MINIMIZE=0 HESSE=0 \n", "\n", " Floating Parameter FinalValue +/- Error \n", " -------------------- --------------------------\n", " a1 -4.8713e-03 +/- 4.03e-03\n", " a2 9.8645e-02 +/- 2.41e-03\n", "\n", "\n", " RooFitResult: minimized FCN value: 119682, estimated distance to minimum: 79498.5\n", " covariance matrix quality: Full, accurate covariance matrix\n", " Status : MINIMIZE=0 HESSE=0 HESSE=0 \n", "\n", " Floating Parameter FinalValue +/- Error \n", " -------------------- --------------------------\n", " a1 -4.8565e-03 +/- 3.00e-02\n", " a2 9.8652e-02 +/- 2.99e-02\n", "\n", "\n", " RooFitResult: minimized FCN value: 31.3747, estimated distance to minimum: 4.135e-08\n", " covariance matrix quality: Full, accurate covariance matrix\n", " Status : MIGRAD=0 HESSE=0 \n", "\n", " Floating Parameter FinalValue +/- Error \n", " -------------------- --------------------------\n", " a1 -9.9890e-03 +/- 2.63e-02\n", " a2 1.0637e-01 +/- 1.02e-02\n", "\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Info in : png file rf403_weightedevts.png has been created\n" ] } ], "source": [ "print(\"==> ML Fit results on 1K unweighted events\")\n", "r_ml_unw10.Print()\n", "print(\"==> ML Fit results on 43K unweighted events\")\n", "r_ml_unw43.Print()\n", "print(\"==> ML Fit results on 1K weighted events with a summed weight of 43K\")\n", "r_ml_wgt.Print()\n", "print(\"==> Corrected ML Fit results on 1K weighted events with a summed weight of 43K\")\n", "r_ml_wgt_corr.Print()\n", "print(\"==> Chi2 Fit results on 1K weighted events with a summed weight of 43K\")\n", "r_chi2_wgt.Print()\n", "\n", "c = ROOT.TCanvas(\"rf403_weightedevts\", \"rf403_weightedevts\", 600, 600)\n", "ROOT.gPad.SetLeftMargin(0.15)\n", "frame.GetYaxis().SetTitleOffset(1.8)\n", "frame.Draw()\n", "\n", "c.SaveAs(\"rf403_weightedevts.png\")" ] }, { "cell_type": "markdown", "id": "d00a2ff1", "metadata": {}, "source": [ "Draw all canvases " ] }, { "cell_type": "code", "execution_count": 24, "id": "39084edb", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:31:44.163724Z", "iopub.status.busy": "2026-05-19T20:31:44.163565Z", "iopub.status.idle": "2026-05-19T20:31:44.346642Z", "shell.execute_reply": "2026-05-19T20:31:44.345906Z" } }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "
\n", "
\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from ROOT import gROOT \n", "gROOT.GetListOfCanvases().Draw()" ] } ], "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": "3.12.12" } }, "nbformat": 4, "nbformat_minor": 5 }