// internal routine to run the inverter
HypoTestInverterResult *
RooStats::HypoTestInvTool::RunInverter(RooWorkspace * w,
const char * modelSBName, const char * modelBName,
const char * dataName, int type, int testStatType,
bool useCLs, int npoints, double poimin, double poimax,
int ntoys,
bool useNumberCounting,
const char * nuisPriorName ){
std::cout << "Running HypoTestInverter on the workspace " << w->GetName() << std::endl;
w->Print();
RooAbsData * data = w->data(dataName);
if (!data) {
Error("StandardHypoTestDemo","Not existing data %s",dataName);
return 0;
}
else
std::cout << "Using data set " << dataName << std::endl;
if (mUseVectorStore) {
RooAbsData::setDefaultStorageType(RooAbsData::Vector);
data->convertToVectorStore() ;
}
// get models from WS
// get the modelConfig out of the file
ModelConfig* bModel = (ModelConfig*) w->obj(modelBName);
ModelConfig* sbModel = (ModelConfig*) w->obj(modelSBName);
if (!sbModel) {
Error("StandardHypoTestDemo","Not existing ModelConfig %s",modelSBName);
return 0;
}
// check the model
if (!sbModel->GetPdf()) {
Error("StandardHypoTestDemo","Model %s has no pdf ",modelSBName);
return 0;
}
if (!sbModel->GetParametersOfInterest()) {
Error("StandardHypoTestDemo","Model %s has no poi ",modelSBName);
return 0;
}
if (!sbModel->GetObservables()) {
Error("StandardHypoTestInvDemo","Model %s has no observables ",modelSBName);
return 0;
}
if (!sbModel->GetSnapshot() ) {
Info("StandardHypoTestInvDemo","Model %s has no snapshot - make one using model poi",modelSBName);
sbModel->SetSnapshot( *sbModel->GetParametersOfInterest() );
}
// 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 || bModel == sbModel) {
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("_with_poi_0"));
RooRealVar * var = dynamic_cast<RooRealVar*>(bModel->GetParametersOfInterest()->first());
if (!var) return 0;
double oldval = var->getVal();
var->setVal(0);
bModel->SetSnapshot( RooArgSet(*var) );
var->setVal(oldval);
}
else {
if (!bModel->GetSnapshot() ) {
Info("StandardHypoTestInvDemo","Model %s has no snapshot - make one using model poi and 0 values ",modelBName);
RooRealVar * var = dynamic_cast<RooRealVar*>(bModel->GetParametersOfInterest()->first());
if (var) {
double oldval = var->getVal();
var->setVal(0);
bModel->SetSnapshot( RooArgSet(*var) );
var->setVal(oldval);
}
else {
Error("StandardHypoTestInvDemo","Model %s has no valid poi",modelBName);
return 0;
}
}
}
// check model has global observables when there are nuisance pdf
// for the hybrid case the globobs are not needed
if (type != 1 ) {
bool hasNuisParam = (sbModel->GetNuisanceParameters() && sbModel->GetNuisanceParameters()->getSize() > 0);
bool hasGlobalObs = (sbModel->GetGlobalObservables() && sbModel->GetGlobalObservables()->getSize() > 0);
if (hasNuisParam && !hasGlobalObs ) {
// try to see if model has nuisance parameters first
RooAbsPdf * constrPdf = RooStats::MakeNuisancePdf(*sbModel,"nuisanceConstraintPdf_sbmodel");
if (constrPdf) {
Warning("StandardHypoTestInvDemo","Model %s has nuisance parameters but no global observables associated",sbModel->GetName());
Warning("StandardHypoTestInvDemo","\tThe effect of the nuisance parameters will not be treated correctly ");
}
}
}
// run first a data fit
const RooArgSet * poiSet = sbModel->GetParametersOfInterest();
RooRealVar *poi = (RooRealVar*)poiSet->first();
std::cout << "StandardHypoTestInvDemo : POI initial value: " << poi->GetName() << " = " << poi->getVal() << std::endl;
// fit the data first (need to use constraint )
TStopwatch tw;
bool doFit = initialFit;
if (testStatType == 0 && initialFit == -1) doFit = false; // case of LEP test statistic
if (type == 3 && initialFit == -1) doFit = false; // case of Asymptoticcalculator with nominal Asimov
double poihat = 0;
if (minimizerType.size()==0) minimizerType = ROOT::Math::MinimizerOptions::DefaultMinimizerType();
else
ROOT::Math::MinimizerOptions::SetDefaultMinimizer(minimizerType.c_str());
Info("StandardHypoTestInvDemo","Using %s as minimizer for computing the test statistic",
ROOT::Math::MinimizerOptions::DefaultMinimizerType().c_str() );
if (doFit) {
// do the fit : By doing a fit the POI snapshot (for S+B) is set to the fit value
// and the nuisance parameters nominal values will be set to the fit value.
