MultivariateGaussianTest.C: comparison of MCMC and PLC in a multi-variate gaussian problem | Roostats tutorials | StandardBayesianMCMCDemo.C: Standard demo of the Bayesian MCMC calculator |
/* OneSidedFrequentistUpperLimitWithBands Author: Kyle Cranmer, Contributions from Haichen Wang and Daniel Whiteson date: Dec. 2010 - Feb. 2011 v1. Jan 28 This is a standard demo that can be used with any ROOT file prepared in the standard way. You specify: - name for input ROOT file - name of workspace inside ROOT file that holds model and data - name of ModelConfig that specifies details for calculator tools - name of dataset With default parameters the macro will attempt to run the standard hist2workspace example and read the ROOT file that it produces. The first ~100 lines define a new test statistic, then the main macro starts. You may want to control: double confidenceLevel=0.95; int nPointsToScan = 30; int nToyMC = 200; This uses a modified version of the profile likelihood ratio as a test statistic for upper limits (eg. test stat = 0 if muhat>mu). Based on the observed data, one defines a set of parameter points to be tested based on the value of the parameter of interest and the conditional MLE (eg. profiled) values of the nuisance parameters. At each parameter point, pseudo-experiments are generated using this fixed reference model and then the test statistic is evaluated. Note, the nuisance parameters are floating in the fits. For each point, the threshold that defines the 95% acceptance region is found. This forms a "Confidence Belt". After constructing the confidence belt, one can find the confidence interval for any particular dataset by finding the intersection of the observed test statistic and the confidence belt. First this is done on the observed data to get an observed 1-sided upper limt. Finally, there expected limit and bands (from background-only) are formed by generating background-only data and finding the upper limit. This is done by hand for now, will later be part of the RooStats tools. On a technical note, this technique is NOT the Feldman-Cousins technique, because that is a 2-sided interval BY DEFINITION. However, like the Feldman-Cousins technique this is a Neyman-Construction. For technical reasons the easiest way to implement this right now is to use the FeldmanCousins tool and then change the test statistic that it is using. Building the confidence belt can be computationally expensive. Once it is built, one could save it to a file and use it in a separate step. 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. Note, if you have a boundary on the parameter of interest (eg. cross-section) the threshold on the one-sided test statistic starts off very small because we are only including downward fluctuations. You can see the threshold in these printouts: [#0] PROGRESS:Generation -- generated toys: 500 / 999 NeymanConstruction: Prog: 12/50 total MC = 39 this test stat = 0 SigXsecOverSM=0.69 alpha_syst1=0.136515 alpha_syst3=0.425415 beta_syst2=1.08496 [-1e+30, 0.011215] in interval = 1 this tells you the values of the parameters being used to generate the pseudo-experiments and the threshold in this case is 0.011215. One would expect for 95% that the threshold would be ~1.35 once the cross-section is far enough away from 0 that it is essentially unaffected by the boundary. As one reaches