{
"cells": [
{
"cell_type": "markdown",
"id": "97b111b3",
"metadata": {},
"source": [
"# rs101_limitexample\n",
"Limits: number counting experiment with uncertainty on both the background rate and signal efficiency.\n",
"\n",
"The usage of a Confidence Interval Calculator to set a limit on the signal is illustrated\n",
"\n",
"\n",
"\n",
"\n",
"**Author:** Artem Busorgin, Kyle Cranmer (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 08:35 PM."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "513b24cc",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:50.282293Z",
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"shell.execute_reply": "2026-05-19T20:35:51.279395Z"
}
},
"outputs": [],
"source": [
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "1f03b875",
"metadata": {},
"source": [
"--------------------------------------\n",
"An example of setting a limit in a number counting experiment with uncertainty on background and signal"
]
},
{
"cell_type": "markdown",
"id": "54a596a8",
"metadata": {},
"source": [
"to time the macro"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "113ded5c",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:51.286899Z",
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"shell.execute_reply": "2026-05-19T20:35:51.404638Z"
}
},
"outputs": [],
"source": [
"t = ROOT.TStopwatch()\n",
"t.Start()"
]
},
{
"cell_type": "markdown",
"id": "1580451a",
"metadata": {},
"source": [
"--------------------------------------\n",
"The Model building stage\n",
"--------------------------------------"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "8ae3975d",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:51.407598Z",
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"shell.execute_reply": "2026-05-19T20:35:51.653186Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"RooWorkspace() contents\n",
"\n",
"variables\n",
"---------\n",
"(b,gSigBkg,gSigEff,obs,ratioBkgEff,ratioSigEff,s)\n",
"\n",
"p.d.f.s\n",
"-------\n",
"RooGaussian::bkgConstraint[ x=gSigBkg mean=ratioBkgEff sigma=0.2 ] = 1\n",
"RooPoisson::countingModel[ x=obs mean=countingModel_2 ] = 0.0325554\n",
"RooProdPdf::modelWithConstraints[ countingModel * sigConstraint * bkgConstraint ] = 0.0325554\n",
"RooGaussian::sigConstraint[ x=gSigEff mean=ratioSigEff sigma=0.05 ] = 1\n",
"\n",
"functions\n",
"--------\n",
"RooAddition::countingModel_2[ countingModel_2_[s_x_ratioSigEff] + countingModel_2_[b_x_ratioBkgEff] ] = 150\n",
"RooProduct::countingModel_2_[b_x_ratioBkgEff][ b * ratioBkgEff ] = 100\n",
"RooProduct::countingModel_2_[s_x_ratioSigEff][ s * ratioSigEff ] = 50\n",
"\n"
]
}
],
"source": [
"wspace = ROOT.RooWorkspace()\n",
"wspace.factory(\n",
" \"Poisson::countingModel(obs[150,0,300], \" \"sum(s[50,0,120]*ratioSigEff[1.,0,3.],b[100]*ratioBkgEff[1.,0.,3.]))\"\n",
") # counting model\n",
"wspace.factory(\"Gaussian::sigConstraint(gSigEff[1,0,3],ratioSigEff,0.05)\") # 5% signal efficiency uncertainty\n",
"wspace.factory(\"Gaussian::bkgConstraint(gSigBkg[1,0,3],ratioBkgEff,0.2)\") # 10% background efficiency uncertainty\n",
"wspace.factory(\"PROD::modelWithConstraints(countingModel,sigConstraint,bkgConstraint)\") # product of terms\n",
"wspace.Print()\n",
"\n",
"modelWithConstraints = wspace[\"modelWithConstraints\"] # get the model\n",
"obs = wspace[\"obs\"] # get the observable\n",
"s = wspace[\"s\"] # get the signal we care about\n",
"b = wspace[\"b\"] # get the background and set it to a constant. Uncertainty included in ratioBkgEff\n",
"b.setConstant()\n",
"\n",
"ratioSigEff = wspace[\"ratioSigEff\"] # get uncertain parameter to constrain\n",
"ratioBkgEff = wspace[\"ratioBkgEff\"] # get uncertain parameter to constrain\n",
"constrainedParams = {ratioSigEff, ratioBkgEff} # need to constrain these in the fit (should change default behavior)\n",
"\n",
"gSigEff = wspace[\"gSigEff\"] # global observables for signal efficiency\n",
"gSigBkg = wspace[\"gSigBkg\"] # global obs for background efficiency\n",
"gSigEff.setConstant()\n",
"gSigBkg.setConstant()"
]
},
{
"cell_type": "markdown",
"id": "e3ad5997",
"metadata": {},
"source": [
"Create an example dataset with 160 observed events"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "8ea941cd",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:51.655878Z",
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"shell.execute_reply": "2026-05-19T20:35:51.826346Z"
}
},
"outputs": [],
"source": [
"obs.setVal(160.0)\n",
"dataOrig = ROOT.RooDataSet(\"exampleData\", \"exampleData\", {obs})\n",
"dataOrig.add(obs)"
]
},
{
"cell_type": "markdown",
"id": "c71db645",
"metadata": {},
"source": [
"not necessary"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "0836f1c2",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:51.829199Z",
"iopub.status.busy": "2026-05-19T20:35:51.829072Z",
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"shell.execute_reply": "2026-05-19T20:35:52.022869Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Minimization -- Including the following constraint terms in minimization: (sigConstraint,bkgConstraint)\n",
