void OneSidedFrequentistUpperLimitWithBands(const char* infile = "", const char* workspaceName = "combined", const char* modelConfigName = "ModelConfig", const char* dataName = "obsData") { double confidenceLevel=0.95; int nPointsToScan = 20; int nToyMC = 200; // ------------------------------------------------------- // First part is just to access a user-defined file // or create the standard example file if it doesn't exist const char* filename = ""; if (!strcmp(infile,"")) { filename = "results/example_combined_GaussExample_model.root"; bool fileExist = !gSystem->AccessPathName(filename); // note opposite return code // if file does not exists generate with histfactory if (!fileExist) { #ifdef _WIN32 cout << "HistFactory file cannot be generated on Windows - exit" << endl; return; #endif // Normally this would be run on the command line cout <<"will run standard hist2workspace example"<<endl; gROOT->ProcessLine(".! prepareHistFactory ."); gROOT->ProcessLine(".! hist2workspace config/example.xml"); cout <<"\n\n---------------------"<<endl; cout <<"Done creating example input"<<endl; cout <<"---------------------\n\n"<<endl; } } else filename = infile; // Try to open the file TFile *file = TFile::Open(filename); // if input file was specified byt not found, quit if(!file ){ cout <<"StandardRooStatsDemoMacro: Input file " << filename << " is not found" << endl; return; } // ------------------------------------------------------- // Now get the data and workspace // get the workspace out of the file RooWorkspace* w = (RooWorkspace*) file->Get(workspaceName); if(!w){ cout <<"workspace not found" << endl; return; } // get the modelConfig out of the file ModelConfig* mc = (ModelConfig*) w->obj(modelConfigName); // get the modelConfig out of the file RooAbsData* data = w->data(dataName); // make sure ingredients are found if(!data || !mc){ w->Print(); cout << "data or ModelConfig was not found" <<endl; return; } // ------------------------------------------------------- // Now get the POI for convenience // you may want to adjust the range of your POI RooRealVar* firstPOI = (RooRealVar*) mc->GetParametersOfInterest()->first(); /* firstPOI->setMin(0);*/ /* firstPOI->setMax(10);*/ // -------------------------------------------- // Create and use the FeldmanCousins tool // to find and plot the 95% confidence interval // on the parameter of interest as specified // in the model config // REMEMBER, we will change the test statistic // so this is NOT a Feldman-Cousins interval FeldmanCousins fc(*data,*mc); fc.SetConfidenceLevel(confidenceLevel); /* fc.AdditionalNToysFactor(0.25); // degrade/improve sampling that defines confidence belt*/ /* fc.UseAdaptiveSampling(true); // speed it up a bit, don't use for expected limits*/ fc.SetNBins(nPointsToScan); // set how many points per parameter of interest to scan fc.CreateConfBelt(true); // save the information in the belt for plotting // ------------------------------------------------------- // Feldman-Cousins is a unified limit by definition // but the tool takes care of a few things for us like which values // of the nuisance parameters should be used to generate toys. // so let's just change the test statistic and realize this is // no longer "Feldman-Cousins" but is a fully frequentist Neyman-Construction. /* ProfileLikelihoodTestStatModified onesided(*mc->GetPdf());*/ /* fc.GetTestStatSampler()->SetTestStatistic(&onesided);*/ /* ((ToyMCSampler*) fc.GetTestStatSampler())->SetGenerateBinned(true); */ ToyMCSampler* toymcsampler = (ToyMCSampler*) fc.GetTestStatSampler(); ProfileLikelihoodTestStat* testStat = dynamic_cast<ProfileLikelihoodTestStat*>(toymcsampler->GetTestStatistic()); testStat->SetOneSided(true); // Since this tool needs to throw toy MC the PDF needs to be // extended or the tool needs to know how many entries in a dataset // per pseudo experiment. // In the 'number counting form' where the entries in the dataset // are counts, and not values of discriminating variables, the // datasets typically only have one entry and the PDF is not // extended. if(!mc->GetPdf()->canBeExtended()){ if(data->numEntries()==1) fc.FluctuateNumDataEntries(false); else cout <<"Not sure what to do about this model" <<endl; } // We can use PROOF to speed things along in parallel // However, the test statistic has to be installed on the workers // so either turn off PROOF or include the modified test statistic // in your `$ROOTSYS/roofit/roostats/inc` directory, // add the additional line to the LinkDef.h file, // and recompile root. if (useProof) { ProofConfig pc(*w, nworkers, "", false); toymcsampler->SetProofConfig(&pc); // enable proof } if(mc->GetGlobalObservables()){ cout << "will use global observables for unconditional ensemble"<<endl; mc->GetGlobalObservables()->Print(); toymcsampler->SetGlobalObservables(*mc->GetGlobalObservables()); } // Now get the interval PointSetInterval* interval = fc.GetInterval(); ConfidenceBelt* belt = fc.GetConfidenceBelt(); // print out the interval on the first Parameter of Interest cout << "\n95% interval on " <<firstPOI->GetName()<<" is : ["<< interval->LowerLimit(*firstPOI) << ", "<< interval->UpperLimit(*firstPOI) <<"] "<<endl; // get