rs101_limitexample.C File Reference

Detailed Description

'Limit Example' RooStats tutorial macro #101 This tutorial shows an example of creating a simple model for a number counting experiment with uncertainty on both the background rate and signal efficiency.

We then use a Confidence Interval Calculator to set a limit on the signal.

Processing /mnt/build/workspace/root-makedoc-v610/rootspi/rdoc/src/v6-10-00-patches/tutorials/roostats/rs101_limitexample.C...

#include "RooProfileLL.h"
#include "RooAbsPdf.h"
#include "RooStats/HypoTestResult.h"
#include "RooRealVar.h"
#include "RooPlot.h"
#include "RooDataSet.h"
#include "RooTreeDataStore.h"
#include "TTree.h"
#include "TCanvas.h"
#include "TLine.h"
#include "TStopwatch.h"

#include "RooStats/ProfileLikelihoodCalculator.h"
#include "RooStats/MCMCCalculator.h"
#include "RooStats/UniformProposal.h"
#include "RooStats/FeldmanCousins.h"
#include "RooStats/NumberCountingPdfFactory.h"
#include "RooStats/ConfInterval.h"
#include "RooStats/PointSetInterval.h"
#include "RooStats/LikelihoodInterval.h"
#include "RooStats/LikelihoodIntervalPlot.h"
#include "RooStats/RooStatsUtils.h"
#include "RooStats/ModelConfig.h"
#include "RooStats/MCMCInterval.h"
#include "RooStats/MCMCIntervalPlot.h"
#include "RooStats/ProposalFunction.h"
#include "RooStats/ProposalHelper.h"
#include "RooFitResult.h"
#include "TGraph2D.h"

// use this order for safety on library loading
using namespace RooFit;
using namespace RooStats;


void rs101_limitexample()
{
   // --------------------------------------
   // An example of setting a limit in a number counting experiment with uncertainty on background and signal

   // to time the macro
   TStopwatch t;
   t.Start();

   // --------------------------------------
   // The Model building stage
   // --------------------------------------
   RooWorkspace* wspace = new RooWorkspace();
   wspace->factory("Poisson::countingModel(obs[150,0,300], sum(s[50,0,120]*ratioSigEff[1.,0,3.],b[100]*ratioBkgEff[1.,0.,3.]))"); // counting model
   //  wspace->factory("Gaussian::sigConstraint(ratioSigEff,1,0.05)"); // 5% signal efficiency uncertainty
   //  wspace->factory("Gaussian::bkgConstraint(ratioBkgEff,1,0.1)"); // 10% background efficiency uncertainty
   wspace->factory("Gaussian::sigConstraint(gSigEff[1,0,3],ratioSigEff,0.05)"); // 5% signal efficiency uncertainty
   wspace->factory("Gaussian::bkgConstraint(gSigBkg[1,0,3],ratioBkgEff,0.2)"); // 10% background efficiency uncertainty
   wspace->factory("PROD::modelWithConstraints(countingModel,sigConstraint,bkgConstraint)"); // product of terms
   wspace->Print();

   RooAbsPdf* modelWithConstraints = wspace->pdf("modelWithConstraints"); // get the model
   RooRealVar* obs = wspace->var("obs"); // get the observable
   RooRealVar* s = wspace->var("s"); // get the signal we care about
   RooRealVar* b = wspace->var("b"); // get the background and set it to a constant.  Uncertainty included in ratioBkgEff
   b->setConstant();

   RooRealVar* ratioSigEff = wspace->var("ratioSigEff"); // get uncertain parameter to constrain
   RooRealVar* ratioBkgEff = wspace->var("ratioBkgEff"); // get uncertain parameter to constrain
   RooArgSet constrainedParams(*ratioSigEff, *ratioBkgEff); // need to constrain these in the fit (should change default behavior)

   RooRealVar * gSigEff = wspace->var("gSigEff");     // global observables for signal efficiency
   RooRealVar * gSigBkg = wspace->var("gSigBkg");  // global obs for background efficiency
   gSigEff->setConstant();
   gSigBkg->setConstant();

   // Create an example dataset with 160 observed events
   obs->setVal(160.);
   RooDataSet* data = new RooDataSet("exampleData", "exampleData", RooArgSet(*obs));
   data->add(*obs);

   RooArgSet all(*s, *ratioBkgEff, *ratioSigEff);

   // not necessary
   modelWithConstraints->fitTo(*data, RooFit::Constrain(RooArgSet(*ratioSigEff, *ratioBkgEff)));

   // Now let's make some confidence intervals for s, our parameter of interest
   RooArgSet paramOfInterest(*s);

   ModelConfig modelConfig(wspace);
   modelConfig.SetPdf(*modelWithConstraints);
   modelConfig.SetParametersOfInterest(paramOfInterest);
   modelConfig.SetNuisanceParameters(constrainedParams);
   modelConfig.SetObservables(*obs);
   modelConfig.SetGlobalObservables( RooArgSet(*gSigEff,*gSigBkg));
   modelConfig.SetName("ModelConfig");
   wspace->import(modelConfig);
   wspace->import(*data);
   wspace->SetName("w");
   wspace->writeToFile("rs101_ws.root");



   // First, let's use a Calculator based on the Profile Likelihood Ratio
   //ProfileLikelihoodCalculator plc(*data, *modelWithConstraints, paramOfInterest);
   ProfileLikelihoodCalculator plc(*data, modelConfig);
   plc.SetTestSize(.05);
   ConfInterval* lrinterval = plc.GetInterval();  // that was easy.