"[#1] INFO:Minimization -- The global observables are not defined , normalize constraints with respect to the parameters (ratioSigEff,ratioBkgEff)\n",
"[#1] INFO:Fitting -- RooAbsPdf::fitTo(modelWithConstraints) 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 957.834 μs\n",
"[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_modelWithConstraints_exampleData) Summation contains a RooNLLVar, using its error level\n",
"[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"modelWithConstraints.fitTo(dataOrig, Constrain=constrainedParams, PrintLevel=-1)"
]
},
{
"cell_type": "markdown",
"id": "70ddbd30",
"metadata": {},
"source": [
"Now let's make some confidence intervals for s, our parameter of interest"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "6a056667",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:52.025615Z",
"iopub.status.busy": "2026-05-19T20:35:52.025469Z",
"iopub.status.idle": "2026-05-19T20:35:52.221116Z",
"shell.execute_reply": "2026-05-19T20:35:52.220574Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:ObjectHandling -- RooWorkspace::import() importing dataset exampleData\n"
]
}
],
"source": [
"modelConfig = ROOT.RooStats.ModelConfig(wspace)\n",
"modelConfig.SetPdf(modelWithConstraints)\n",
"modelConfig.SetParametersOfInterest({s})\n",
"modelConfig.SetNuisanceParameters(constrainedParams)\n",
"modelConfig.SetObservables(obs)\n",
"modelConfig.SetGlobalObservables({gSigEff, gSigBkg})\n",
"modelConfig.SetName(\"ModelConfig\")\n",
"wspace.Import(modelConfig)\n",
"wspace.Import(dataOrig)\n",
"wspace.SetName(\"w\")"
]
},
{
"cell_type": "markdown",
"id": "66fd48d3",
"metadata": {},
"source": [
"wspace.writeToFile(\"rs101_ws.root\")"
]
},
{
"cell_type": "markdown",
"id": "2137c011",
"metadata": {},
"source": [
"Make sure we reference the data in the workspace from now on"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "838d2ab9",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:52.223078Z",
"iopub.status.busy": "2026-05-19T20:35:52.222948Z",
"iopub.status.idle": "2026-05-19T20:35:52.331741Z",
"shell.execute_reply": "2026-05-19T20:35:52.330749Z"
}
},
"outputs": [],
"source": [
"data = wspace[dataOrig.GetName()]"
]
},
{
"cell_type": "markdown",
"id": "094ebfbc",
"metadata": {},
"source": [
"First, let's use a Calculator based on the Profile Likelihood Ratio"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "6c9dd3d9",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:52.333379Z",
"iopub.status.busy": "2026-05-19T20:35:52.333256Z",
"iopub.status.idle": "2026-05-19T20:35:52.453266Z",
"shell.execute_reply": "2026-05-19T20:35:52.452557Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:InputArguments -- The deprecated RooFit::CloneData(1) option passed to createNLL() is ignored.\n",
"[#1] INFO:Minimization -- Including the following constraint terms in minimization: (sigConstraint,bkgConstraint)\n",
"[#1] INFO:Minimization -- The following global observables have been defined and their values are taken from the model: (gSigEff,gSigBkg)\n",
"[#1] INFO:Fitting -- RooAbsPdf::fitTo(modelWithConstraints) fixing normalization set for coefficient determination to observables in data\n",
"[#1] INFO:Fitting -- Creation of NLL object took 344.542 μs\n",
"[#0] PROGRESS:Minimization -- ProfileLikelihoodCalcultor::DoGLobalFit - find MLE \n",
"[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_modelWithConstraints_exampleData) Summation contains a RooNLLVar, using its error level\n",
"[#0] PROGRESS:Minimization -- ProfileLikelihoodCalcultor::DoMinimizeNLL - using Minuit2 / Migrad with strategy 1\n",
"[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
"[#1] INFO:Minimization -- \n",
" RooFitResult: minimized FCN value: 0.689755, estimated distance to minimum: 1.66436e-06\n",
" covariance matrix quality: Full, accurate covariance matrix\n",
" Status : MINIMIZE=0 \n",
"\n",
" Floating Parameter FinalValue +/- Error \n",
" -------------------- --------------------------\n",
" ratioBkgEff 1.0001e+00 +/- 1.99e-01\n",
" ratioSigEff 9.9991e-01 +/- 5.00e-02\n",
" s 5.9992e+01 +/- 2.32e+01\n",
"\n"
]
}
],
"source": [
"plc = ROOT.RooStats.ProfileLikelihoodCalculator(data, modelConfig)\n",
"plc.SetTestSize(0.05)\n",
"lrinterval = plc.GetInterval()"
]
},
{
"cell_type": "markdown",
"id": "2e866a74",
"metadata": {},
"source": [
"Let's make a plot"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "09e38eed",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:52.459124Z",
"iopub.status.busy": "2026-05-19T20:35:52.458991Z",
"iopub.status.idle": "2026-05-19T20:35:52.648093Z",
"shell.execute_reply": "2026-05-19T20:35:52.647040Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Minimization -- RooProfileLL::evaluate(RooEvaluatorWrapper_Profile[s]) Creating instance of MINUIT\n",
"[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_modelWithConstraints_exampleData) Summation contains a RooNLLVar, using its error level\n",