the last points in the scan, the theshold starts to get artificially high. This is because the range of the parameter in the fit is the same as the range in the scan. In the future, these should be independently controled, but they are not now. As a result the ~50% of pseudo-experiments that have an upward fluctuation end up with muhat = muMax. Because of this, the upper range of the parameter should be well above the expected upper limit... but not too high or one will need a very large value of nPointsToScan to resolve the relevant region. This can be improved, but this is the first version of this script. Important note: when the model includes external constraint terms, like a Gaussian constraint to a nuisance parameter centered around some nominal value there is a subtlety. The asymptotic results are all based on the assumption that all the measurements fluctuate... including the nominal values from auxiliary measurements. If these do not fluctuate, this corresponds to an "conditional ensemble". The result is that the distribution of the test statistic can become very non-chi^2. This results in thresholds that become very large. This can be seen in the following thought experiment. Say the model is Pois(N | s + b) * G(b0|b,sigma) where G(b0|b,sigma) is the external constraint and b0 is 100. If N is also 100 then the profiled value of b given s is going to be some trade off betwen 100-s and b0. If sigma is \sqrt(N), then the profiled value of b is probably 100 - s/2 So for s=60 we are going to have a profiled value of b~70. Now when we generate pseudo-experiments for s=60, b=70 we will have N~130 and the average shat will be 30, not 60. In practice, this is only an issue for values of s that are very excluded. For values of s near the 95% limit this should not be a big effect. This can be avoided if the nominal values of the constraints also fluctuate, but that requires that those parameters are RooRealVars in the model. This version does not deal with this issue, but it will be addressed in a future version. */ #include "TFile.h" #include "TROOT.h" #include "TH1F.h" #include "TCanvas.h" #include "TSystem.h" #include "RooWorkspace.h" #include "RooSimultaneous.h" #include "RooAbsData.h" #include "RooStats/ModelConfig.h" #include "RooStats/FeldmanCousins.h" #include "RooStats/ToyMCSampler.h" #include "RooStats/PointSetInterval.h" #include "RooStats/ConfidenceBelt.h" #include "RooStats/ProfileLikelihoodTestStat.h" using namespace RooFit; using namespace RooStats; ///////////////////////////////////////////////////////////////////////// // The actual macro void OneSidedFrequentistUpperLimitWithBands(const char* infile = "", const char* workspaceName = "combined", const char* modelConfigName = "ModelConfig", const char* dataName = "obsData"){ #ifdef __CINT__ cout << "DO NOT RUN WITH CINT: we are using a custom test statistic "; cout << "which requires that this tutorial must be compiled "; cout << "with ACLIC" << endl; return; #endif double confidenceLevel=0.95; int nPointsToScan = 30; int nToyMC = 500; ///////////////////////////////////////////////////////////// // 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; } ///////////////////////////////////////////////////////////// // 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 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); // 