/* TwoSidedFrequentistUpperLimitWithBands Author: Kyle Cranmer, Contributions from Aaron Armbruster, Haoshuang Ji, Haichen Wang and Daniel Whiteson date: Dec. 2010 - Feb. 2011 v1. Jan 28, 2010 v2. March, 2010 v3. May, 2010 (uses 5.29 to fix global obs for simpdf) 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. You may want to control: double confidenceLevel=0.95; double additionalToysFac = 1.; int nPointsToScan = 30; int nToyMC = 500; 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. The auxiliary measurments (global observables) associated with the constraint terms in nuisance parameters are also fluctuated in the process of generating the pseudo-experiments in a frequentist manner forming an 'unconditional ensemble'. One could form a 'conditional' ensemble in which these auxiliary measuements are fixed. Note that the nuisance parameters are not randomized, which is a Bayesian procedure. 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. The background-only is defined as such that the nuisance parameters are fixed to their best fit value based on the data with the signal rate fixed to 0. The bands are done by hand for now, will later be part of the RooStats tools. On a technical note, this technique IS the generalization of Feldman-Cousins with nuisance parameters. 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 two-sided test statistic starts off at moderate values and plateaus. [#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. */ #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; ///////////////////////////////////////////////////////////////////////// void TwoSidedFrequentistUpperLimitWithBands(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 = 500; // number of toys used to define the expected limit and band ///////////////////////////////////////////////////////////// // 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. // fc.GetTestStatSampler()->SetTestStatistic(&onesided); // ((ToyMCSampler*) fc.GetTestStatSampler())->SetGenerateBinned(true); ToyMCSampler* toymcsampler = (ToyMCSampler*) fc.GetTestStatSampler(); ProfileLikelihoodTestStat* testStat = dynamic_cast<ProfileLikelihoodTestStat*>(toymcsampler->GetTestStatistic()); // 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",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"); 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 for the main measurement 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. // In ROOT 5.28 there is a problem with generating global observables // with a simultaneous PDF. In 5.29 there is a solution with // RooSimultaneous::generateSimGlobal, but this may change to // the standard generate interface in 5.30. 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 { RooDataSet* one = simPdf->generateSimGlobal(*mc->GetGlobalObservables(),1); const RooArgSet *values = one->get(); RooArgSet *allVars = mc->GetPdf()->getVariables(); *allVars = *values; delete allVars; delete values; delete one; } // 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; } } 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("two-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=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); } 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; } TwoSidedFrequentistUpperLimitWithBands.C:1 TwoSidedFrequentistUpperLimitWithBands.C:2 TwoSidedFrequentistUpperLimitWithBands.C:3 TwoSidedFrequentistUpperLimitWithBands.C:4 TwoSidedFrequentistUpperLimitWithBands.C:5 TwoSidedFrequentistUpperLimitWithBands.C:6 TwoSidedFrequentistUpperLimitWithBands.C:7 TwoSidedFrequentistUpperLimitWithBands.C:8 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TwoSidedFrequentistUpperLimitWithBands.C:207 