"[#1] INFO:Minimization -- RooProfileLL::evaluate(RooEvaluatorWrapper_Profile[s]) determining minimum likelihood for current configurations w.r.t all observable\n",
"[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
"[#1] INFO:Minimization -- RooProfileLL::evaluate(RooEvaluatorWrapper_Profile[s]) minimum found at (s=59.992)\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
"\n",
"[#1] INFO:Minimization -- RooProfileLL::evaluate(RooEvaluatorWrapper_Profile[s]) Creating instance of MINUIT\n",
"[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_modelWithConstraints_exampleData) Summation contains a RooNLLVar, using its error level\n",
"[#1] INFO:Minimization -- RooProfileLL::evaluate(RooEvaluatorWrapper_Profile[s]) determining minimum likelihood for current configurations w.r.t all observable\n",
"[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
"[#0] ERROR:InputArguments -- RooArgSet::checkForDup: ERROR argument with name s is already in this set\n",
"[#1] INFO:Minimization -- RooProfileLL::evaluate(RooEvaluatorWrapper_Profile[s]) minimum found at (s=60.0341)\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
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".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
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".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
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".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
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".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
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".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
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".[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n"
]
}
],
"source": [
"dataCanvas = ROOT.TCanvas(\"dataCanvas\")\n",
"dataCanvas.Divide(2, 1)\n",
"dataCanvas.cd(1)\n",
"\n",
"plotInt = ROOT.RooStats.LikelihoodIntervalPlot(lrinterval)\n",
"plotInt.SetTitle(\"Profile Likelihood Ratio and Posterior for S\")\n",
"plotInt.Draw()"
]
},
{
"cell_type": "markdown",
"id": "0632d4af",
"metadata": {},
"source": [
"Second, use a Calculator based on the Feldman Cousins technique"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "184ab34b",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:52.653308Z",
"iopub.status.busy": "2026-05-19T20:35:52.653167Z",
"iopub.status.idle": "2026-05-19T20:35:52.771092Z",
"shell.execute_reply": "2026-05-19T20:35:52.770574Z"
}
},
"outputs": [],
"source": [
"fc = ROOT.RooStats.FeldmanCousins(data, modelConfig)\n",
"fc.UseAdaptiveSampling(True)\n",
"fc.FluctuateNumDataEntries(False) # number counting analysis: dataset always has 1 entry with N events observed\n",
"fc.SetNBins(100) # number of points to test per parameter\n",
"fc.SetTestSize(0.05)"
]
},
{
"cell_type": "markdown",
"id": "cdb613f8",
"metadata": {},
"source": [
"fc.SaveBeltToFile(True) # optional"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "044002b6",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:52.773022Z",
"iopub.status.busy": "2026-05-19T20:35:52.772903Z",
"iopub.status.idle": "2026-05-19T20:35:56.084959Z",
"shell.execute_reply": "2026-05-19T20:35:56.083885Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"=== Using the following for ModelConfig ===\n",
"Observables: RooArgSet:: = (obs)\n",
"Parameters of Interest: RooArgSet:: = (s)\n",
"Nuisance Parameters: RooArgSet:: = (ratioSigEff,ratioBkgEff)\n",
"Global Observables: RooArgSet:: = (gSigEff,gSigBkg)\n",
"PDF: RooProdPdf::modelWithConstraints[ countingModel * sigConstraint * bkgConstraint ] = 0.00366119\n",
"\n",
"FeldmanCousins: ntoys per point: adaptive\n",
"FeldmanCousins: nEvents per toy will not fluctuate, will always be 1\n",
"FeldmanCousins: Model has nuisance parameters, will do profile construction\n",
"FeldmanCousins: # points to test = 100\n",
"NeymanConstruction: Prog: 1/100 total MC = 80 this test stat = 3.21178\n",
" s=0.6 ratioSigEff=0.999975 ratioBkgEff=1.43644 [-inf, 4.68588] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 2/100 total MC = 80 this test stat = 3.08184\n",
" s=1.8 ratioSigEff=1.00018 ratioBkgEff=1.42694 [-inf, 3.7189] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 3/100 total MC = 80 this test stat = 2.95515\n",
" s=3 ratioSigEff=1.00055 ratioBkgEff=1.41769 [-inf, 3.91249] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 4/100 total MC = 80 this test stat = 2.83091\n",
" s=4.2 ratioSigEff=1.00106 ratioBkgEff=1.40849 [-inf, 3.65947] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 5/100 total MC = 80 this test stat = 2.7092\n",
" s=5.4 ratioSigEff=1.00133 ratioBkgEff=1.39955 [-inf, 3.10323] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 6/100 total MC = 80 this test stat = 2.59009\n",
" s=6.6 ratioSigEff=1.00159 ratioBkgEff=1.3906 [-inf, 2.97611] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 7/100 total MC = 240 this test stat = 2.47431\n",