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. ProofConfig pc(*w, 4, "workers=4"); 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"); 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-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"); 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 Constriant)]" << endl; cout << "median of band " << bandMedian << 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; } OneSidedFrequentistUpperLimitWithBands.C:1 OneSidedFrequentistUpperLimitWithBands.C:2 OneSidedFrequentistUpperLimitWithBands.C:3 OneSidedFrequentistUpperLimitWithBands.C:4 OneSidedFrequentistUpperLimitWithBands.C:5 OneSidedFrequentistUpperLimitWithBands.C:6 OneSidedFrequentistUpperLimitWithBands.C:7 OneSidedFrequentistUpperLimitWithBands.C:8 OneSidedFrequentistUpperLimitWithBands.C:9 OneSidedFrequentistUpperLimitWithBands.C:10 OneSidedFrequentistUpperLimitWithBands.C:11 OneSidedFrequentistUpperLimitWithBands.C:12 OneSidedFrequentistUpperLimitWithBands.C:13 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OneSidedFrequentistUpperLimitWithBands.C:168 OneSidedFrequentistUpperLimitWithBands.C:169 OneSidedFrequentistUpperLimitWithBands.C:170 OneSidedFrequentistUpperLimitWithBands.C:171 OneSidedFrequentistUpperLimitWithBands.C:172 OneSidedFrequentistUpperLimitWithBands.C:173 OneSidedFrequentistUpperLimitWithBands.C:174 OneSidedFrequentistUpperLimitWithBands.C:175 OneSidedFrequentistUpperLimitWithBands.C:176 OneSidedFrequentistUpperLimitWithBands.C:177 OneSidedFrequentistUpperLimitWithBands.C:178 OneSidedFrequentistUpperLimitWithBands.C:179 OneSidedFrequentistUpperLimitWithBands.C:180 OneSidedFrequentistUpperLimitWithBands.C:181 OneSidedFrequentistUpperLimitWithBands.C:182 OneSidedFrequentistUpperLimitWithBands.C:183 OneSidedFrequentistUpperLimitWithBands.C:184 OneSidedFrequentistUpperLimitWithBands.C:185 OneSidedFrequentistUpperLimitWithBands.C:186 OneSidedFrequentistUpperLimitWithBands.C:187 OneSidedFrequentistUpperLimitWithBands.C:188 OneSidedFrequentistUpperLimitWithBands.C:189 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OneSidedFrequentistUpperLimitWithBands.C:212 OneSidedFrequentistUpperLimitWithBands.C:213 OneSidedFrequentistUpperLimitWithBands.C:214 OneSidedFrequentistUpperLimitWithBands.C:215 OneSidedFrequentistUpperLimitWithBands.C:216 OneSidedFrequentistUpperLimitWithBands.C:217 OneSidedFrequentistUpperLimitWithBands.C:218 OneSidedFrequentistUpperLimitWithBands.C:219 OneSidedFrequentistUpperLimitWithBands.C:220 OneSidedFrequentistUpperLimitWithBands.C:221 OneSidedFrequentistUpperLimitWithBands.C:222 OneSidedFrequentistUpperLimitWithBands.C:223 OneSidedFrequentistUpperLimitWithBands.C:224 OneSidedFrequentistUpperLimitWithBands.C:225 OneSidedFrequentistUpperLimitWithBands.C:226 OneSidedFrequentistUpperLimitWithBands.C:227 OneSidedFrequentistUpperLimitWithBands.C:228 OneSidedFrequentistUpperLimitWithBands.C:229 OneSidedFrequentistUpperLimitWithBands.C:230 OneSidedFrequentistUpperLimitWithBands.C:231 OneSidedFrequentistUpperLimitWithBands.C:232 OneSidedFrequentistUpperLimitWithBands.C:233 OneSidedFrequentistUpperLimitWithBands.C:234 OneSidedFrequentistUpperLimitWithBands.C:235 OneSidedFrequentistUpperLimitWithBands.C:236 OneSidedFrequentistUpperLimitWithBands.C:237 OneSidedFrequentistUpperLimitWithBands.C:238 OneSidedFrequentistUpperLimitWithBands.C:239 