TwoSidedFrequentistUpperLimitWithBands.C:208 TwoSidedFrequentistUpperLimitWithBands.C:209 TwoSidedFrequentistUpperLimitWithBands.C:210 TwoSidedFrequentistUpperLimitWithBands.C:211 TwoSidedFrequentistUpperLimitWithBands.C:212 TwoSidedFrequentistUpperLimitWithBands.C:213 TwoSidedFrequentistUpperLimitWithBands.C:214 TwoSidedFrequentistUpperLimitWithBands.C:215 TwoSidedFrequentistUpperLimitWithBands.C:216 TwoSidedFrequentistUpperLimitWithBands.C:217 TwoSidedFrequentistUpperLimitWithBands.C:218 TwoSidedFrequentistUpperLimitWithBands.C:219 TwoSidedFrequentistUpperLimitWithBands.C:220 TwoSidedFrequentistUpperLimitWithBands.C:221 TwoSidedFrequentistUpperLimitWithBands.C:222 TwoSidedFrequentistUpperLimitWithBands.C:223 TwoSidedFrequentistUpperLimitWithBands.C:224 TwoSidedFrequentistUpperLimitWithBands.C:225 TwoSidedFrequentistUpperLimitWithBands.C:226 TwoSidedFrequentistUpperLimitWithBands.C:227 TwoSidedFrequentistUpperLimitWithBands.C:228 TwoSidedFrequentistUpperLimitWithBands.C:229 TwoSidedFrequentistUpperLimitWithBands.C:230 TwoSidedFrequentistUpperLimitWithBands.C:231 TwoSidedFrequentistUpperLimitWithBands.C:232 TwoSidedFrequentistUpperLimitWithBands.C:233 TwoSidedFrequentistUpperLimitWithBands.C:234 TwoSidedFrequentistUpperLimitWithBands.C:235 TwoSidedFrequentistUpperLimitWithBands.C:236 TwoSidedFrequentistUpperLimitWithBands.C:237 TwoSidedFrequentistUpperLimitWithBands.C:238 TwoSidedFrequentistUpperLimitWithBands.C:239 TwoSidedFrequentistUpperLimitWithBands.C:240 TwoSidedFrequentistUpperLimitWithBands.C:241 TwoSidedFrequentistUpperLimitWithBands.C:242 TwoSidedFrequentistUpperLimitWithBands.C:243 TwoSidedFrequentistUpperLimitWithBands.C:244 TwoSidedFrequentistUpperLimitWithBands.C:245 TwoSidedFrequentistUpperLimitWithBands.C:246 TwoSidedFrequentistUpperLimitWithBands.C:247 TwoSidedFrequentistUpperLimitWithBands.C:248 TwoSidedFrequentistUpperLimitWithBands.C:249 TwoSidedFrequentistUpperLimitWithBands.C:250 TwoSidedFrequentistUpperLimitWithBands.C:251 TwoSidedFrequentistUpperLimitWithBands.C:252 TwoSidedFrequentistUpperLimitWithBands.C:253 TwoSidedFrequentistUpperLimitWithBands.C:254 TwoSidedFrequentistUpperLimitWithBands.C:255 TwoSidedFrequentistUpperLimitWithBands.C:256 TwoSidedFrequentistUpperLimitWithBands.C:257 TwoSidedFrequentistUpperLimitWithBands.C:258 TwoSidedFrequentistUpperLimitWithBands.C:259 TwoSidedFrequentistUpperLimitWithBands.C:260 TwoSidedFrequentistUpperLimitWithBands.C:261 TwoSidedFrequentistUpperLimitWithBands.C:262 TwoSidedFrequentistUpperLimitWithBands.C:263 TwoSidedFrequentistUpperLimitWithBands.C:264 TwoSidedFrequentistUpperLimitWithBands.C:265 TwoSidedFrequentistUpperLimitWithBands.C:266 TwoSidedFrequentistUpperLimitWithBands.C:267 TwoSidedFrequentistUpperLimitWithBands.C:268 TwoSidedFrequentistUpperLimitWithBands.C:269 TwoSidedFrequentistUpperLimitWithBands.C:270 TwoSidedFrequentistUpperLimitWithBands.C:271 TwoSidedFrequentistUpperLimitWithBands.C:272 TwoSidedFrequentistUpperLimitWithBands.C:273 TwoSidedFrequentistUpperLimitWithBands.C:274 TwoSidedFrequentistUpperLimitWithBands.C:275 TwoSidedFrequentistUpperLimitWithBands.C:276 TwoSidedFrequentistUpperLimitWithBands.C:277 TwoSidedFrequentistUpperLimitWithBands.C:278 TwoSidedFrequentistUpperLimitWithBands.C:279 TwoSidedFrequentistUpperLimitWithBands.C:280 TwoSidedFrequentistUpperLimitWithBands.C:281 TwoSidedFrequentistUpperLimitWithBands.C:282 TwoSidedFrequentistUpperLimitWithBands.C:283 TwoSidedFrequentistUpperLimitWithBands.C:284 TwoSidedFrequentistUpperLimitWithBands.C:285 TwoSidedFrequentistUpperLimitWithBands.C:286 TwoSidedFrequentistUpperLimitWithBands.C:287 TwoSidedFrequentistUpperLimitWithBands.C:288 