" s=7.8 ratioSigEff=1.00102 ratioBkgEff=1.38084 [-inf, 3.25381] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 8/100 total MC = 80 this test stat = 2.36072\n",
" s=9 ratioSigEff=1.00134 ratioBkgEff=1.37175 [-inf, 2.92353] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 9/100 total MC = 80 this test stat = 2.24982\n",
" s=10.2 ratioSigEff=1.00166 ratioBkgEff=1.36272 [-inf, 3.4069] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 10/100 total MC = 80 this test stat = 2.14164\n",
" s=11.4 ratioSigEff=1.00196 ratioBkgEff=1.35374 [-inf, 3.07011] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 11/100 total MC = 80 this test stat = 2.03623\n",
" s=12.6 ratioSigEff=1.00273 ratioBkgEff=1.34405 [-inf, 3.24614] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 12/100 total MC = 80 this test stat = 1.93333\n",
" s=13.8 ratioSigEff=1.00294 ratioBkgEff=1.33528 [-inf, 2.4475] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 13/100 total MC = 80 this test stat = 1.83331\n",
" s=15 ratioSigEff=1.0023 ratioBkgEff=1.32684 [-inf, 2.70017] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 14/100 total MC = 80 this test stat = 1.73555\n",
" s=16.2 ratioSigEff=1.00257 ratioBkgEff=1.31792 [-inf, 2.77026] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 15/100 total MC = 80 this test stat = 1.64101\n",
" s=17.4 ratioSigEff=1.00283 ratioBkgEff=1.30904 [-inf, 2.84104] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 16/100 total MC = 80 this test stat = 1.54913\n",
" s=18.6 ratioSigEff=1.00364 ratioBkgEff=1.2991 [-inf, 2.44366] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 17/100 total MC = 80 this test stat = 1.45967\n",
" s=19.8 ratioSigEff=1.0038 ratioBkgEff=1.29046 [-inf, 2.51046] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 18/100 total MC = 80 this test stat = 1.3729\n",
" s=21 ratioSigEff=1.00395 ratioBkgEff=1.28178 [-inf, 2.3088] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 19/100 total MC = 80 this test stat = 1.28897\n",
" s=22.2 ratioSigEff=1.00408 ratioBkgEff=1.27309 [-inf, 2.28612] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 20/100 total MC = 80 this test stat = 1.20763\n",
" s=23.4 ratioSigEff=1.0042 ratioBkgEff=1.26436 [-inf, 2.0941] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 21/100 total MC = 80 this test stat = 1.12898\n",
" s=24.6 ratioSigEff=1.00431 ratioBkgEff=1.25562 [-inf, 2.07266] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 22/100 total MC = 80 this test stat = 1.05305\n",
" s=25.8 ratioSigEff=1.0044 ratioBkgEff=1.24687 [-inf, 2.4819] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 23/100 total MC = 80 this test stat = 0.979804\n",
" s=27 ratioSigEff=1.00448 ratioBkgEff=1.2381 [-inf, 1.94868] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 24/100 total MC = 80 this test stat = 0.909232\n",
" s=28.2 ratioSigEff=1.00454 ratioBkgEff=1.22932 [-inf, 2.09127] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 25/100 total MC = 80 this test stat = 0.841264\n",
" s=29.4 ratioSigEff=1.00408 ratioBkgEff=1.22097 [-inf, 1.9082] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 26/100 total MC = 80 this test stat = 0.776027\n",
" s=30.6 ratioSigEff=1.00408 ratioBkgEff=1.21214 [-inf, 2.04865] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 27/100 total MC = 80 this test stat = 0.713453\n",
" s=31.8 ratioSigEff=1.00406 ratioBkgEff=1.2033 [-inf, 1.4258] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 28/100 total MC = 80 this test stat = 0.653398\n",
" s=33 ratioSigEff=1.00403 ratioBkgEff=1.19446 [-inf, 1.92614] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 29/100 total MC = 80 this test stat = 0.596234\n",
" s=34.2 ratioSigEff=1.00399 ratioBkgEff=1.18562 [-inf, 1.53064] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 30/100 total MC = 80 this test stat = 0.541678\n",
" s=35.4 ratioSigEff=1.00393 ratioBkgEff=1.17679 [-inf, 1.65725] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 31/100 total MC = 80 this test stat = 0.489749\n",
" s=36.6 ratioSigEff=1.00386 ratioBkgEff=1.16795 [-inf, 1.42567] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 32/100 total MC = 80 this test stat = 0.440357\n",
" s=37.8 ratioSigEff=1.00378 ratioBkgEff=1.15913 [-inf, 1.40855] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 33/100 total MC = 80 this test stat = 0.393811\n",
" s=39 ratioSigEff=1.00369 ratioBkgEff=1.15032 [-inf, 1.2593] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 34/100 total MC = 80 this test stat = 0.349798\n",
" s=40.2 ratioSigEff=1.00358 ratioBkgEff=1.14152 [-inf, 1.30825] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 35/100 total MC = 80 this test stat = 0.30842\n",
" s=41.4 ratioSigEff=1.00347 ratioBkgEff=1.13274 [-inf, 0.874179] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 36/100 total MC = 80 this test stat = 0.269673\n",
" s=42.6 ratioSigEff=1.00334 ratioBkgEff=1.12397 [-inf, 1.14949] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 37/100 total MC = 80 this test stat = 0.233551\n",
