double countingExperiment95CLUpperLimit (int nObserved, double bkgMean, double bkgSigma, int nToys=500) {
// expect nothing beyond 5 sigma
double bkgMaxExpected = bkgMean+5*bkgSigma; // 5 sigma
double signalMaxExpected = nObserved+5*sqrt(double(nObserved))-bkgMean+5*bkgSigma;
// variables
RooRealVar signal ("signal", "signal", 0, 0, signalMaxExpected);
RooRealVar bkg ("bkg", "bkg", bkgMean, 0, bkgMaxExpected);
RooRealVar flatUnit ("flatUnit","flatUnit",0.,1.);
// sets
RooArgSet nuisPar (bkg);
RooArgSet poi (signal);
// constants
RooRealVar bkgMeanVar ("bkgMean", "bkgMean", bkgMean);
RooRealVar bkgSigmaVar ("bkgSigma", "bkgSigma", bkgSigma);
// PDFs
RooUniform signalPdf ("signalPdf","signalPdf",flatUnit);
RooUniform backgroundPdf ("backgroundPdf","backgroundPdf",flatUnit);
RooAddPdf modelPdf ("model","model",RooArgList(signalPdf,backgroundPdf),RooArgList(signal,bkg));
RooExtendPdf modelBkgPdf ("modelBkg","modelBkg",backgroundPdf,bkg);
RooGaussian priorBkgPdf ("priorBkg","priorBkg",bkg,bkgMeanVar,bkgSigmaVar);
RooDataSet* data = modelPdf.generate(flatUnit, nObserved);
HybridCalculator hc(*data, modelPdf, modelBkgPdf, &nuisPar, &priorBkgPdf);
hc.SetTestStatistic(2); // # of events
hc.SetNumberOfToys(nToys);
hc.UseNuisance(true);
HypoTestInverter myInverter(hc,signal);
double targetP = 0.05; // 95% C.L.
myInverter.RunAutoScan(0, signalMaxExpected, targetP, 0.1*targetP);
HypoTestInverterResult* results = myInverter.GetInterval();
results->SetConfidenceLevel (1-2.*targetP);
double upperLimit = results->UpperLimit();
delete data;
// delete results;
return upperLimit;
}