TwoSidedFrequentistUpperLimitWithBands.C:289 TwoSidedFrequentistUpperLimitWithBands.C:290 TwoSidedFrequentistUpperLimitWithBands.C:291 TwoSidedFrequentistUpperLimitWithBands.C:292 TwoSidedFrequentistUpperLimitWithBands.C:293 TwoSidedFrequentistUpperLimitWithBands.C:294 TwoSidedFrequentistUpperLimitWithBands.C:295 TwoSidedFrequentistUpperLimitWithBands.C:296 TwoSidedFrequentistUpperLimitWithBands.C:297 TwoSidedFrequentistUpperLimitWithBands.C:298 TwoSidedFrequentistUpperLimitWithBands.C:299 TwoSidedFrequentistUpperLimitWithBands.C:300 TwoSidedFrequentistUpperLimitWithBands.C:301 TwoSidedFrequentistUpperLimitWithBands.C:302 TwoSidedFrequentistUpperLimitWithBands.C:303 TwoSidedFrequentistUpperLimitWithBands.C:304 TwoSidedFrequentistUpperLimitWithBands.C:305 TwoSidedFrequentistUpperLimitWithBands.C:306 TwoSidedFrequentistUpperLimitWithBands.C:307 TwoSidedFrequentistUpperLimitWithBands.C:308 TwoSidedFrequentistUpperLimitWithBands.C:309 TwoSidedFrequentistUpperLimitWithBands.C:310 TwoSidedFrequentistUpperLimitWithBands.C:311 TwoSidedFrequentistUpperLimitWithBands.C:312 TwoSidedFrequentistUpperLimitWithBands.C:313 TwoSidedFrequentistUpperLimitWithBands.C:314 TwoSidedFrequentistUpperLimitWithBands.C:315 TwoSidedFrequentistUpperLimitWithBands.C:316 TwoSidedFrequentistUpperLimitWithBands.C:317 TwoSidedFrequentistUpperLimitWithBands.C:318 TwoSidedFrequentistUpperLimitWithBands.C:319 TwoSidedFrequentistUpperLimitWithBands.C:320 TwoSidedFrequentistUpperLimitWithBands.C:321 TwoSidedFrequentistUpperLimitWithBands.C:322 TwoSidedFrequentistUpperLimitWithBands.C:323 TwoSidedFrequentistUpperLimitWithBands.C:324 TwoSidedFrequentistUpperLimitWithBands.C:325 TwoSidedFrequentistUpperLimitWithBands.C:326 TwoSidedFrequentistUpperLimitWithBands.C:327 TwoSidedFrequentistUpperLimitWithBands.C:328 TwoSidedFrequentistUpperLimitWithBands.C:329 TwoSidedFrequentistUpperLimitWithBands.C:330 TwoSidedFrequentistUpperLimitWithBands.C:331 TwoSidedFrequentistUpperLimitWithBands.C:332 TwoSidedFrequentistUpperLimitWithBands.C:333 TwoSidedFrequentistUpperLimitWithBands.C:334 TwoSidedFrequentistUpperLimitWithBands.C:335 TwoSidedFrequentistUpperLimitWithBands.C:336 TwoSidedFrequentistUpperLimitWithBands.C:337 TwoSidedFrequentistUpperLimitWithBands.C:338 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TwoSidedFrequentistUpperLimitWithBands.C:361 TwoSidedFrequentistUpperLimitWithBands.C:362 TwoSidedFrequentistUpperLimitWithBands.C:363 TwoSidedFrequentistUpperLimitWithBands.C:364 TwoSidedFrequentistUpperLimitWithBands.C:365 TwoSidedFrequentistUpperLimitWithBands.C:366 TwoSidedFrequentistUpperLimitWithBands.C:367 TwoSidedFrequentistUpperLimitWithBands.C:368 TwoSidedFrequentistUpperLimitWithBands.C:369 TwoSidedFrequentistUpperLimitWithBands.C:370 TwoSidedFrequentistUpperLimitWithBands.C:371 TwoSidedFrequentistUpperLimitWithBands.C:372 TwoSidedFrequentistUpperLimitWithBands.C:373 TwoSidedFrequentistUpperLimitWithBands.C:374 TwoSidedFrequentistUpperLimitWithBands.C:375 TwoSidedFrequentistUpperLimitWithBands.C:376 TwoSidedFrequentistUpperLimitWithBands.C:377 TwoSidedFrequentistUpperLimitWithBands.C:378 TwoSidedFrequentistUpperLimitWithBands.C:379 TwoSidedFrequentistUpperLimitWithBands.C:380 TwoSidedFrequentistUpperLimitWithBands.C:381 TwoSidedFrequentistUpperLimitWithBands.C:382 TwoSidedFrequentistUpperLimitWithBands.C:383 TwoSidedFrequentistUpperLimitWithBands.C:384 TwoSidedFrequentistUpperLimitWithBands.C:385 TwoSidedFrequentistUpperLimitWithBands.C:386 TwoSidedFrequentistUpperLimitWithBands.C:387 TwoSidedFrequentistUpperLimitWithBands.C:388 TwoSidedFrequentistUpperLimitWithBands.C:389 TwoSidedFrequentistUpperLimitWithBands.C:390 