// This is relevant when using LEP test statistics
Info( "StandardHypoTestInvDemo"," Doing a first fit to the observed data ");
RooArgSet constrainParams;
if (sbModel->GetNuisanceParameters() ) constrainParams.add(*sbModel->GetNuisanceParameters());
RooStats::RemoveConstantParameters(&constrainParams);
tw.Start();
RooFitResult * fitres = sbModel->GetPdf()->fitTo(*data,InitialHesse(false), Hesse(false),
Minimizer(minimizerType.c_str(),"Migrad"), Strategy(0), PrintLevel(mPrintLevel), Constrain(constrainParams), Save(true) );
if (fitres->status() != 0) {
Warning("StandardHypoTestInvDemo","Fit to the model failed - try with strategy 1 and perform first an Hesse computation");
fitres = sbModel->GetPdf()->fitTo(*data,InitialHesse(true), Hesse(false),Minimizer(minimizerType.c_str(),"Migrad"), Strategy(1), PrintLevel(mPrintLevel+1), Constrain(constrainParams), Save(true) );
}
if (fitres->status() != 0)
Warning("StandardHypoTestInvDemo"," Fit still failed - continue anyway.....");
poihat = poi->getVal();
std::cout << "StandardHypoTestInvDemo - Best Fit value : " << poi->GetName() << " = "
<< poihat << " +/- " << poi->getError() << std::endl;
std::cout << "Time for fitting : "; tw.Print();
//save best fit value in the poi snapshot
sbModel->SetSnapshot(*sbModel->GetParametersOfInterest());
std::cout << "StandardHypoTestInvo: snapshot of S+B Model " << sbModel->GetName()
<< " is set to the best fit value" << std::endl;
}
// print a message in case of LEP test statistics because it affects result by doing or not doing a fit
if (testStatType == 0) {
if (!doFit)
Info("StandardHypoTestInvDemo","Using LEP test statistic - an initial fit is not done and the TS will use the nuisances at the model value");
else
Info("StandardHypoTestInvDemo","Using LEP test statistic - an initial fit has been done and the TS will use the nuisances at the best fit value");
}
// build test statistics and hypotest calculators for running the inverter
SimpleLikelihoodRatioTestStat slrts(*sbModel->GetPdf(),*bModel->GetPdf());
// null parameters must includes snapshot of poi plus the nuisance values
RooArgSet nullParams(*sbModel->GetSnapshot());
if (sbModel->GetNuisanceParameters()) nullParams.add(*sbModel->GetNuisanceParameters());
if (sbModel->GetSnapshot()) slrts.SetNullParameters(nullParams);
RooArgSet altParams(*bModel->GetSnapshot());
if (bModel->GetNuisanceParameters()) altParams.add(*bModel->GetNuisanceParameters());
if (bModel->GetSnapshot()) slrts.SetAltParameters(altParams);
// ratio of profile likelihood - need to pass snapshot for the alt
RatioOfProfiledLikelihoodsTestStat
ropl(*sbModel->GetPdf(), *bModel->GetPdf(), bModel->GetSnapshot());
ropl.SetSubtractMLE(false);
if (testStatType == 11) ropl.SetSubtractMLE(true);
ropl.SetPrintLevel(mPrintLevel);
ropl.SetMinimizer(minimizerType.c_str());
ProfileLikelihoodTestStat profll(*sbModel->GetPdf());
if (testStatType == 3) profll.SetOneSided(true);
if (testStatType == 4) profll.SetSigned(true);
profll.SetMinimizer(minimizerType.c_str());
profll.SetPrintLevel(mPrintLevel);
profll.SetReuseNLL(mOptimize);
slrts.SetReuseNLL(mOptimize);
ropl.SetReuseNLL(mOptimize);
if (mOptimize) {
profll.SetStrategy(0);
ropl.SetStrategy(0);
ROOT::Math::MinimizerOptions::SetDefaultStrategy(0);
}
if (mMaxPoi > 0) poi->setMax(mMaxPoi); // increase limit
MaxLikelihoodEstimateTestStat maxll(*sbModel->GetPdf(),*poi);
NumEventsTestStat nevtts;
AsymptoticCalculator::SetPrintLevel(mPrintLevel);
// create the HypoTest calculator class
HypoTestCalculatorGeneric * hc = 0;
if (type == 0) hc = new FrequentistCalculator(*data, *bModel, *sbModel);