observed UL and value of test statistic evaluated there RooArgSet tmpPOI(*firstPOI); double observedUL = interval->UpperLimit(*firstPOI); firstPOI->setVal(observedUL); double obsTSatObsUL = fc.GetTestStatSampler()->EvaluateTestStatistic(*data,tmpPOI); // Ask the calculator which points were scanned RooDataSet* parameterScan = (RooDataSet*) fc.GetPointsToScan(); RooArgSet* tmpPoint; // make a histogram of parameter vs. threshold TH1F* histOfThresholds = new TH1F("histOfThresholds","", parameterScan->numEntries(), firstPOI->getMin(), firstPOI->getMax()); histOfThresholds->GetXaxis()->SetTitle(firstPOI->GetName()); histOfThresholds->GetYaxis()->SetTitle("Threshold"); // loop through the points that were tested and ask confidence belt // what the upper/lower thresholds were. // For FeldmanCousins, the lower cut off is always 0 for(Int_t i=0; i<parameterScan->numEntries(); ++i){ tmpPoint = (RooArgSet*) parameterScan->get(i)->clone("temp"); //cout <<"get threshold"<<endl; double arMax = belt->GetAcceptanceRegionMax(*tmpPoint); double poiVal = tmpPoint->getRealValue(firstPOI->GetName()) ; histOfThresholds->Fill(poiVal,arMax); } TCanvas* c1 = new TCanvas(); c1->Divide(2); c1->cd(1); histOfThresholds->SetMinimum(0); histOfThresholds->Draw(); c1->cd(2); // ------------------------------------------------------- // Now we generate the expected bands and power-constraint // First: find parameter point for mu=0, with conditional MLEs for nuisance parameters RooAbsReal* nll = mc->GetPdf()->createNLL(*data); RooAbsReal* profile = nll->createProfile(*mc->GetParametersOfInterest()); firstPOI->setVal(0.); profile->getVal(); // this will do fit and set nuisance parameters to profiled values RooArgSet* poiAndNuisance = new RooArgSet(); if(mc->GetNuisanceParameters()) poiAndNuisance->add(*mc->GetNuisanceParameters()); poiAndNuisance->add(*mc->GetParametersOfInterest()); w->saveSnapshot("paramsToGenerateData",*poiAndNuisance); RooArgSet* paramsToGenerateData = (RooArgSet*) poiAndNuisance->snapshot(); cout << "\nWill use these parameter points to generate pseudo data for bkg only" << endl; paramsToGenerateData->Print("v"); RooArgSet unconditionalObs; unconditionalObs.add(*mc->GetObservables()); unconditionalObs.add(*mc->GetGlobalObservables()); // comment this out for the original conditional ensemble double CLb=0; double CLbinclusive=0; // Now we generate background only and find distribution of upper limits TH1F* histOfUL = new TH1F("histOfUL","",100,0,firstPOI->getMax()); histOfUL->GetXaxis()->SetTitle("Upper Limit (background only)"); histOfUL->GetYaxis()->SetTitle("Entries"); for(int imc=0; imc<nToyMC; ++imc){ // set parameters back to values for generating pseudo data // cout << "\n get current nuis, set vals, print again" << endl; w->loadSnapshot("paramsToGenerateData"); // poiAndNuisance->Print("v"); RooDataSet* toyData = 0; // now generate a toy dataset if(!mc->GetPdf()->canBeExtended()){ if(data->numEntries()==1) toyData = mc->GetPdf()->generate(*mc->GetObservables(),1); else cout <<"Not sure what to do about this model" <<endl; } else{ // cout << "generating extended dataset"<<endl; toyData = mc->GetPdf()->generate(*mc->GetObservables(),Extended()); } // generate global observables // need to be careful for simpdf // RooDataSet* globalData = mc->GetPdf()->generate(*mc->GetGlobalObservables(),1); RooSimultaneous* simPdf = dynamic_cast<RooSimultaneous*>(mc->GetPdf()); if(!simPdf){ RooDataSet *one = mc->GetPdf()->generate(*mc->GetGlobalObservables(), 1); const RooArgSet *values = one->get(); RooArgSet *allVars = mc->GetPdf()->getVariables(); *allVars = *values; delete allVars; delete values; delete one; } else { //try fix for sim pdf TIterator* iter = simPdf->indexCat().typeIterator() ; RooCatType* tt = NULL; while((tt=(RooCatType*) iter->Next())) { // Get pdf associated with state from simpdf RooAbsPdf* pdftmp = simPdf->getPdf(tt->GetName()) ; // Generate only global variables defined by the pdf associated with this state RooArgSet* globtmp = pdftmp->getObservables(*mc->GetGlobalObservables()) ; RooDataSet* tmp = pdftmp->generate(*globtmp,1) ; // Transfer values to output placeholder *globtmp = *tmp->get(0) ; // Cleanup delete globtmp ; delete tmp ; } } // globalData->Print("v"); // unconditionalObs = *globalData->get(); // mc->GetGlobalObservables()->Print("v"); // delete globalData; // cout << "toy data = " << endl; // toyData->get()->Print("v"); // get test stat at observed UL in observed data firstPOI->setVal(observedUL); double toyTSatObsUL = fc.GetTestStatSampler()->EvaluateTestStatistic(*toyData,tmpPOI); // toyData->get()->Print("v"); // cout <<"obsTSatObsUL " <<obsTSatObsUL << "toyTS " << toyTSatObsUL << endl; if(obsTSatObsUL < toyTSatObsUL) // not sure about <= part yet CLb+= (1.)/nToyMC; if(obsTSatObsUL <= toyTSatObsUL) // not sure about <= part yet CLbinclusive+= (1.)