TwoSidedFrequentistUpperLimitWithBands.C:391 TwoSidedFrequentistUpperLimitWithBands.C:392 TwoSidedFrequentistUpperLimitWithBands.C:393 TwoSidedFrequentistUpperLimitWithBands.C:394 TwoSidedFrequentistUpperLimitWithBands.C:395 TwoSidedFrequentistUpperLimitWithBands.C:396 TwoSidedFrequentistUpperLimitWithBands.C:397 TwoSidedFrequentistUpperLimitWithBands.C:398 TwoSidedFrequentistUpperLimitWithBands.C:399 TwoSidedFrequentistUpperLimitWithBands.C:400 TwoSidedFrequentistUpperLimitWithBands.C:401 TwoSidedFrequentistUpperLimitWithBands.C:402 TwoSidedFrequentistUpperLimitWithBands.C:403 TwoSidedFrequentistUpperLimitWithBands.C:404 TwoSidedFrequentistUpperLimitWithBands.C:405 TwoSidedFrequentistUpperLimitWithBands.C:406 TwoSidedFrequentistUpperLimitWithBands.C:407 TwoSidedFrequentistUpperLimitWithBands.C:408 TwoSidedFrequentistUpperLimitWithBands.C:409 TwoSidedFrequentistUpperLimitWithBands.C:410 TwoSidedFrequentistUpperLimitWithBands.C:411 TwoSidedFrequentistUpperLimitWithBands.C:412 TwoSidedFrequentistUpperLimitWithBands.C:413 TwoSidedFrequentistUpperLimitWithBands.C:414 TwoSidedFrequentistUpperLimitWithBands.C:415 TwoSidedFrequentistUpperLimitWithBands.C:416 TwoSidedFrequentistUpperLimitWithBands.C:417 TwoSidedFrequentistUpperLimitWithBands.C:418 TwoSidedFrequentistUpperLimitWithBands.C:419 TwoSidedFrequentistUpperLimitWithBands.C:420 TwoSidedFrequentistUpperLimitWithBands.C:421 TwoSidedFrequentistUpperLimitWithBands.C:422 TwoSidedFrequentistUpperLimitWithBands.C:423 TwoSidedFrequentistUpperLimitWithBands.C:424 TwoSidedFrequentistUpperLimitWithBands.C:425 TwoSidedFrequentistUpperLimitWithBands.C:426 TwoSidedFrequentistUpperLimitWithBands.C:427 TwoSidedFrequentistUpperLimitWithBands.C:428 TwoSidedFrequentistUpperLimitWithBands.C:429 TwoSidedFrequentistUpperLimitWithBands.C:430 TwoSidedFrequentistUpperLimitWithBands.C:431 TwoSidedFrequentistUpperLimitWithBands.C:432 TwoSidedFrequentistUpperLimitWithBands.C:433 TwoSidedFrequentistUpperLimitWithBands.C:434 TwoSidedFrequentistUpperLimitWithBands.C:435 TwoSidedFrequentistUpperLimitWithBands.C:436 TwoSidedFrequentistUpperLimitWithBands.C:437 TwoSidedFrequentistUpperLimitWithBands.C:438 TwoSidedFrequentistUpperLimitWithBands.C:439 TwoSidedFrequentistUpperLimitWithBands.C:440 TwoSidedFrequentistUpperLimitWithBands.C:441 TwoSidedFrequentistUpperLimitWithBands.C:442 TwoSidedFrequentistUpperLimitWithBands.C:443 TwoSidedFrequentistUpperLimitWithBands.C:444 TwoSidedFrequentistUpperLimitWithBands.C:445 TwoSidedFrequentistUpperLimitWithBands.C:446 TwoSidedFrequentistUpperLimitWithBands.C:447 TwoSidedFrequentistUpperLimitWithBands.C:448 TwoSidedFrequentistUpperLimitWithBands.C:449 TwoSidedFrequentistUpperLimitWithBands.C:450 TwoSidedFrequentistUpperLimitWithBands.C:451 TwoSidedFrequentistUpperLimitWithBands.C:452 TwoSidedFrequentistUpperLimitWithBands.C:453 TwoSidedFrequentistUpperLimitWithBands.C:454 TwoSidedFrequentistUpperLimitWithBands.C:455 TwoSidedFrequentistUpperLimitWithBands.C:456 TwoSidedFrequentistUpperLimitWithBands.C:457 TwoSidedFrequentistUpperLimitWithBands.C:458 TwoSidedFrequentistUpperLimitWithBands.C:459 TwoSidedFrequentistUpperLimitWithBands.C:460 TwoSidedFrequentistUpperLimitWithBands.C:461 TwoSidedFrequentistUpperLimitWithBands.C:462 TwoSidedFrequentistUpperLimitWithBands.C:463 TwoSidedFrequentistUpperLimitWithBands.C:464 TwoSidedFrequentistUpperLimitWithBands.C:465 TwoSidedFrequentistUpperLimitWithBands.C:466 TwoSidedFrequentistUpperLimitWithBands.C:467 TwoSidedFrequentistUpperLimitWithBands.C:468 TwoSidedFrequentistUpperLimitWithBands.C:469 TwoSidedFrequentistUpperLimitWithBands.C:470 TwoSidedFrequentistUpperLimitWithBands.C:471 |
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