else if (type == 1) hc = new HybridCalculator(*data, *bModel, *sbModel);
// else if (type == 2 ) hc = new AsymptoticCalculator(*data, *bModel, *sbModel, false, mAsimovBins);
// else if (type == 3 ) hc = new AsymptoticCalculator(*data, *bModel, *sbModel, true, mAsimovBins); // for using Asimov data generated with nominal values
else if (type == 2 ) hc = new AsymptoticCalculator(*data, *bModel, *sbModel, false );
else if (type == 3 ) hc = new AsymptoticCalculator(*data, *bModel, *sbModel, true ); // for using Asimov data generated with nominal values
else {
Error("StandardHypoTestInvDemo","Invalid - calculator type = %d supported values are only :\n\t\t\t 0 (Frequentist) , 1 (Hybrid) , 2 (Asymptotic) ",type);
return 0;
}
// set the test statistic
TestStatistic * testStat = 0;
if (testStatType == 0) testStat = &slrts;
if (testStatType == 1 || testStatType == 11) testStat = &ropl;
if (testStatType == 2 || testStatType == 3 || testStatType == 4) testStat = &profll;
if (testStatType == 5) testStat = &maxll;
if (testStatType == 6) testStat = &nevtts;
if (testStat == 0) {
Error("StandardHypoTestInvDemo","Invalid - test statistic type = %d supported values are only :\n\t\t\t 0 (SLR) , 1 (Tevatron) , 2 (PLR), 3 (PLR1), 4(MLE)",testStatType);
return 0;
}
ToyMCSampler *toymcs = (ToyMCSampler*)hc->GetTestStatSampler();
if (toymcs && (type == 0 || type == 1) ) {
// look if pdf is number counting or extended
if (sbModel->GetPdf()->canBeExtended() ) {
if (useNumberCounting) Warning("StandardHypoTestInvDemo","Pdf is extended: but number counting flag is set: ignore it ");
}
else {
// for not extended pdf
if (!useNumberCounting ) {
int nEvents = data->numEntries();
Info("StandardHypoTestInvDemo","Pdf is not extended: number of events to generate taken from observed data set is %d",nEvents);
toymcs->SetNEventsPerToy(nEvents);
}
else {
Info("StandardHypoTestInvDemo","using a number counting pdf");
toymcs->SetNEventsPerToy(1);
}
}
toymcs->SetTestStatistic(testStat);
if (data->isWeighted() && !mGenerateBinned) {
Info("StandardHypoTestInvDemo","Data set is weighted, nentries = %d and sum of weights = %8.1f but toy generation is unbinned - it would be faster to set mGenerateBinned to true\n",data->numEntries(), data->sumEntries());
}
toymcs->SetGenerateBinned(mGenerateBinned);
toymcs->SetUseMultiGen(mOptimize);
if (mGenerateBinned && sbModel->GetObservables()->getSize() > 2) {
Warning("StandardHypoTestInvDemo","generate binned is activated but the number of ovservable is %d. Too much memory could be needed for allocating all the bins",sbModel->GetObservables()->getSize() );
}
// set the random seed if needed
if (mRandomSeed >= 0) RooRandom::randomGenerator()->SetSeed(mRandomSeed);
}
// specify if need to re-use same toys
if (reuseAltToys) {
hc->UseSameAltToys();
}
if (type == 1) {
HybridCalculator *hhc = dynamic_cast<HybridCalculator*> (hc);
assert(hhc);
hhc->SetToys(ntoys,ntoys/mNToysRatio); // can use less ntoys for b hypothesis
// remove global observables from ModelConfig (this is probably not needed anymore in 5.32)
bModel->SetGlobalObservables(RooArgSet() );
sbModel->SetGlobalObservables(RooArgSet() );
// check for nuisance prior pdf in case of nuisance parameters
if (bModel->GetNuisanceParameters() || sbModel->GetNuisanceParameters() ) {
// fix for using multigen (does not work in this case)
toymcs->SetUseMultiGen(false);
ToyMCSampler::SetAlwaysUseMultiGen(false);
RooAbsPdf * nuisPdf = 0;
if (nuisPriorName) nuisPdf = w->pdf(nuisPriorName);
// use prior defined first in bModel (then in SbModel)
if (!nuisPdf) {