/nToyMC; // loop over points in belt to find upper limit for this toy data double thisUL = 0; for(Int_t i=0; i<parameterScan->numEntries(); ++i){ tmpPoint = (RooArgSet*) parameterScan->get(i)->clone("temp"); double arMax = belt->GetAcceptanceRegionMax(*tmpPoint); firstPOI->setVal( tmpPoint->getRealValue(firstPOI->GetName()) ); // double thisTS = profile->getVal(); double thisTS = fc.GetTestStatSampler()->EvaluateTestStatistic(*toyData,tmpPOI); // cout << "poi = " << firstPOI->getVal() // << " max is " << arMax << " this profile = " << thisTS << endl; // cout << "thisTS = " << thisTS<<endl; if(thisTS<=arMax){ thisUL = firstPOI->getVal(); } else{ break; } } /* // loop over points in belt to find upper limit for this toy data double thisUL = 0; for(Int_t i=0; i<histOfThresholds->GetNbinsX(); ++i){ tmpPoint = (RooArgSet*) parameterScan->get(i)->clone("temp"); cout <<"---------------- "<<i<<endl; tmpPoint->Print("v"); cout << "from hist " << histOfThresholds->GetBinCenter(i+1) <<endl; double arMax = histOfThresholds->GetBinContent(i+1); // cout << " threhold from Hist = aMax " << arMax<<endl; // double arMax2 = belt->GetAcceptanceRegionMax(*tmpPoint); // cout << "from scan arMax2 = "<< arMax2 << endl; // not the same due to TH1F not TH1D // cout << "scan - hist" << arMax2-arMax << endl; firstPOI->setVal( histOfThresholds->GetBinCenter(i+1)); // double thisTS = profile->getVal(); double thisTS = fc.GetTestStatSampler()->EvaluateTestStatistic(*toyData,tmpPOI); // cout << "poi = " << firstPOI->getVal() // << " max is " << arMax << " this profile = " << thisTS << endl; // cout << "thisTS = " << thisTS<<endl; // NOTE: need to add a small epsilon term for single precision vs. double precision if(thisTS<=arMax + 1e-7){ thisUL = firstPOI->getVal(); } else{ break; } } */ histOfUL->Fill(thisUL); // for few events, data is often the same, and UL is often the same // cout << "thisUL = " << thisUL<<endl; delete toyData; } histOfUL->Draw(); c1->SaveAs("one-sided_upper_limit_output.pdf"); // if you want to see a plot of the sampling distribution for a particular scan point: /* SamplingDistPlot sampPlot; int indexInScan = 0; tmpPoint = (RooArgSet*) parameterScan->get(indexInScan)->clone("temp"); firstPOI->setVal( tmpPoint->getRealValue(firstPOI->GetName()) ); toymcsampler->SetParametersForTestStat(tmpPOI); SamplingDistribution* samp = toymcsampler->GetSamplingDistribution(*tmpPoint); sampPlot.AddSamplingDistribution(samp); sampPlot.Draw(); */ // Now find bands and power constraint Double_t* bins = histOfUL->GetIntegral(); TH1F* cumulative = (TH1F*) histOfUL->Clone("cumulative"); cumulative->SetContent(bins); double band2sigDown, band1sigDown, bandMedian, band1sigUp,band2sigUp; for(int i=1; i<=cumulative->GetNbinsX(); ++i){ if(bins[i]<RooStats::SignificanceToPValue(2)) band2sigDown=cumulative->GetBinCenter(i); if(bins[i]<RooStats::SignificanceToPValue(1)) band1sigDown=cumulative->GetBinCenter(i); if(bins[i]<0.5) bandMedian=cumulative->GetBinCenter(i); if(bins[i]<RooStats::SignificanceToPValue(-1)) band1sigUp=cumulative->GetBinCenter(i); if(bins[i]<RooStats::SignificanceToPValue(-2)) band2sigUp=cumulative->GetBinCenter(i); } cout << "-2 sigma band " << band2sigDown << endl; cout << "-1 sigma band " << band1sigDown << " [Power Constraint)]" << endl; cout << "median of band " << bandMedian << endl; cout << "+1 sigma band " << band1sigUp << endl; cout << "+2 sigma band " << band2sigUp << endl; // print out the interval on the first Parameter of Interest cout << "\nobserved 95% upper-limit "<< interval->UpperLimit(*firstPOI) <<endl; cout << "CLb strict [P(toy>obs|0)] for observed 95% upper-limit "<< CLb <<endl; cout << "CLb inclusive [P(toy>=obs|0)] for observed 95% upper-limit "<< CLbinclusive <<endl; delete profile; delete nll; }
void OneSidedFrequentistUpperLimitWithBands_intermediate(const char* infile = "", const char* workspaceName = "combined", const char* modelConfigName = "ModelConfig", const char* dataName = "obsData"){ double confidenceLevel=0.95; // degrade/improve number of pseudo-experiments used to define the confidence belt. // value of 1 corresponds to default number of toys in the tail, which is 50/(1-confidenceLevel) double additionalToysFac = 1.; int nPointsToScan = 30; // number of steps in the parameter of interest int nToyMC = 100; // number of toys used to define the expected limit and band TStopwatch t; t.Start(); ///////////////////////////////////////////////////////////// // First part is just to access a user-defined file // or create the standard example file if it doesn't exist //////////////////////////////////////////////////////////// const char* filename = ""; if (!strcmp(infile,"")) filename = "results/example_combined_GaussExample_model.root"; else filename = infile; // Check if example input file exists TFile *file = TFile::Open(filename); // if input file was specified byt not found, quit if(!file && strcmp(infile,"")){ cout <<"file not found" << endl; return; } // if default file not found, try to create it if(!file ){ // Normally this would be run on the command line cout <<"will run standard hist2workspace example"<<endl; gROOT->ProcessLine(".! prepareHistFactory ."); gROOT->ProcessLine(".! hist2workspace config/example.xml"); cout <<"\n\n---------------------"<<endl; cout <<"Done creating example input"<<endl; cout <<"---------------------\n\n"<<endl; } // now try to access the file again file = TFile::Open(filename); if(!file){ // if it is still not there, then we can't continue cout << "Not able to run hist2workspace to create example input" <<endl; return; } ///////////////////////////////////////////////////////////// // Now get the data and workspace //////////////////////////////////////////////////////////// // get the workspace out of the file RooWorkspace* w = (RooWorkspace*) file->Get(workspaceName); if(!w){ cout <<"workspace not found" << endl; return; } // get the modelConfig out of the file ModelConfig* mc = (ModelConfig*) w->obj(modelConfigName); // get the modelConfig out of the file RooAbsData* data = w->data(dataName); // make sure ingredients are found if(!data || !mc){ w->Print(); cout << "data or ModelConfig was not found" <<endl; return; } cout << "Found data and ModelConfig:" <<endl; mc->Print(); ///////////////////////////////////////////////////////////// // Now get the POI for convenience // you may want to adjust the range of your POI //////////////////////////////////////////////////////////// RooRealVar* firstPOI = (RooRealVar*) mc->GetParametersOfInterest()->first(); // firstPOI->setMin(0); // firstPOI->setMax(10); ///////////////////////////////////////////// // create and use the FeldmanCousins tool // to find and plot the 95% confidence interval // on the parameter of interest as specified // in the model config // REMEMBER, we will change the test statistic // so this is NOT a Feldman-Cousins interval FeldmanCousins fc(*data,*mc); fc.SetConfidenceLevel(confidenceLevel); fc.AdditionalNToysFactor(additionalToysFac); // improve sampling that defines confidence belt // fc.UseAdaptiveSampling(true); // speed it up a bit, but don't use for expectd limits fc.SetNBins(nPointsToScan); // set how many points per parameter of interest to scan fc.CreateConfBelt(true); // save the information in the belt for plotting ///////////////////////////////////////////// // Feldman-Cousins is a unified limit by definition // but the tool takes care of a few things for us like which values // of the nuisance parameters should be used to generate toys. // so let's just change the test statistic and realize this is // no longer "Feldman-Cousins" but is a fully frequentist Neyman-Construction. // ProfileLikelihoodTestStatModified onesided(*mc->GetPdf()); // fc.GetTestStatSampler()->SetTestStatistic(&onesided); // ((ToyMCSampler*) fc.GetTestStatSampler())->SetGenerateBinned(true); ToyMCSampler* toymcsampler = (ToyMCSampler*) fc.GetTestStatSampler(); ProfileLikelihoodTestStat* testStat = dynamic_cast<ProfileLikelihoodTestStat*>(toymcsampler->GetTestStatistic()); testStat->SetOneSided(true); // test speedups: testStat->SetReuseNLL(true); // toymcsampler->setUseMultiGen(true); // not fully validated // Since this tool needs to throw toy MC the PDF needs to be // extended or the tool needs to know how many entries in a dataset // per pseudo experiment. // In the 'number counting form' where the entries in the dataset // are counts, and not values of discriminating variables, the // datasets typically only have one entry and the PDF is not // extended. if(!mc->GetPdf()->canBeExtended()){ if(data->numEntries()==1) fc.FluctuateNumDataEntries(false); else cout <<"Not sure what to do about this model" <<endl; } // We can use PROOF to speed things along in parallel ProofConfig pc(*w, 4, "",false); if(mc->GetGlobalObservables()){ cout << "will use global observables for unconditional ensemble"<<endl; mc->GetGlobalObservables()->Print(); toymcsampler->SetGlobalObservables(*mc->GetGlobalObservables()); } toymcsampler->SetProofConfig(&pc); // enable proof // Now get the interval PointSetInterval* interval = fc.GetInterval(); ConfidenceBelt* belt = fc.GetConfidenceBelt(); // print out the iterval on the first Parameter of Interest cout << "\n95% interval on " <<firstPOI->GetName()<<" is : ["<< interval->LowerLimit(*firstPOI) << ", "<< interval->UpperLimit(*firstPOI) <<"] "<<endl; // get observed UL and value of test statistic evaluated there RooArgSet tmpPOI(*firstPOI); double observedUL = interval->UpperLimit(*firstPOI); firstPOI->setVal(observedUL); double obsTSatObsUL = fc.GetTestStatSampler()->EvaluateTestStatistic(*data,tmpPOI); // Ask the calculator which points were scanned RooDataSet* parameterScan = (RooDataSet*) fc.GetPointsToScan(); RooArgSet* tmpPoint; // make a histogram of parameter vs. threshold TH1F* histOfThresholds = new TH1F("histOfThresholds","", parameterScan->numEntries(), firstPOI->getMin(), firstPOI->getMax()); histOfThresholds->GetXaxis()->SetTitle(firstPOI->GetName()); histOfThresholds->GetYaxis()->SetTitle("Threshold"); // loop through the points that were tested and ask confidence belt // what the upper/lower thresholds were. // For FeldmanCousins, the lower cut off is always 0 for(Int_t i=0; i<parameterScan->numEntries(); ++i){ tmpPoint = (RooArgSet*) parameterScan->get(i)->clone("temp"); double arMax = belt->GetAcceptanceRegionMax(*tmpPoint); double poiVal = tmpPoint->getRealValue(firstPOI->GetName()) ; histOfThresholds->Fill(poiVal,arMax); } TCanvas* c1 = new