" s=43.8 ratioSigEff=1.00319 ratioBkgEff=1.11574 [-inf, 1.07403] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 38/100 total MC = 80 this test stat = 0.200042\n",
" s=45 ratioSigEff=1.00303 ratioBkgEff=1.10705 [-inf, 1.30848] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 39/100 total MC = 80 this test stat = 0.169154\n",
" s=46.2 ratioSigEff=1.00285 ratioBkgEff=1.09838 [-inf, 0.987229] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 40/100 total MC = 80 this test stat = 0.140876\n",
" s=47.4 ratioSigEff=1.00267 ratioBkgEff=1.08972 [-inf, 0.917557] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 41/100 total MC = 80 this test stat = 0.115202\n",
" s=48.6 ratioSigEff=1.00247 ratioBkgEff=1.08109 [-inf, 0.850481] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 42/100 total MC = 80 this test stat = 0.0921253\n",
" s=49.8 ratioSigEff=1.00226 ratioBkgEff=1.07247 [-inf, 0.891152] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 43/100 total MC = 80 this test stat = 0.0716406\n",
" s=51 ratioSigEff=1.00204 ratioBkgEff=1.06387 [-inf, 1.04631] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 44/100 total MC = 80 this test stat = 0.0537413\n",
" s=52.2 ratioSigEff=1.00181 ratioBkgEff=1.05529 [-inf, 0.574131] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 45/100 total MC = 80 this test stat = 0.0384208\n",
" s=53.4 ratioSigEff=1.00156 ratioBkgEff=1.04672 [-inf, 0.749926] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 46/100 total MC = 80 this test stat = 0.0256726\n",
" s=54.6 ratioSigEff=1.00131 ratioBkgEff=1.03818 [-inf, 0.839739] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 47/100 total MC = 80 this test stat = 0.0154896\n",
" s=55.8 ratioSigEff=1.00104 ratioBkgEff=1.02966 [-inf, 0.715031] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 48/100 total MC = 80 this test stat = 0.00786498\n",
" s=57 ratioSigEff=1.00075 ratioBkgEff=1.02116 [-inf, 0.574092] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 49/100 total MC = 80 this test stat = 0.00303984\n",
" s=58.2 ratioSigEff=1.00152 ratioBkgEff=1.01164 [-inf, 0.731975] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 50/100 total MC = 80 this test stat = 0.000296144\n",
" s=59.4 ratioSigEff=1.00057 ratioBkgEff=1.0038 [-inf, 0.692058] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 51/100 total MC = 80 this test stat = 0.000277433\n",
" s=60.6 ratioSigEff=0.999598 ratioBkgEff=0.995997 [-inf, 0.645915] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 52/100 total MC = 80 this test stat = 0.00297545\n",
" s=61.8 ratioSigEff=0.998613 ratioBkgEff=0.988241 [-inf, 0.513395] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 53/100 total MC = 80 this test stat = 0.00784733\n",
" s=63 ratioSigEff=0.999173 ratioBkgEff=0.978981 [-inf, 0.477501] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 54/100 total MC = 80 this test stat = 0.0154172\n",
" s=64.2 ratioSigEff=0.998822 ratioBkgEff=0.970614 [-inf, 0.721422] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 55/100 total MC = 80 this test stat = 0.0254769\n",
" s=65.4 ratioSigEff=0.998461 ratioBkgEff=0.962271 [-inf, 0.678264] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 56/100 total MC = 80 this test stat = 0.0380399\n",
" s=66.6 ratioSigEff=0.998087 ratioBkgEff=0.953952 [-inf, 0.636603] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 57/100 total MC = 80 this test stat = 0.0530874\n",
" s=67.8 ratioSigEff=0.997703 ratioBkgEff=0.945657 [-inf, 0.596425] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 58/100 total MC = 80 this test stat = 0.0706058\n",
" s=69 ratioSigEff=0.997308 ratioBkgEff=0.937388 [-inf, 0.70275] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 59/100 total MC = 80 this test stat = 0.0905894\n",
" s=70.2 ratioSigEff=0.996902 ratioBkgEff=0.929144 [-inf, 0.93255] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 60/100 total MC = 80 this test stat = 0.11303\n",
" s=71.4 ratioSigEff=0.996485 ratioBkgEff=0.920926 [-inf, 1.06482] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 61/100 total MC = 80 this test stat = 0.137918\n",
" s=72.6 ratioSigEff=0.996057 ratioBkgEff=0.912734 [-inf, 0.780337] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 62/100 total MC = 80 this test stat = 0.165246\n",
" s=73.8 ratioSigEff=0.995619 ratioBkgEff=0.904568 [-inf, 0.684448] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 63/100 total MC = 80 this test stat = 0.195001\n",
" s=75 ratioSigEff=0.995169 ratioBkgEff=0.89643 [-inf, 1.03027] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 64/100 total MC = 80 this test stat = 0.227176\n",
" s=76.2 ratioSigEff=0.99471 ratioBkgEff=0.888318 [-inf, 0.978263] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 65/100 total MC = 80 this test stat = 0.261776\n",
" s=77.4 ratioSigEff=0.99424 ratioBkgEff=0.880234 [-inf, 1.11256] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 66/100 total MC = 80 this test stat = 0.298772\n",
" s=78.6 ratioSigEff=0.993759 ratioBkgEff=0.872179 [-inf, 1.18776] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 67/100 total MC = 80 this test stat = 0.338144\n",