Info("StandardHypoTestInvDemo","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("StandardHypoTestInvDemo","No nuisance pdf given - try to use %s that is defined as a prior pdf in the B model",nuisPdf->GetName());
}
else {
Error("StandardHypoTestInvDemo","Cannnot run Hybrid calculator because no prior on the nuisance parameter is specified or can be derived");
return 0;
}
}
assert(nuisPdf);
Info("StandardHypoTestInvDemo","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("StandardHypoTestInvDemo","Prior nuisance does not depend on nuisance parameters. They will be smeared in their full range");
}
delete np;
hhc->ForcePriorNuisanceAlt(*nuisPdf);
hhc->ForcePriorNuisanceNull(*nuisPdf);
}
}
else if (type == 2 || type == 3) {
if (testStatType == 3) ((AsymptoticCalculator*) hc)->SetOneSided(true);
if (testStatType != 2 && testStatType != 3)
Warning("StandardHypoTestInvDemo","Only the PL test statistic can be used with AsymptoticCalculator - use by default a two-sided PL");
}
else if (type == 0 || type == 1)
((FrequentistCalculator*) hc)->SetToys(ntoys,ntoys/mNToysRatio);
// Get the result
RooMsgService::instance().getStream(1).removeTopic(RooFit::NumIntegration);
HypoTestInverter calc(*hc);
calc.SetConfidenceLevel(0.95);
calc.UseCLs(useCLs);
calc.SetVerbose(true);
// can speed up using proof-lite
if (mUseProof && mNWorkers > 1) {
ProofConfig pc(*w, mNWorkers, "", kFALSE);
toymcs->SetProofConfig(&pc); // enable proof
}
if (npoints > 0) {
if (poimin > poimax) {
// if no min/max given scan between MLE and +4 sigma
poimin = int(poihat);
poimax = int(poihat + 4 * poi->getError());
}
std::cout << "Doing a fixed scan in interval : " << poimin << " , " << poimax << std::endl;
calc.SetFixedScan(npoints,poimin,poimax);
}
else {
//poi->setMax(10*int( (poihat+ 10 *poi->getError() )/10 ) );
std::cout << "Doing an automatic scan in interval : " << poi->getMin() << " , " << poi->getMax() << std::endl;
}
tw.Start();
HypoTestInverterResult * r = calc.GetInterval();
std::cout << "Time to perform limit scan \n";
tw.Print();
if (mRebuild) {
calc.SetCloseProof(1);
tw.Start();
SamplingDistribution * limDist = calc.GetUpperLimitDistribution(true,mNToyToRebuild);
std::cout << "Time to rebuild distributions " << std::endl;
tw.Print();
if (limDist) {
std::cout << "expected up limit " << limDist->InverseCDF(0.5) << " +/- "
<< limDist->InverseCDF(0.16) << " "
<< limDist->InverseCDF(0.84) << "\n";
//update r to a new updated result object containing the rebuilt expected p-values distributions
// (it will not recompute the expected limit)
if (r) delete r; // need to delete previous object since GetInterval will return a cloned copy
r = calc.GetInterval();
}
else
std::cout << "ERROR : failed to re-build distributions " << std::endl;
}
return r;
}
//void RunToyScan5(TString fileName, double startVal, double stopVal, TString outFile) {
void frequentist(TString fileName) {
cout << "Starting frequentist " << time(NULL) << endl;
double startVal = 0;
double stopVal = 200;
TString outFile = "";
int nToys = 1 ;
int nscanpoints = 2 ;
/*
gROOT->LoadMacro("RooBetaPdf.cxx+") ;
gROOT->LoadMacro("RooRatio.cxx+") ;
gROOT->LoadMacro("RooPosDefCorrGauss.cxx+") ;
*/
// get relevant objects out of the "ws" file
TFile *file = TFile::Open(fileName);
if(!file){
cout <<"file not found" << endl;
return;
}
RooWorkspace* w = (RooWorkspace*) file->Get("workspace");
if(!w){
cout <<"workspace not found" << endl;
return;
}
ModelConfig* mc = (ModelConfig*) w->obj("S+B_model");
RooAbsData* data = w->data("data");
if( !data || !mc ){
w->Print();
cout << "data or ModelConfig was not found" <<endl;
return;
}
RooRealVar* myPOI = (RooRealVar*) mc->GetParametersOfInterest()->first();