TCanvas(); c1->Divide(2); c1->cd(1); histOfThresholds->SetMinimum(0); histOfThresholds->Draw(); c1->cd(2); ///////////////////////////////////////////////////////////// // Now we generate the expected bands and power-constriant //////////////////////////////////////////////////////////// // First: find parameter point for mu=0, with conditional MLEs for nuisance parameters RooAbsReal* nll = mc->GetPdf()->createNLL(*data); RooAbsReal* profile = nll->createProfile(*mc->GetParametersOfInterest()); firstPOI->setVal(0.); profile->getVal(); // this will do fit and set nuisance parameters to profiled values RooArgSet* poiAndNuisance = new RooArgSet(); if(mc->GetNuisanceParameters()) poiAndNuisance->add(*mc->GetNuisanceParameters()); poiAndNuisance->add(*mc->GetParametersOfInterest()); w->saveSnapshot("paramsToGenerateData",*poiAndNuisance); RooArgSet* paramsToGenerateData = (RooArgSet*) poiAndNuisance->snapshot(); cout << "\nWill use these parameter points to generate pseudo data for bkg only" << endl; paramsToGenerateData->Print("v"); double CLb=0; double CLbinclusive=0; // Now we generate background only and find distribution of upper limits TH1F* histOfUL = new TH1F("histOfUL","",100,0,firstPOI->getMax()); histOfUL->GetXaxis()->SetTitle("Upper Limit (background only)"); histOfUL->GetYaxis()->SetTitle("Entries"); for(int imc=0; imc<nToyMC; ++imc){ // set parameters back to values for generating pseudo data w->loadSnapshot("paramsToGenerateData"); // in 5.30 there is a nicer way to generate toy data & randomize global obs RooAbsData* toyData = toymcsampler->GenerateToyData(*paramsToGenerateData); // get test stat at observed UL in observed data firstPOI->setVal(observedUL); double toyTSatObsUL = fc.GetTestStatSampler()->EvaluateTestStatistic(*toyData,tmpPOI); // toyData->get()->Print("v"); // cout <<"obsTSatObsUL " <<obsTSatObsUL << "toyTS " << toyTSatObsUL << endl; if(obsTSatObsUL < toyTSatObsUL) // (should be checked) CLb+= (1.)/nToyMC; if(obsTSatObsUL <= toyTSatObsUL) // (should be checked) CLbinclusive+= (1.)/nToyMC; // loop over points in belt to find upper limit for this toy data double thisUL = 0; for(Int_t i=0; i<parameterScan->numEntries(); ++i){ tmpPoint = (RooArgSet*) parameterScan->get(i)->clone("temp"); double arMax = belt->GetAcceptanceRegionMax(*tmpPoint); firstPOI->setVal( tmpPoint->getRealValue(firstPOI->GetName()) ); double thisTS = fc.GetTestStatSampler()->EvaluateTestStatistic(*toyData,tmpPOI); if(thisTS<=arMax){ thisUL = firstPOI->getVal(); } else{ break; } } histOfUL->Fill(thisUL); delete toyData; } histOfUL->Draw(); c1->SaveAs("one-sided_upper_limit_output.pdf"); // if you want to see a plot of the sampling distribution for a particular scan point: // Now find bands and power constraint Double_t* bins = histOfUL->GetIntegral(); TH1F* cumulative = (TH1F*) histOfUL->Clone("cumulative"); cumulative->SetContent(bins); double band2sigDown=0, band1sigDown=0, bandMedian=0, band1sigUp=0,band2sigUp=0; for(int i=1; i<=cumulative->GetNbinsX(); ++i){ if(bins[i]<RooStats::SignificanceToPValue(2)) band2sigDown=cumulative->GetBinCenter(i); if(bins[i]<RooStats::SignificanceToPValue(1)) band1sigDown=cumulative->GetBinCenter(i); if(bins[i]<0.5) bandMedian=cumulative->GetBinCenter(i); if(bins[i]<RooStats::SignificanceToPValue(-1)) band1sigUp=cumulative->GetBinCenter(i); if(bins[i]<RooStats::SignificanceToPValue(-2)) band2sigUp=cumulative->GetBinCenter(i); } t.Stop(); t.Print(); cout << "-2 sigma band " << band2sigDown << endl; cout << "-1 sigma band " << band1sigDown << endl; cout << "median of band " << bandMedian << " [Power Constriant)]" << endl; cout << "+1 sigma band " << band1sigUp << endl; cout << "+2 sigma band " << band2sigUp << endl; // print out the iterval on the first Parameter of Interest cout << "\nobserved 95% upper-limit "<< interval->UpperLimit(*firstPOI) <<endl; cout << "CLb strict [P(toy>obs|0)] for observed 95% upper-limit "<< CLb <<endl; cout << "CLb inclusive [P(toy>=obs|0)] for observed 95% upper-limit "<< CLbinclusive <<endl; delete profile; delete nll; }
double StandardFrequentistDiscovery( const char* infile = "", const char* workspaceName = "channel1", const char* modelConfigNameSB = "ModelConfig", const char* dataName = "obsData", int toys = 1000, double poiValueForBackground = 0.0, double poiValueForSignal = 1.0 ) { // The workspace contains the model for s+b. The b model is "autogenerated" // by copying s+b and setting the one parameter of interest to zero. // To keep the script simple, multiple parameters of interest or different // functional forms of the b model are not supported. // for now, assume there is only one parameter of interest, and these are // its values: ///////////////////////////////////////////////////////////// // First part is just to access a user-defined file // or create the standard example file if it doesn't exist //////////////////////////////////////////////////////////// const char* filename = ""; if (!strcmp(infile,"")) { filename = "results/example_channel1_GammaExample_model.root"; bool fileExist = !gSystem->AccessPathName(filename); // note opposite return code // if file does not exists generate with histfactory if (!fileExist) { #ifdef _WIN32 cout << "HistFactory file cannot be