" s=79.8 ratioSigEff=0.993269 ratioBkgEff=0.864151 [-inf, 1.48101] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 68/100 total MC = 80 this test stat = 0.379914\n",
" s=81 ratioSigEff=0.992768 ratioBkgEff=0.856152 [-inf, 1.56755] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 69/100 total MC = 80 this test stat = 0.424071\n",
" s=82.2 ratioSigEff=0.992257 ratioBkgEff=0.848182 [-inf, 1.21708] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 70/100 total MC = 80 this test stat = 0.470561\n",
" s=83.4 ratioSigEff=0.991736 ratioBkgEff=0.840241 [-inf, 1.43809] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 71/100 total MC = 80 this test stat = 0.519388\n",
" s=84.6 ratioSigEff=0.991205 ratioBkgEff=0.83233 [-inf, 1.84094] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 72/100 total MC = 80 this test stat = 0.570571\n",
" s=85.8 ratioSigEff=0.990664 ratioBkgEff=0.824449 [-inf, 1.31514] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 73/100 total MC = 80 this test stat = 0.624119\n",
" s=87 ratioSigEff=0.990113 ratioBkgEff=0.816598 [-inf, 1.18918] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 74/100 total MC = 80 this test stat = 0.679954\n",
" s=88.2 ratioSigEff=0.989553 ratioBkgEff=0.808777 [-inf, 1.33503] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 75/100 total MC = 80 this test stat = 0.738105\n",
" s=89.4 ratioSigEff=0.988983 ratioBkgEff=0.800988 [-inf, 1.56456] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 76/100 total MC = 80 this test stat = 0.798548\n",
" s=90.6 ratioSigEff=0.988403 ratioBkgEff=0.79323 [-inf, 1.49965] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 77/100 total MC = 80 this test stat = 0.861306\n",
" s=91.8 ratioSigEff=0.987814 ratioBkgEff=0.785503 [-inf, 1.66275] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 78/100 total MC = 80 this test stat = 0.926319\n",
" s=93 ratioSigEff=0.987216 ratioBkgEff=0.777809 [-inf, 1.44643] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 79/100 total MC = 80 this test stat = 0.993583\n",
" s=94.2 ratioSigEff=0.986608 ratioBkgEff=0.770146 [-inf, 2.19051] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 80/100 total MC = 80 this test stat = 1.06308\n",
" s=95.4 ratioSigEff=0.985991 ratioBkgEff=0.762516 [-inf, 1.54054] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 81/100 total MC = 80 this test stat = 1.13458\n",
" s=96.6 ratioSigEff=0.985365 ratioBkgEff=0.754919 [-inf, 1.86615] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 82/100 total MC = 80 this test stat = 1.20859\n",
" s=97.8 ratioSigEff=0.98473 ratioBkgEff=0.747355 [-inf, 2.40993] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 83/100 total MC = 80 this test stat = 1.28501\n",
" s=99 ratioSigEff=0.984086 ratioBkgEff=0.739824 [-inf, 2.32724] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 84/100 total MC = 80 this test stat = 1.36342\n",
" s=100.2 ratioSigEff=0.983433 ratioBkgEff=0.732327 [-inf, 2.43281] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 85/100 total MC = 80 this test stat = 1.44405\n",
" s=101.4 ratioSigEff=0.982771 ratioBkgEff=0.724864 [-inf, 2.44403] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 86/100 total MC = 80 this test stat = 1.52687\n",
" s=102.6 ratioSigEff=0.982101 ratioBkgEff=0.717436 [-inf, 2.09032] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 87/100 total MC = 80 this test stat = 1.61182\n",
" s=103.8 ratioSigEff=0.981422 ratioBkgEff=0.710041 [-inf, 2.76135] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 88/100 total MC = 80 this test stat = 1.69896\n",
" s=105 ratioSigEff=0.980734 ratioBkgEff=0.702682 [-inf, 2.38331] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 89/100 total MC = 80 this test stat = 1.78823\n",
" s=106.2 ratioSigEff=0.980038 ratioBkgEff=0.695358 [-inf, 2.39444] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 90/100 total MC = 80 this test stat = 1.87929\n",
" s=107.4 ratioSigEff=0.979333 ratioBkgEff=0.688069 [-inf, 2.89798] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 91/100 total MC = 80 this test stat = 1.97313\n",
" s=108.6 ratioSigEff=0.97862 ratioBkgEff=0.680815 [-inf, 3.1204] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 92/100 total MC = 80 this test stat = 2.06825\n",
" s=109.8 ratioSigEff=0.977383 ratioBkgEff=0.67064 [-inf, 3.13169] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 93/100 total MC = 80 this test stat = 2.16592\n",
" s=111 ratioSigEff=0.976625 ratioBkgEff=0.663285 [-inf, 2.93195] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 94/100 total MC = 80 this test stat = 2.26567\n",
" s=112.2 ratioSigEff=0.975857 ratioBkgEff=0.655961 [-inf, 2.54424] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 95/100 total MC = 80 this test stat = 2.36747\n",
" s=113.4 ratioSigEff=0.975049 ratioBkgEff=0.648488 [-inf, 3.05911] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 96/100 total MC = 80 this test stat = 2.47112\n",