myPOI->setRange(0, 1000.);
ModelConfig* bModel = (ModelConfig*) w->obj("B_model");
ModelConfig* sbModel = (ModelConfig*) w->obj("S+B_model");
ProfileLikelihoodTestStat profll(*sbModel->GetPdf());
profll.SetPrintLevel(2);
profll.SetOneSided(1);
TestStatistic * testStat = &profll;
HypoTestCalculatorGeneric * hc = 0;
hc = new FrequentistCalculator(*data, *bModel, *sbModel);
ToyMCSampler *toymcs = (ToyMCSampler*)hc->GetTestStatSampler();
toymcs->SetMaxToys(10000);
toymcs->SetNEventsPerToy(1);
toymcs->SetTestStatistic(testStat);
((FrequentistCalculator *)hc)->SetToys(nToys,nToys);
HypoTestInverter calc(*hc);
calc.SetConfidenceLevel(0.95);
calc.UseCLs(true);
//calc.SetVerbose(true);
calc.SetVerbose(2);
cout << "About to set fixed scan " << time(NULL) << endl;
calc.SetFixedScan(nscanpoints,startVal,stopVal);
cout << "About to do inverter " << time(NULL) << endl;
HypoTestInverterResult * res_toysCLs_calculator = calc.GetInterval();
cout << "CLs = " << res_toysCLs_calculator->UpperLimit()
<< " CLs_exp = " << res_toysCLs_calculator->GetExpectedUpperLimit(0)
<< " CLs_exp(-1s) = " << res_toysCLs_calculator->GetExpectedUpperLimit(-1)
<< " CLs_exp(+1s) = " << res_toysCLs_calculator->GetExpectedUpperLimit(1) << endl ;
/*
// dump results string to output file
ofstream outStream ;
outStream.open(outFile,ios::app) ;
outStream << "CLs = " << res_toysCLs_calculator->UpperLimit()
<< " CLs_exp = " << res_toysCLs_calculator->GetExpectedUpperLimit(0)
<< " CLs_exp(-1s) = " << res_toysCLs_calculator->GetExpectedUpperLimit(-1)
<< " CLs_exp(+1s) = " << res_toysCLs_calculator->GetExpectedUpperLimit(1) << endl ;
outStream.close() ;
*/
cout << "End of frequentist " << time(NULL) << endl;
return ;
}
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;
}
}
}
// internal routine to run the inverter
HypoTestInverterResult * RunInverter(RooWorkspace * w, const char * modelSBName, const char * modelBName,
const char * dataName, int type, int testStatType,
int npoints, double poimin, double poimax,
int ntoys, bool useCls )
{
std::cout << "Running HypoTestInverter on the workspace " << w->GetName() << std::endl;
w->Print();
RooAbsData * data = w->data(dataName);
if (!data) {
Error("RA2bHypoTestDemo","Not existing data %s",dataName);
return 0;
}
else
std::cout << "Using data set " << dataName << std::endl;
// get models from WS
// get the modelConfig out of the file
ModelConfig* bModel = (ModelConfig*) w->obj(modelBName);
ModelConfig* sbModel = (ModelConfig*) w->obj(modelSBName);
if (!sbModel) {
Error("RA2bHypoTestDemo","Not existing ModelConfig %s",modelSBName);
return 0;
}
// check the model
if (!sbModel->GetPdf()) {
Error("RA2bHypoTestDemo","Model %s has no pdf ",modelSBName);
return 0;
}
if (!sbModel->GetParametersOfInterest()) {
Error("RA2bHypoTestDemo","Model %s has no poi ",modelSBName);
return 0;
}
if (!sbModel->GetParametersOfInterest()) {
Error("RA2bHypoTestInvDemo","Model %s has no poi ",modelSBName);
return 0;
}
if (!sbModel->GetSnapshot() ) {
Info("RA2bHypoTestInvDemo","Model %s has no snapshot - make one using model poi",modelSBName);
sbModel->SetSnapshot( *sbModel->GetParametersOfInterest() );
}
if (!bModel || bModel == sbModel) {
Info("RA2bHypoTestInvDemo","The background model %s does not exist",modelBName);
Info("RA2bHypoTestInvDemo","Copy it from ModelConfig %s and set POI to zero",modelSBName);
bModel = (ModelConfig*) sbModel->Clone();
bModel->SetName(TString(modelSBName)+TString("_with_poi_0"));
RooRealVar * var = dynamic_cast<RooRealVar*>(bModel->GetParametersOfInterest()->first());
if (!var) return 0;
double oldval = var->getVal();
var->setVal(0);