generated on Windows - exit" << endl; return -1; #endif // Normally this would be run on the command line cout <<"will run standard hist2workspace example"<<endl; gROOT->ProcessLine(".! prepareHistFactory ."); gROOT->ProcessLine(".! hist2workspace config/example.xml"); cout <<"\n\n---------------------"<<endl; cout <<"Done creating example input"<<endl; cout <<"---------------------\n\n"<<endl; } } else filename = infile; // Try to open the file TFile *file = TFile::Open(filename); // if input file was specified byt not found, quit if(!file ){ cout <<"StandardRooStatsDemoMacro: Input file " << filename << " is not found" << endl; return -1; } ///////////////////////////////////////////////////////////// // Tutorial starts here //////////////////////////////////////////////////////////// TStopwatch *mn_t = new TStopwatch; mn_t->Start(); // get the workspace out of the file RooWorkspace* w = (RooWorkspace*) file->Get(workspaceName); if (!w) { cout << "workspace not found" << endl; return -1.0; } // get the modelConfig out of the file ModelConfig* mc = (ModelConfig*) w->obj(modelConfigNameSB); // get the data out of the file RooAbsData* data = w->data(dataName); // make sure ingredients are found if (!data || !mc) { w->Print(); cout << "data or ModelConfig was not found" << endl; return -1.0; } RooRealVar* firstPOI = (RooRealVar*) mc->GetParametersOfInterest()->first(); firstPOI->setVal(poiValueForSignal); mc->SetSnapshot(*mc->GetParametersOfInterest()); // create null model ModelConfig *mcNull = mc->Clone("ModelConfigNull"); firstPOI->setVal(poiValueForBackground); mcNull->SetSnapshot(*(RooArgSet*)mcNull->GetParametersOfInterest()->snapshot()); // ---------------------------------------------------- // Configure a ProfileLikelihoodTestStat and a SimpleLikelihoodRatioTestStat // to use simultaneously with ToyMCSampler ProfileLikelihoodTestStat* plts = new ProfileLikelihoodTestStat(*mc->GetPdf()); plts->SetOneSidedDiscovery(true); plts->SetVarName( "q_{0}/2" ); // ---------------------------------------------------- // configure the ToyMCImportanceSampler with two test statistics ToyMCSampler toymcs(*plts, 50); // Since this tool needs to throw toy MC the PDF needs to be // extended or the tool needs to know how many entries in a dataset // per pseudo experiment. // In the 'number counting form' where the entries in the dataset // are counts, and not values of discriminating variables, the // datasets typically only have one entry and the PDF is not // extended. if (!mc->GetPdf()->canBeExtended()) { if (data->numEntries() == 1) { toymcs.SetNEventsPerToy(1); } else cout << "Not sure what to do about this model" << endl; } // We can use PROOF to speed things along in parallel // ProofConfig pc(*w, 2, "user@yourfavoriteproofcluster", false); ProofConfig pc(*w, 2, "", false); //toymcs.SetProofConfig(&pc); // enable proof // instantiate the calculator FrequentistCalculator freqCalc(*data, *mc, *mcNull, &toymcs); freqCalc.SetToys( toys,toys ); // null toys, alt toys // Run the calculator and print result HypoTestResult* freqCalcResult = freqCalc.GetHypoTest(); freqCalcResult->GetNullDistribution()->SetTitle( "b only" ); freqCalcResult->GetAltDistribution()->SetTitle( "s+b" ); freqCalcResult->Print(); double pvalue = freqCalcResult->NullPValue(); // stop timing mn_t->Stop(); cout << "total CPU time: " << mn_t->CpuTime() << endl; cout << "total real time: " << mn_t->RealTime() << endl; // plot TCanvas* c1 = new TCanvas(); HypoTestPlot *plot = new HypoTestPlot(*freqCalcResult, 100, -0.49, 9.51 ); plot->SetLogYaxis(true); // add chi2 to plot int nPOI = 1; TF1* f = new TF1("f", TString::Format("1*ROOT::Math::chisquared_pdf(2*x,%d,0)",nPOI), 0,20); f->SetLineColor( kBlack ); f->SetLineStyle( 7 ); plot->AddTF1( f, TString::Format("#chi^{2}(2x,%d)",nPOI) ); plot->Draw(); c1->SaveAs("standard_discovery_output.pdf"); return pvalue; }
void StandardHypoTestDemo(const char* infile = "", const char* workspaceName = "combined", const char* modelSBName = "ModelConfig", const char* modelBName = "", const char* dataName = "obsData", int calcType = 0, // 0 freq 1 hybrid, 2 asymptotic int testStatType = 3, // 0 LEP, 1 TeV, 2 LHC, 3 LHC - one sided int ntoys = 5000, bool useNC = false, const char * nuisPriorName = 0) { /* Other Parameter to pass in tutorial apart from standard for filename, ws, modelconfig and data type = 0 Freq calculator type = 1 Hybrid calculator type = 2 Asymptotic calculator testStatType = 0 LEP = 1 Tevatron = 2 Profile Likelihood = 3 Profile Likelihood one sided (i.e. = 0 if mu < mu_hat) ntoys: number of toys to use useNumberCounting: set to true when using number counting events nuisPriorName: name of prior for the nnuisance. This is often expressed as constraint term in the global model It is needed only when using the HybridCalculator (type=1) If not given by default the prior pdf from ModelConfig is used. extra options are available as global paramwters of the macro. They major ones are: generateBinned generate binned data sets for toys (default is false) - be careful not to activate with a too large (>=3) number of observables nToyRatio ratio of S+B/B toys (default is 