OneSidedFrequentistUpperLimitWithBands.C:240 OneSidedFrequentistUpperLimitWithBands.C:241 OneSidedFrequentistUpperLimitWithBands.C:242 OneSidedFrequentistUpperLimitWithBands.C:243 OneSidedFrequentistUpperLimitWithBands.C:244 OneSidedFrequentistUpperLimitWithBands.C:245 OneSidedFrequentistUpperLimitWithBands.C:246 OneSidedFrequentistUpperLimitWithBands.C:247 OneSidedFrequentistUpperLimitWithBands.C:248 OneSidedFrequentistUpperLimitWithBands.C:249 OneSidedFrequentistUpperLimitWithBands.C:250 OneSidedFrequentistUpperLimitWithBands.C:251 OneSidedFrequentistUpperLimitWithBands.C:252 OneSidedFrequentistUpperLimitWithBands.C:253 OneSidedFrequentistUpperLimitWithBands.C:254 OneSidedFrequentistUpperLimitWithBands.C:255 OneSidedFrequentistUpperLimitWithBands.C:256 OneSidedFrequentistUpperLimitWithBands.C:257 OneSidedFrequentistUpperLimitWithBands.C:258 OneSidedFrequentistUpperLimitWithBands.C:259 OneSidedFrequentistUpperLimitWithBands.C:260 OneSidedFrequentistUpperLimitWithBands.C:261 OneSidedFrequentistUpperLimitWithBands.C:262 OneSidedFrequentistUpperLimitWithBands.C:263 OneSidedFrequentistUpperLimitWithBands.C:264 OneSidedFrequentistUpperLimitWithBands.C:265 OneSidedFrequentistUpperLimitWithBands.C:266 OneSidedFrequentistUpperLimitWithBands.C:267 OneSidedFrequentistUpperLimitWithBands.C:268 OneSidedFrequentistUpperLimitWithBands.C:269 OneSidedFrequentistUpperLimitWithBands.C:270 OneSidedFrequentistUpperLimitWithBands.C:271 OneSidedFrequentistUpperLimitWithBands.C:272 OneSidedFrequentistUpperLimitWithBands.C:273 OneSidedFrequentistUpperLimitWithBands.C:274 OneSidedFrequentistUpperLimitWithBands.C:275 OneSidedFrequentistUpperLimitWithBands.C:276 OneSidedFrequentistUpperLimitWithBands.C:277 OneSidedFrequentistUpperLimitWithBands.C:278 OneSidedFrequentistUpperLimitWithBands.C:279 OneSidedFrequentistUpperLimitWithBands.C:280 OneSidedFrequentistUpperLimitWithBands.C:281 OneSidedFrequentistUpperLimitWithBands.C:282 OneSidedFrequentistUpperLimitWithBands.C:283 OneSidedFrequentistUpperLimitWithBands.C:284 OneSidedFrequentistUpperLimitWithBands.C:285 OneSidedFrequentistUpperLimitWithBands.C:286 OneSidedFrequentistUpperLimitWithBands.C:287 OneSidedFrequentistUpperLimitWithBands.C:288 OneSidedFrequentistUpperLimitWithBands.C:289 OneSidedFrequentistUpperLimitWithBands.C:290 OneSidedFrequentistUpperLimitWithBands.C:291 OneSidedFrequentistUpperLimitWithBands.C:292 OneSidedFrequentistUpperLimitWithBands.C:293 OneSidedFrequentistUpperLimitWithBands.C:294 OneSidedFrequentistUpperLimitWithBands.C:295 OneSidedFrequentistUpperLimitWithBands.C:296 OneSidedFrequentistUpperLimitWithBands.C:297 OneSidedFrequentistUpperLimitWithBands.C:298 OneSidedFrequentistUpperLimitWithBands.C:299 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OneSidedFrequentistUpperLimitWithBands.C:322 OneSidedFrequentistUpperLimitWithBands.C:323 OneSidedFrequentistUpperLimitWithBands.C:324 OneSidedFrequentistUpperLimitWithBands.C:325 OneSidedFrequentistUpperLimitWithBands.C:326 OneSidedFrequentistUpperLimitWithBands.C:327 OneSidedFrequentistUpperLimitWithBands.C:328 OneSidedFrequentistUpperLimitWithBands.C:329 OneSidedFrequentistUpperLimitWithBands.C:330 OneSidedFrequentistUpperLimitWithBands.C:331 OneSidedFrequentistUpperLimitWithBands.C:332 OneSidedFrequentistUpperLimitWithBands.C:333 OneSidedFrequentistUpperLimitWithBands.C:334 OneSidedFrequentistUpperLimitWithBands.C:335 