bModel->SetSnapshot( RooArgSet(*var) );
var->setVal(oldval);
}
else {
if (!bModel->GetSnapshot() ) {
Info("RA2bHypoTestInvDemo","Model %s has no snapshot - make one using model poi and 0 values ",modelBName);
RooRealVar * var = dynamic_cast<RooRealVar*>(bModel->GetParametersOfInterest()->first());
if (var) {
double oldval = var->getVal();
var->setVal(0);
bModel->SetSnapshot( RooArgSet(*var) );
var->setVal(oldval);
}
else {
Error("RA2bHypoTestInvDemo","Model %s has no valid poi",modelBName);
return 0;
}
}
}
SimpleLikelihoodRatioTestStat slrts(*sbModel->GetPdf(),*bModel->GetPdf());
if (sbModel->GetSnapshot()) slrts.SetNullParameters(*sbModel->GetSnapshot());
if (bModel->GetSnapshot()) slrts.SetAltParameters(*bModel->GetSnapshot());
// ratio of profile likelihood - need to pass snapshot for the alt
RatioOfProfiledLikelihoodsTestStat
ropl(*sbModel->GetPdf(), *bModel->GetPdf(), bModel->GetSnapshot());
ropl.SetSubtractMLE(false);
//MyProfileLikelihoodTestStat profll(*sbModel->GetPdf());
ProfileLikelihoodTestStat profll(*sbModel->GetPdf());
if (testStatType == 3) profll.SetOneSided(1);
if (optimize) profll.SetReuseNLL(true);
TestStatistic * testStat = &slrts;
if (testStatType == 1) testStat = &ropl;
if (testStatType == 2 || testStatType == 3) testStat = &profll;
HypoTestCalculatorGeneric * hc = 0;
if (type == 0) hc = new FrequentistCalculator(*data, *bModel, *sbModel);
else hc = new HybridCalculator(*data, *bModel, *sbModel);
ToyMCSampler *toymcs = (ToyMCSampler*)hc->GetTestStatSampler();
//=== DEBUG
///// toymcs->SetWS( w ) ;
//=== DEBUG
toymcs->SetNEventsPerToy(1);
toymcs->SetTestStatistic(testStat);
if (optimize) toymcs->SetUseMultiGen(true);
if (type == 1) {
HybridCalculator *hhc = (HybridCalculator*) hc;
hhc->SetToys(ntoys,ntoys);
// check for nuisance prior pdf
if (bModel->GetPriorPdf() && sbModel->GetPriorPdf() ) {
hhc->ForcePriorNuisanceAlt(*bModel->GetPriorPdf());
hhc->ForcePriorNuisanceNull(*sbModel->GetPriorPdf());
}
else {
if (bModel->GetNuisanceParameters() || sbModel->GetNuisanceParameters() ) {
Error("RA2bHypoTestInvDemo","Cannnot run Hybrid calculator because no prior on the nuisance parameter is specified");
return 0;
}
}
}
else
((FrequentistCalculator*) hc)->SetToys(ntoys,ntoys);
// Get the result
RooMsgService::instance().getStream(1).removeTopic(RooFit::NumIntegration);
TStopwatch tw; tw.Start();
const RooArgSet * poiSet = sbModel->GetParametersOfInterest();
RooRealVar *poi = (RooRealVar*)poiSet->first();
// fit the data first
sbModel->GetPdf()->fitTo(*data);
double poihat = poi->getVal();
HypoTestInverter calc(*hc);
calc.SetConfidenceLevel(0.95);
calc.UseCLs(useCls);
calc.SetVerbose(true);
// can speed up using proof-lite
if (useProof && nworkers > 1) {
ProofConfig pc(*w, nworkers, "", kFALSE);
toymcs->SetProofConfig(&pc); // enable proof
}
printf(" npoints = %d, poimin = %7.2f, poimax = %7.2f\n\n", npoints, poimin, poimax ) ;
cout << flush ;
if ( npoints==1 ) {
std::cout << "Evaluating one point : " << poimax << std::endl;
calc.RunOnePoint(poimax);
} else if (npoints > 0) {
if (poimin >= poimax) {
// if no min/max given scan between MLE and +4 sigma
poimin = int(poihat);
poimax = int(poihat + 4 * poi->getError());
}
std::cout << "Doing a fixed scan in interval : " << poimin << " , " << poimax << std::endl;
calc.SetFixedScan(npoints,poimin,poimax);
}
else {
//poi->setMax(10*int( (poihat+ 10 *poi->getError() )/10 ) );
std::cout << "Doing an automatic scan in interval : " << poi->getMin() << " , " << poi->getMax() << std::endl;
}
cout << "\n\n right before calc.GetInterval(), ntoys = " << ntoys << " \n\n" << flush ;