" s=114.6 ratioSigEff=0.97426 ratioBkgEff=0.641205 [-inf, 2.96555] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 97/100 total MC = 80 this test stat = 2.57725\n",
" s=115.8 ratioSigEff=0.973462 ratioBkgEff=0.633952 [-inf, 3.5205] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 98/100 total MC = 240 this test stat = 2.68512\n",
" s=117 ratioSigEff=0.972655 ratioBkgEff=0.626728 [-inf, 3.19934] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 99/100 total MC = 80 this test stat = 2.79507\n",
" s=118.2 ratioSigEff=0.971839 ratioBkgEff=0.619534 [-inf, 3.77433] in interval = 1\n",
"\n",
"NeymanConstruction: Prog: 100/100 total MC = 80 this test stat = 2.90706\n",
" s=119.4 ratioSigEff=0.971014 ratioBkgEff=0.61237 [-inf, 3.66884] in interval = 1\n",
"\n",
"[#1] INFO:Eval -- 100 points in interval\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"[#1] INFO:Minimization -- Including the following constraint terms in minimization: (sigConstraint,bkgConstraint)\n",
"[#1] INFO:Minimization -- The global observables are not defined , normalize constraints with respect to the parameters (b,ratioBkgEff,ratioSigEff,s)\n",
"[#1] INFO:Fitting -- RooAbsPdf::fitTo(modelWithConstraints) fixing normalization set for coefficient determination to observables in data\n",
"[#1] INFO:Fitting -- Creation of NLL object took 325.192 μs\n",
"[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_modelWithConstraints_exampleData) Summation contains a RooNLLVar, using its error level\n",
"[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n"
]
}
],
"source": [
"fcint = fc.GetInterval()\n",
"\n",
"fit = modelWithConstraints.fitTo(data, Save=True, PrintLevel=-1)"
]
},
{
"cell_type": "markdown",
"id": "8d5f36fd",
"metadata": {},
"source": [
"Third, use a Calculator based on Markov Chain monte carlo\n",
"Before configuring the calculator, let's make a ProposalFunction\n",
"that will achieve a high acceptance rate"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "0d7d8e75",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:56.093003Z",
"iopub.status.busy": "2026-05-19T20:35:56.092814Z",
"iopub.status.idle": "2026-05-19T20:35:57.141542Z",
"shell.execute_reply": "2026-05-19T20:35:57.140804Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Minimization -- Including the following constraint terms in minimization: (sigConstraint,bkgConstraint)\n",
"[#1] INFO:Minimization -- The following global observables have been defined and their values are taken from the model: (gSigEff,gSigBkg)\n",
"[#1] INFO:Fitting -- RooAbsPdf::fitTo(modelWithConstraints) fixing normalization set for coefficient determination to observables in data\n",
"[#1] INFO:Fitting -- Creation of NLL object took 337.811 μs\n",
"Metropolis-Hastings progress: ....................................................................................................\n",
"[#1] INFO:Eval -- Proposal acceptance rate: 48.36%\n",
"[#1] INFO:Eval -- Number of steps in chain: 9672\n"
]
}
],
"source": [
"ph = ROOT.RooStats.ProposalHelper()\n",
"ph.SetVariables(fit.floatParsFinal())\n",
"ph.SetCovMatrix(fit.covarianceMatrix())\n",
"ph.SetUpdateProposalParameters(True)\n",
"ph.SetCacheSize(100)\n",
"pdfProp = ph.GetProposalFunction()\n",
"\n",
"mc = ROOT.RooStats.MCMCCalculator(data, modelConfig)\n",
"mc.SetNumIters(20000) # steps to propose in the chain\n",
"mc.SetTestSize(0.05) # 95% CL\n",
"mc.SetNumBurnInSteps(40) # ignore first N steps in chain as \"burn in\"\n",
"mc.SetProposalFunction(pdfProp)\n",
"mc.SetLeftSideTailFraction(0.5) # find a \"central\" interval\n",
"mcInt = mc.GetInterval()"
]
},
{
"cell_type": "markdown",
"id": "8c67d6e9",
"metadata": {},
"source": [
"Get Lower and Upper limits from Profile Calculator"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "e659b3cd",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:57.143060Z",
"iopub.status.busy": "2026-05-19T20:35:57.142939Z",
"iopub.status.idle": "2026-05-19T20:35:57.255219Z",
"shell.execute_reply": "2026-05-19T20:35:57.254495Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Profile lower limit on s = 13.949699331790107\n",
"Profile upper limit on s = 107.9503135662626\n"
]
}
],
"source": [
"print(\"Profile lower limit on s = \", lrinterval.LowerLimit(s))\n",
"print(\"Profile upper limit on s = \", lrinterval.UpperLimit(s))"
]
},
{
"cell_type": "markdown",
"id": "80820b8e",
"metadata": {},
"source": [
"Get Lower and Upper limits from FeldmanCousins with profile construction"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "a3204005",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:57.256780Z",
"iopub.status.busy": "2026-05-19T20:35:57.256653Z",
"iopub.status.idle": "2026-05-19T20:35:57.469450Z",
"shell.execute_reply": "2026-05-19T20:35:57.468969Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"FC lower limit on s = 0.6\n",
"FC upper limit on s = 119.39999999999999\n"
]
},
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"
\n",
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"if fcint:\n",