OneSidedFrequentistUpperLimitWithBands.C:336 OneSidedFrequentistUpperLimitWithBands.C:337 OneSidedFrequentistUpperLimitWithBands.C:338 OneSidedFrequentistUpperLimitWithBands.C:339 OneSidedFrequentistUpperLimitWithBands.C:340 OneSidedFrequentistUpperLimitWithBands.C:341 OneSidedFrequentistUpperLimitWithBands.C:342 OneSidedFrequentistUpperLimitWithBands.C:343 OneSidedFrequentistUpperLimitWithBands.C:344 OneSidedFrequentistUpperLimitWithBands.C:345 OneSidedFrequentistUpperLimitWithBands.C:346 OneSidedFrequentistUpperLimitWithBands.C:347 OneSidedFrequentistUpperLimitWithBands.C:348 OneSidedFrequentistUpperLimitWithBands.C:349 OneSidedFrequentistUpperLimitWithBands.C:350 OneSidedFrequentistUpperLimitWithBands.C:351 OneSidedFrequentistUpperLimitWithBands.C:352 OneSidedFrequentistUpperLimitWithBands.C:353 OneSidedFrequentistUpperLimitWithBands.C:354 OneSidedFrequentistUpperLimitWithBands.C:355 OneSidedFrequentistUpperLimitWithBands.C:356 OneSidedFrequentistUpperLimitWithBands.C:357 OneSidedFrequentistUpperLimitWithBands.C:358 OneSidedFrequentistUpperLimitWithBands.C:359 OneSidedFrequentistUpperLimitWithBands.C:360 OneSidedFrequentistUpperLimitWithBands.C:361 OneSidedFrequentistUpperLimitWithBands.C:362 OneSidedFrequentistUpperLimitWithBands.C:363 OneSidedFrequentistUpperLimitWithBands.C:364 OneSidedFrequentistUpperLimitWithBands.C:365 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OneSidedFrequentistUpperLimitWithBands.C:388 OneSidedFrequentistUpperLimitWithBands.C:389 OneSidedFrequentistUpperLimitWithBands.C:390 OneSidedFrequentistUpperLimitWithBands.C:391 OneSidedFrequentistUpperLimitWithBands.C:392 OneSidedFrequentistUpperLimitWithBands.C:393 OneSidedFrequentistUpperLimitWithBands.C:394 OneSidedFrequentistUpperLimitWithBands.C:395 OneSidedFrequentistUpperLimitWithBands.C:396 OneSidedFrequentistUpperLimitWithBands.C:397 OneSidedFrequentistUpperLimitWithBands.C:398 OneSidedFrequentistUpperLimitWithBands.C:399 OneSidedFrequentistUpperLimitWithBands.C:400 OneSidedFrequentistUpperLimitWithBands.C:401 OneSidedFrequentistUpperLimitWithBands.C:402 OneSidedFrequentistUpperLimitWithBands.C:403 OneSidedFrequentistUpperLimitWithBands.C:404 OneSidedFrequentistUpperLimitWithBands.C:405 OneSidedFrequentistUpperLimitWithBands.C:406 OneSidedFrequentistUpperLimitWithBands.C:407 OneSidedFrequentistUpperLimitWithBands.C:408 OneSidedFrequentistUpperLimitWithBands.C:409 OneSidedFrequentistUpperLimitWithBands.C:410 OneSidedFrequentistUpperLimitWithBands.C:411 OneSidedFrequentistUpperLimitWithBands.C:412 OneSidedFrequentistUpperLimitWithBands.C:413 OneSidedFrequentistUpperLimitWithBands.C:414 OneSidedFrequentistUpperLimitWithBands.C:415 OneSidedFrequentistUpperLimitWithBands.C:416 OneSidedFrequentistUpperLimitWithBands.C:417 OneSidedFrequentistUpperLimitWithBands.C:418 OneSidedFrequentistUpperLimitWithBands.C:419 OneSidedFrequentistUpperLimitWithBands.C:420 OneSidedFrequentistUpperLimitWithBands.C:421 OneSidedFrequentistUpperLimitWithBands.C:422 OneSidedFrequentistUpperLimitWithBands.C:423 OneSidedFrequentistUpperLimitWithBands.C:424 OneSidedFrequentistUpperLimitWithBands.C:425 OneSidedFrequentistUpperLimitWithBands.C:426 OneSidedFrequentistUpperLimitWithBands.C:427 OneSidedFrequentistUpperLimitWithBands.C:428 OneSidedFrequentistUpperLimitWithBands.C:429 OneSidedFrequentistUpperLimitWithBands.C:430 OneSidedFrequentistUpperLimitWithBands.C:431 