HypoTestInverterResult * r = calc.GetInterval();
return r;
}
void HypoTestInvDemo(const char * fileName ="GausModel_b.root",
const char * wsName = "w",
const char * modelSBName = "model_sb",
const char * modelBName = "model_b",
const char * dataName = "data_obs",
int type = 0, // calculator type
int testStatType = 0, // test stat type
int npoints = 10,
int ntoys=1000,
bool useCls = true )
{
/*
type = 0 Freq calculator
type = 1 Hybrid
testStatType = 0 LEP
= 1 Tevatron
= 2 PL
*/
if (fileName==0) {
std::cout << "give input filename " << std::endl;
return;
}
TFile * file = new TFile(fileName);
RooWorkspace * w = dynamic_cast<RooWorkspace*>( file->Get(wsName) );
if (!w) {
return;
}
w->Print();
RooAbsData * data = w->data(dataName);
if (!data) {
Error("HypoTestDemo","Not existing data %s",dataName);
}
// get models from WS
// get the modelConfig out of the file
ModelConfig* bModel = (ModelConfig*) w->obj(modelBName);
ModelConfig* sbModel = (ModelConfig*) w->obj(modelSBName);
SimpleLikelihoodRatioTestStat slrts(*bModel->GetPdf(),*sbModel->GetPdf());
slrts.SetNullParameters(*bModel->GetSnapshot());
slrts.SetAltParameters(*sbModel->GetSnapshot());
RatioOfProfiledLikelihoodsTestStat
ropl(*bModel->GetPdf(), *sbModel->GetPdf(), sbModel->GetSnapshot());
ropl.SetSubtractMLE(false);
ProfileLikelihoodTestStat profll(*sbModel->GetPdf());
profll.SetOneSided(0);
TestStatistic * testStat = &slrts;
if (testStatType == 1) testStat = &ropl;
if (testStatType == 2) testStat = &profll;
HypoTestCalculatorGeneric * hc = 0;
if (type == 0) hc = new FrequentistCalculator(*data, *sbModel, *bModel);
else new HybridCalculator(*data, *sbModel, *bModel);
ToyMCSampler *toymcs = (ToyMCSampler*)hc->GetTestStatSampler();
//toymcs->SetNEventsPerToy(1);
toymcs->SetTestStatistic(testStat);
if (type == 1) {
HybridCalculator *hhc = (HybridCalculator*) hc;
hhc->SetToys(ntoys,ntoys);
// hhc->ForcePriorNuisanceAlt(*pdfNuis);
// hhc->ForcePriorNuisanceNull(*pdfNuis);
}
else
((FrequentistCalculator*) hc)->SetToys(ntoys,ntoys);
// Get the result
RooMsgService::instance().getStream(1).removeTopic(RooFit::NumIntegration);
TStopwatch tw; tw.Start();
const RooArgSet * poiSet = sbModel->GetParametersOfInterest();
RooRealVar *poi = (RooRealVar*)poiSet->first();
// fit the data first
sbModel->GetPdf()->fitTo(*data);
double poihat = poi->getVal();
//poi->setVal(30);
//poi->setError(10);
HypoTestInverter calc(*hc);
// GENA: for two-sided interval
//calc.SetConfidenceLevel(0.95);
// GENA: for 95% upper limit
calc.SetConfidenceLevel(0.90);
calc.UseCLs(useCls);
calc.SetVerbose(true);
// can spped up using proof
ProofConfig pc(*w, 2, "workers=2", kFALSE);
//ProofConfig pc(*w, 30, "localhost", kFALSE);
//ToyMCSampler * toymcs = dynamic_cast<ToyMCSampler *> (calc.GetHypoTestCalculator()->GetTestStatSampler() );
// GENA: disable proof for now
//toymcs->SetProofConfig(&pc); // enable proof
if (npoints > 0) {
// GENA
double poimin = TMath::Max(poihat - 4 * poi->getError(), 0.0);
//poimin = poihat;
double poimax = poihat + 4 * poi->getError();
poimin = 0;
poimax = 20;
//double poimin = poi->getMin();
//double poimax = poi->getMax();
std::cout << "Doing a fixed scan in interval : " << poimin << " , " << poimax << std::endl;
calc.SetFixedScan(npoints,poimin,poimax);
}
HypoTestInverterResult * r = calc.GetInterval();
// write to a file the results
TString resultFileName = (useCls) ? "CLs_" : "Cls+b_";
resultFileName += fileName;
// GENA
//TFile * file = new TFile(resultFileName,"RECREATE");
file = new TFile(resultFileName,"RECREATE");
r->Write();
file->Close();
double ulError = r->UpperLimitEstimatedError();
double upperLimit = r->UpperLimit();