2) printLevel */ // disable - can cause some problems //ToyMCSampler::SetAlwaysUseMultiGen(true); SimpleLikelihoodRatioTestStat::SetAlwaysReuseNLL(true); ProfileLikelihoodTestStat::SetAlwaysReuseNLL(true); RatioOfProfiledLikelihoodsTestStat::SetAlwaysReuseNLL(true); //RooRandom::randomGenerator()->SetSeed(0); // to change minimizers // ROOT::Math::MinimizerOptions::SetDefaultStrategy(0); // ROOT::Math::MinimizerOptions::SetDefaultMinimizer("Minuit2"); // ROOT::Math::MinimizerOptions::SetDefaultTolerance(1); ///////////////////////////////////////////////////////////// // First part is just to access a user-defined file // or create the standard example file if it doesn't exist //////////////////////////////////////////////////////////// const char* filename = ""; if (!strcmp(infile,"")) filename = "results/example_combined_GaussExample_model.root"; else filename = infile; // Check if example input file exists TFile *file = TFile::Open(filename); // if input file was specified byt not found, quit if(!file && strcmp(infile,"")){ cout <<"file not found" << endl; return; } // if default file not found, try to create it if(!file ){ // Normally this would be run on the command line cout <<"will run standard hist2workspace example"<<endl; gROOT->ProcessLine(".! prepareHistFactory ."); gROOT->ProcessLine(".! hist2workspace config/example.xml"); cout <<"\n\n---------------------"<<endl; cout <<"Done creating example input"<<endl; cout <<"---------------------\n\n"<<endl; } // now try to access the file again file = TFile::Open(filename); if(!file){ // if it is still not there, then we can't continue cout << "Not able to run hist2workspace to create example input" <<endl; return; } ///////////////////////////////////////////////////////////// // Tutorial starts here //////////////////////////////////////////////////////////// // get the workspace out of the file RooWorkspace* w = (RooWorkspace*) file->Get(workspaceName); if(!w){ cout <<"workspace not found" << endl; return; } w->Print(); // get the modelConfig out of the file ModelConfig* sbModel = (ModelConfig*) w->obj(modelSBName); // get the modelConfig out of the file RooAbsData* data = w->data(dataName); // make sure ingredients are found if(!data || !sbModel){ w->Print(); cout << "data or ModelConfig was not found" <<endl; return; } // make b model ModelConfig* bModel = (ModelConfig*) w->obj(modelBName); // case of no systematics // remove nuisance parameters from model if (noSystematics) { const RooArgSet * nuisPar = sbModel->GetNuisanceParameters(); if (nuisPar && nuisPar->getSize() > 0) { std::cout << "StandardHypoTestInvDemo" << " - Switch off all systematics by setting them constant to their initial values" << std::endl; RooStats::SetAllConstant(*nuisPar); } if (bModel) { const RooArgSet * bnuisPar = bModel->GetNuisanceParameters(); if (bnuisPar) RooStats::SetAllConstant(*bnuisPar); } } if (!bModel ) { Info("StandardHypoTestInvDemo","The background model %s does not exist",modelBName); Info("StandardHypoTestInvDemo","Copy it from ModelConfig %s and set POI to zero",modelSBName); bModel = (ModelConfig*) sbModel->Clone(); bModel->SetName(TString(modelSBName)+TString("B_only")); RooRealVar * var = dynamic_cast<RooRealVar*>(bModel->GetParametersOfInterest()->first()); if (!var) return; double oldval = var->getVal(); var->setVal(0); //bModel->SetSnapshot( RooArgSet(*var, *w->var("lumi")) ); bModel->SetSnapshot( RooArgSet(*var) ); var->setVal(oldval); } if (!sbModel->GetSnapshot() || poiValue > 0) { Info("StandardHypoTestDemo","Model %s has no snapshot - make one using model poi",modelSBName); RooRealVar * var = dynamic_cast<RooRealVar*>(sbModel->GetParametersOfInterest()->first()); if (!var) return; double oldval = var->getVal(); if (poiValue > 0) var->setVal(poiValue); //sbModel->SetSnapshot( RooArgSet(*var, *w->var("lumi") ) ); sbModel->SetSnapshot( RooArgSet(*var) ); if (poiValue > 0) var->setVal(oldval); //sbModel->SetSnapshot( *sbModel->GetParametersOfInterest() ); } // part 1, hypothesis testing SimpleLikelihoodRatioTestStat * slrts = new SimpleLikelihoodRatioTestStat(*bModel->GetPdf(), *sbModel->GetPdf()); // null parameters must includes snapshot of poi plus the nuisance values RooArgSet nullParams(*bModel->GetSnapshot()); if (bModel->GetNuisanceParameters()) nullParams.add(*bModel->GetNuisanceParameters()); slrts->SetNullParameters(nullParams); RooArgSet altParams(*sbModel->GetSnapshot()); if (sbModel->GetNuisanceParameters()) altParams.add(*sbModel->GetNuisanceParameters()); slrts->SetAltParameters(altParams); ProfileLikelihoodTestStat * profll = new ProfileLikelihoodTestStat(*bModel->GetPdf()); RatioOfProfiledLikelihoodsTestStat * ropl = new RatioOfProfiledLikelihoodsTestStat(*bModel->GetPdf(), *sbModel->GetPdf(), sbModel->GetSnapshot()); ropl->SetSubtractMLE(false); if (testStatType == 3) profll->SetOneSidedDiscovery(1); profll->SetPrintLevel(printLevel); // profll.SetReuseNLL(mOptimize); // slrts.SetReuseNLL(mOptimize); // ropl.SetReuseNLL(mOptimize); AsymptoticCalculator::SetPrintLevel(printLevel); HypoTestCalculatorGeneric * hypoCalc = 0; // note here Null is B and Alt is S+B if (calcType == 0) hypoCalc = new FrequentistCalculator(*data, *sbModel, *bModel); else if (calcType == 1) hypoCalc= new HybridCalculator(*data, *sbModel, *bModel); else if (calcType == 2) hypoCalc= new AsymptoticCalculator(*data, *sbModel, *bModel); if (calcType == 0) ((FrequentistCalculator*)hypoCalc)->SetToys(ntoys, ntoys/nToysRatio); if (calcType == 1) ((HybridCalculator*)hypoCalc)->SetToys(ntoys, ntoys/nToysRatio); if (calcType == 2 ) { if (testStatType == 3) ((AsymptoticCalculator*) hypoCalc)->SetOneSidedDiscovery(true); if (testStatType != 2 && testStatType != 3) Warning("StandardHypoTestDemo","Only the PL test statistic can be used with AsymptoticCalculator - use by default a two-sided PL"); } // check for nuisance prior pdf in case of nuisance parameters if (calcType == 1 && (bModel->GetNuisanceParameters() || sbModel->GetNuisanceParameters() )) { RooAbsPdf * nuisPdf = 0; if (nuisPriorName) nuisPdf = w->pdf(nuisPriorName); // use prior defined first in bModel (then in SbModel) if (!nuisPdf) { Info("StandardHypoTestDemo","No nuisance pdf given for the HybridCalculator - try to deduce pdf from the model"); if (bModel->GetPdf() && bModel->GetObservables() ) nuisPdf = RooStats::MakeNuisancePdf(*bModel,"nuisancePdf_bmodel"); else nuisPdf = RooStats::MakeNuisancePdf(*sbModel,"nuisancePdf_sbmodel"); } if (!nuisPdf ) { if (bModel->GetPriorPdf()) { nuisPdf = bModel->GetPriorPdf(); Info("StandardHypoTestDemo","No nuisance pdf given - try to use %s that is defined as a prior pdf in the B model",nuisPdf->GetName()); } else { Error("StandardHypoTestDemo","Cannnot run Hybrid calculator because no prior on the nuisance parameter is specified or can be derived"); return; } } assert(nuisPdf); Info("StandardHypoTestDemo","Using as nuisance Pdf ... " ); nuisPdf->Print(); const RooArgSet * nuisParams = (bModel->GetNuisanceParameters() ) ? bModel->GetNuisanceParameters() : sbModel->GetNuisanceParameters(); RooArgSet * np = nuisPdf->getObservables(*nuisParams); if (np->getSize() == 0) { Warning("StandardHypoTestDemo","Prior nuisance does not depend on nuisance parameters. They will be smeared in their full range"); } delete np; ((HybridCalculator*)hypoCalc)->ForcePriorNuisanceAlt(*nuisPdf); ((HybridCalculator*)hypoCalc)->ForcePriorNuisanceNull(*nuisPdf); } // hypoCalc->ForcePriorNuisanceAlt(*sbModel->GetPriorPdf()); // hypoCalc->ForcePriorNuisanceNull(*bModel->GetPriorPdf()); ToyMCSampler * sampler = (ToyMCSampler *)hypoCalc->GetTestStatSampler(); if (sampler && (calcType == 0 || calcType == 1) ) { // look if pdf is number counting or extended if (sbModel->GetPdf()->canBeExtended() ) { if (useNC) Warning("StandardHypoTestDemo","Pdf is extended: but number counting flag is set: ignore it "); } else { // for not extended pdf if (!useNC) { int nEvents = data->numEntries(); Info("StandardHypoTestDemo","Pdf is not extended: number of events to generate taken from observed data set is %d",nEvents); sampler->SetNEventsPerToy(nEvents); } else { Info("StandardHypoTestDemo","using a number counting pdf"); sampler->SetNEventsPerToy(1); } } if (data->isWeighted() && !generateBinned) { Info("StandardHypoTestDemo","Data set is weighted, nentries = %d and sum of weights = %8.1f but toy generation is unbinned - it would be faster to set generateBinned to true\n",data->numEntries(), data->sumEntries()); } if (generateBinned) sampler->SetGenerateBinned(generateBinned); // set the test statistic if (testStatType == 0) sampler->SetTestStatistic(slrts); if (testStatType == 1) sampler->SetTestStatistic(ropl); if (testStatType == 2 || testStatType == 3) sampler->SetTestStatistic(profll); } HypoTestResult * htr = hypoCalc->GetHypoTest(); htr->SetPValueIsRightTail(true); htr->SetBackgroundAsAlt(false); htr->Print(); // how to get meaningfull CLs at this point? delete sampler; delete slrts; delete ropl; delete profll; if (calcType != 2) { HypoTestPlot * plot = new HypoTestPlot(*htr,100); plot->SetLogYaxis(true); plot->Draw(); } else { std::cout << "Asymptotic results " << std::endl; } // look at expected significances // found median of S+B distribution if (calcType != 2) { SamplingDistribution * altDist = htr->GetAltDistribution(); HypoTestResult htExp("Expected Result"); htExp.Append(htr); // find quantiles in alt (S+B) distribution double p[5]; double q[5]; for (int i = 0; i < 5; ++i) { double sig = -2 + i; p[i] = ROOT::Math::normal_cdf(sig,1); } std::vector<double> values = altDist->GetSamplingDistribution(); TMath::Quantiles( values.size(), 5, &values[0], q, p, false); for (int i = 0; i < 5; ++i) { htExp.SetTestStatisticData( q[i] ); double sig = -2 + i; std::cout << " Expected p -value and significance at " << sig << " sigma = " << htExp.NullPValue() << " significance " << htExp.Significance() << " sigma " << std::endl; } } else { // case of asymptotic calculator for (int i = 0; i < 5; ++i) { double sig = -2 + i; // sigma is inverted here double pval = AsymptoticCalculator::GetExpectedPValues( htr->NullPValue(), htr->AlternatePValue(), -sig, false); std::cout << " Expected p -value and significance at " << sig << " sigma = " << pval << " significance " << ROOT::Math::normal_quantile_c(pval,1) << " sigma " << std::endl; } } }