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OneSidedFrequentistUpperLimitWithBands.C:454 OneSidedFrequentistUpperLimitWithBands.C:455 OneSidedFrequentistUpperLimitWithBands.C:456 OneSidedFrequentistUpperLimitWithBands.C:457 OneSidedFrequentistUpperLimitWithBands.C:458 OneSidedFrequentistUpperLimitWithBands.C:459 OneSidedFrequentistUpperLimitWithBands.C:460 OneSidedFrequentistUpperLimitWithBands.C:461 OneSidedFrequentistUpperLimitWithBands.C:462 OneSidedFrequentistUpperLimitWithBands.C:463 OneSidedFrequentistUpperLimitWithBands.C:464 OneSidedFrequentistUpperLimitWithBands.C:465 OneSidedFrequentistUpperLimitWithBands.C:466 OneSidedFrequentistUpperLimitWithBands.C:467 OneSidedFrequentistUpperLimitWithBands.C:468 OneSidedFrequentistUpperLimitWithBands.C:469 OneSidedFrequentistUpperLimitWithBands.C:470 OneSidedFrequentistUpperLimitWithBands.C:471 OneSidedFrequentistUpperLimitWithBands.C:472 OneSidedFrequentistUpperLimitWithBands.C:473 OneSidedFrequentistUpperLimitWithBands.C:474 OneSidedFrequentistUpperLimitWithBands.C:475 OneSidedFrequentistUpperLimitWithBands.C:476 OneSidedFrequentistUpperLimitWithBands.C:477 OneSidedFrequentistUpperLimitWithBands.C:478 OneSidedFrequentistUpperLimitWithBands.C:479 OneSidedFrequentistUpperLimitWithBands.C:480 OneSidedFrequentistUpperLimitWithBands.C:481 OneSidedFrequentistUpperLimitWithBands.C:482 OneSidedFrequentistUpperLimitWithBands.C:483 OneSidedFrequentistUpperLimitWithBands.C:484 OneSidedFrequentistUpperLimitWithBands.C:485 OneSidedFrequentistUpperLimitWithBands.C:486 OneSidedFrequentistUpperLimitWithBands.C:487 OneSidedFrequentistUpperLimitWithBands.C:488 OneSidedFrequentistUpperLimitWithBands.C:489 OneSidedFrequentistUpperLimitWithBands.C:490 OneSidedFrequentistUpperLimitWithBands.C:491 OneSidedFrequentistUpperLimitWithBands.C:492 OneSidedFrequentistUpperLimitWithBands.C:493 OneSidedFrequentistUpperLimitWithBands.C:494 OneSidedFrequentistUpperLimitWithBands.C:495 OneSidedFrequentistUpperLimitWithBands.C:496 OneSidedFrequentistUpperLimitWithBands.C:497 OneSidedFrequentistUpperLimitWithBands.C:498 OneSidedFrequentistUpperLimitWithBands.C:499 OneSidedFrequentistUpperLimitWithBands.C:500 OneSidedFrequentistUpperLimitWithBands.C:501 OneSidedFrequentistUpperLimitWithBands.C:502 OneSidedFrequentistUpperLimitWithBands.C:503 OneSidedFrequentistUpperLimitWithBands.C:504 OneSidedFrequentistUpperLimitWithBands.C:505 OneSidedFrequentistUpperLimitWithBands.C:506 OneSidedFrequentistUpperLimitWithBands.C:507 OneSidedFrequentistUpperLimitWithBands.C:508 OneSidedFrequentistUpperLimitWithBands.C:509 OneSidedFrequentistUpperLimitWithBands.C:510 OneSidedFrequentistUpperLimitWithBands.C:511 OneSidedFrequentistUpperLimitWithBands.C:512 OneSidedFrequentistUpperLimitWithBands.C:513 OneSidedFrequentistUpperLimitWithBands.C:514 OneSidedFrequentistUpperLimitWithBands.C:515 OneSidedFrequentistUpperLimitWithBands.C:516 OneSidedFrequentistUpperLimitWithBands.C:517 OneSidedFrequentistUpperLimitWithBands.C:518 OneSidedFrequentistUpperLimitWithBands.C:519 OneSidedFrequentistUpperLimitWithBands.C:520 OneSidedFrequentistUpperLimitWithBands.C:521 OneSidedFrequentistUpperLimitWithBands.C:522 OneSidedFrequentistUpperLimitWithBands.C:523 OneSidedFrequentistUpperLimitWithBands.C:524 OneSidedFrequentistUpperLimitWithBands.C:525 |
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