std::cout << "The computed upper limit is: " << upperLimit << std::endl;
std::cout << "an estimated error on this upper limit is: " << ulError << std::endl;
// check using interpolation
// double interpLimit = r->FindInterpolatedLimit(1.-r->ConfidenceLevel() );
// cout << "The computer interpolated limits is " << interpLimit << endl;
const int nEntries = r->ArraySize();
std::vector<Double_t> xArray(nEntries);
std::vector<Double_t> yArray(nEntries);
std::vector<Double_t> yErrArray(nEntries);
for (int i=0; i<nEntries; i++) {
xArray[i] = r->GetXValue(i);
yArray[i] = r->GetYValue(i);
yErrArray[i] = r->GetYError(i);
std::cout << xArray[i] << " , " << yArray[i] << " err = " << yErrArray[i] << std::endl;
}
// see expected result (bands)
TGraph * g0 = new TGraph(nEntries);
TGraphAsymmErrors * g1 = new TGraphAsymmErrors(nEntries);
TGraphAsymmErrors * g2l = new TGraphAsymmErrors(nEntries);
TGraphAsymmErrors * g2u = new TGraphAsymmErrors(nEntries);
double p[7];
double q[7];
p[0] = ROOT::Math::normal_cdf(-2);
p[1] = ROOT::Math::normal_cdf(-1.5);
p[2] = ROOT::Math::normal_cdf(-1);
p[3] = 0.5;
p[4] = ROOT::Math::normal_cdf(1);
p[5] = ROOT::Math::normal_cdf(1.5);
p[6] = ROOT::Math::normal_cdf(2);
for (int i=0; i<nEntries; i++) {
SamplingDistribution * s = r->GetExpectedDistribution(i);
// GENA
//const std::vector<double> & values = s->GetSamplingDistribution();
const std::vector<Double_t> & cValues = s->GetSamplingDistribution();
std::vector<Double_t> values;
for (std::vector<Double_t>::const_iterator val = cValues.begin();
val != cValues.end();
++val) values.push_back(*val);
TMath::Quantiles(values.size(), 7, &values[0],q,p,false);
double p0 = q[3];
double p2l = q[1];
double p2u = q[5];
g0->SetPoint(i, r->GetXValue(i), p0 ) ;
g1->SetPoint(i, r->GetXValue(i), p0);
g2l->SetPoint(i, r->GetXValue(i), p2l);
g2u->SetPoint(i, r->GetXValue(i), p2u);
//g2->SetPoint(i, r->GetXValue(i), s->InverseCDF(0.50));
g1->SetPointEYlow(i, q[3] - q[2]); // -1 sigma errorr
g1->SetPointEYhigh(i, q[4] - q[3]);//+1 sigma error
g2l->SetPointEYlow(i, q[1]-q[0]); // -2 -- -1 sigma error
g2l->SetPointEYhigh(i, q[2]-q[1]);
g2u->SetPointEYlow(i, q[5]-q[4]);
g2u->SetPointEYhigh(i, q[6]-q[5]);
if (plotHypoTestResult) {
HypoTestResult * hr = new HypoTestResult();
hr->SetNullDistribution( r->GetBackgroundDistribution() );
hr->SetAltDistribution( r->GetSignalAndBackgroundDistribution(i) );
new TCanvas();
HypoTestPlot * pl = new HypoTestPlot(*hr);
pl->Draw();
}
}
HypoTestInverterPlot *plot = new HypoTestInverterPlot("result","",r);
TGraphErrors * g = plot->MakePlot();
g->Draw("APL");
g2l->SetFillColor(kYellow);
g2l->Draw("3");
g2u->SetFillColor(kYellow);
g2u->Draw("3");
g1->SetFillColor(kGreen);
g1->Draw("3");
g0->SetLineColor(kBlue);
g0->SetLineStyle(2);
g0->SetLineWidth(2);
g0->Draw("L");
//g1->Draw("P");
//g2->Draw("P");
g->SetLineWidth(2);
g->Draw("PL");
// GENA: two-sided interval
//double alpha = 1.-r->ConfidenceLevel();
// GENA: upper limit
double alpha = (1.-r->ConfidenceLevel())/2.0;
double x1 = g->GetXaxis()->GetXmin();
double x2 = g->GetXaxis()->GetXmax();
TLine * line = new TLine(x1, alpha, x2,alpha);
line->SetLineColor(kRed);
line->Draw();
// see the expected limit and -1 +1 sigma bands
// SamplingDistribution * limits = r->GetUpperLimitDistribution();
// std::cout << " expected limit (median) " << limits->InverseCDF(0.50) << std::endl;
// std::cout << " expected limit (-1 sig) " << limits->InverseCDF((ROOT::Math::normal_cdf(-1))) << std::endl;
// std::cout << " expected limit (+1 sig) " << limits->InverseCDF((ROOT::Math::normal_cdf(+1))) << std::endl;
tw.Print();
}