" fcul = fcint.UpperLimit(s)\n",
" fcll = fcint.LowerLimit(s)\n",
" print(\"FC lower limit on s = \", fcll)\n",
" print(\"FC upper limit on s = \", fcul)\n",
" fcllLine = ROOT.TLine(fcll, 0, fcll, 1)\n",
" fculLine = ROOT.TLine(fcul, 0, fcul, 1)\n",
" fcllLine.SetLineColor(\"kRed\")\n",
" fculLine.SetLineColor(\"kRed\")\n",
" fcllLine.Draw(\"same\")\n",
" fculLine.Draw(\"same\")\n",
" dataCanvas.Update()"
]
},
{
"cell_type": "markdown",
"id": "32aa1097",
"metadata": {},
"source": [
"Plot MCMC interval and print some statistics"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "6add1341",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:57.471256Z",
"iopub.status.busy": "2026-05-19T20:35:57.471135Z",
"iopub.status.idle": "2026-05-19T20:35:57.601922Z",
"shell.execute_reply": "2026-05-19T20:35:57.601278Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"MCMC lower limit on s = 19.047442766582563\n",
"MCMC upper limit on s = 102.7400864812879\n",
"MCMC Actual confidence level: 0.9500150557061127\n"
]
}
],
"source": [
"mcPlot = ROOT.RooStats.MCMCIntervalPlot(mcInt)\n",
"mcPlot.SetLineColor(\"kMagenta\")\n",
"mcPlot.SetLineWidth(2)\n",
"mcPlot.Draw(\"same\")\n",
"\n",
"mcul = mcInt.UpperLimit(s)\n",
"mcll = mcInt.LowerLimit(s)\n",
"print(\"MCMC lower limit on s = \", mcll)\n",
"print(\"MCMC upper limit on s = \", mcul)\n",
"print(\"MCMC Actual confidence level: \", mcInt.GetActualConfidenceLevel())"
]
},
{
"cell_type": "markdown",
"id": "d0e8fc3a",
"metadata": {},
"source": [
"3-d plot of the parameter points"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "0848a317",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:57.603888Z",
"iopub.status.busy": "2026-05-19T20:35:57.603768Z",
"iopub.status.idle": "2026-05-19T20:35:57.707765Z",
"shell.execute_reply": "2026-05-19T20:35:57.707127Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dataCanvas.cd(2)"
]
},
{
"cell_type": "markdown",
"id": "e7e2ee22",
"metadata": {},
"source": [
"also plot the points in the markov chain"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "d99d08b5",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:57.709740Z",
"iopub.status.busy": "2026-05-19T20:35:57.709592Z",
"iopub.status.idle": "2026-05-19T20:35:57.862740Z",
"shell.execute_reply": "2026-05-19T20:35:57.862084Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"plotting the chain data - nentries = 9672\n"
]
},
{
"data": {
"text/plain": [
"9672"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"chainData = mcInt.GetChainAsDataSet()\n",
"\n",
"print(\"plotting the chain data - nentries = \", chainData.numEntries())\n",
"chain = ROOT.RooStats.GetAsTTree(\"chainTreeData\", \"chainTreeData\", chainData)\n",
"chain.SetMarkerStyle(6)\n",
"chain.SetMarkerColor(\"kRed\")\n",
"\n",
"chain.Draw(\"s:ratioSigEff:ratioBkgEff\", \"nll_MarkovChain_local_\", \"box\") # 3-d box proportional to posterior"
]
},
{
"cell_type": "markdown",
"id": "047e4be9",
"metadata": {},
"source": [
"the points used in the profile construction"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "ea26494e",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:57.864687Z",
"iopub.status.busy": "2026-05-19T20:35:57.864556Z",
"iopub.status.idle": "2026-05-19T20:35:57.987980Z",
"shell.execute_reply": "2026-05-19T20:35:57.987639Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"plotting the scanned points used in the frequentist construction - npoints = 100\n"
]
}
],
"source": [
"parScanData = fc.GetPointsToScan()\n",
"print(\"plotting the scanned points used in the frequentist construction - npoints = \", parScanData.numEntries())\n",
"\n",
"gr = ROOT.TGraph2D(parScanData.numEntries())\n",
"for ievt in range(parScanData.numEntries()):\n",
" evt = parScanData.get(ievt)\n",
" x = evt.getRealValue(\"ratioBkgEff\")\n",
" y = evt.getRealValue(\"ratioSigEff\")\n",
" z = evt.getRealValue(\"s\")\n",
" gr.SetPoint(ievt, x, y, z)\n",
"\n",
"gr.SetMarkerStyle(24)\n",
"gr.Draw(\"P SAME\")"
]
},
{
"cell_type": "markdown",
"id": "aa526895",
"metadata": {},
"source": [
"print timing info"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "d0aa278e",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:57.997456Z",
"iopub.status.busy": "2026-05-19T20:35:57.997330Z",
"iopub.status.idle": "2026-05-19T20:35:58.204033Z",
"shell.execute_reply": "2026-05-19T20:35:58.203636Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Real time 0:00:06, CP time 4.960\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rs101_limitexample.png has been created\n"
]
}
],
"source": [
"t.Stop()\n",
"t.Print()\n",
"\n",
"dataCanvas.SaveAs(\"rs101_limitexample.png\")"
]
},
{
"cell_type": "markdown",
"id": "3c77e0e3",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "43bd1db4",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:35:58.215057Z",
"iopub.status.busy": "2026-05-19T20:35:58.214911Z",
"iopub.status.idle": "2026-05-19T20:35:58.333474Z",
"shell.execute_reply": "2026-05-19T20:35:58.332828Z"
}
},
"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
}