   // Let's make a plot
   TCanvas* dataCanvas = new TCanvas("dataCanvas");
   dataCanvas->Divide(2,1);

   dataCanvas->cd(1);
   LikelihoodIntervalPlot plotInt((LikelihoodInterval*)lrinterval);
   plotInt.SetTitle("Profile Likelihood Ratio and Posterior for S");
   plotInt.Draw();

   // Second, use a Calculator based on the Feldman Cousins technique
   FeldmanCousins fc(*data, modelConfig);
   fc.UseAdaptiveSampling(true);
   fc.FluctuateNumDataEntries(false); // number counting analysis: dataset always has 1 entry with N events observed
   fc.SetNBins(100); // number of points to test per parameter
   fc.SetTestSize(.05);
   //  fc.SaveBeltToFile(true); // optional
   ConfInterval* fcint = NULL;
   fcint = fc.GetInterval();  // that was easy.

   RooFitResult* fit = modelWithConstraints->fitTo(*data, Save(true));

   // Third, use a Calculator based on Markov Chain monte carlo
   // Before configuring the calculator, let's make a ProposalFunction
   // that will achieve a high acceptance rate
   ProposalHelper ph;
   ph.SetVariables((RooArgSet&)fit->floatParsFinal());
   ph.SetCovMatrix(fit->covarianceMatrix());
   ph.SetUpdateProposalParameters(true);
   ph.SetCacheSize(100);
   ProposalFunction* pdfProp = ph.GetProposalFunction();  // that was easy

   MCMCCalculator mc(*data, modelConfig);
   mc.SetNumIters(20000); // steps to propose in the chain
   mc.SetTestSize(.05); // 95% CL
   mc.SetNumBurnInSteps(40); // ignore first N steps in chain as "burn in"
   mc.SetProposalFunction(*pdfProp);
   mc.SetLeftSideTailFraction(0.5);  // find a "central" interval
   MCMCInterval* mcInt = (MCMCInterval*)mc.GetInterval();  // that was easy


   // Get Lower and Upper limits from Profile Calculator
   cout << "Profile lower limit on s = " << ((LikelihoodInterval*) lrinterval)->LowerLimit(*s) << endl;
   cout << "Profile upper limit on s = " << ((LikelihoodInterval*) lrinterval)->UpperLimit(*s) << endl;

   // Get Lower and Upper limits from FeldmanCousins with profile construction
   if (fcint != NULL) {
      double fcul = ((PointSetInterval*) fcint)->UpperLimit(*s);
      double fcll = ((PointSetInterval*) fcint)->LowerLimit(*s);
      cout << "FC lower limit on s = " << fcll << endl;
      cout << "FC upper limit on s = " << fcul << endl;
      TLine* fcllLine = new TLine(fcll, 0, fcll, 1);
      TLine* fculLine = new TLine(fcul, 0, fcul, 1);
      fcllLine->SetLineColor(kRed);
      fculLine->SetLineColor(kRed);
      fcllLine->Draw("same");
      fculLine->Draw("same");
      dataCanvas->Update();
   }

   // Plot MCMC interval and print some statistics
   MCMCIntervalPlot mcPlot(*mcInt);
   mcPlot.SetLineColor(kMagenta);
   mcPlot.SetLineWidth(2);
   mcPlot.Draw("same");

   double mcul = mcInt->UpperLimit(*s);
   double mcll = mcInt->LowerLimit(*s);
   cout << "MCMC lower limit on s = " << mcll << endl;
   cout << "MCMC upper limit on s = " << mcul << endl;
   cout << "MCMC Actual confidence level: "
      << mcInt->GetActualConfidenceLevel() << endl;

   // 3-d plot of the parameter points
   dataCanvas->cd(2);
   // also plot the points in the markov chain
   RooDataSet * chainData = mcInt->GetChainAsDataSet();

   assert(chainData);
   std::cout << "plotting the chain data - nentries = " << chainData->numEntries() << std::endl;
   TTree* chain =  RooStats::GetAsTTree("chainTreeData","chainTreeData",*chainData);
   assert(chain);
   chain->SetMarkerStyle(6);
   chain->SetMarkerColor(kRed);

   chain->Draw("s:ratioSigEff:ratioBkgEff","nll_MarkovChain_local_","box"); // 3-d box proportional to posterior

   // the points used in the profile construction
   RooDataSet * parScanData = (RooDataSet*) fc.GetPointsToScan();
   assert(parScanData);
   std::cout << "plotting the scanned points used in the frequentist construction - npoints = " << parScanData->numEntries() << std::endl;
   // getting the tree and drawing it -crashes (very strange....);
   // TTree* parameterScan =  RooStats::GetAsTTree("parScanTreeData","parScanTreeData",*parScanData);
   // assert(parameterScan);
   // parameterScan->Draw("s:ratioSigEff:ratioBkgEff","","goff");
   TGraph2D *gr = new TGraph2D(parScanData->numEntries());
   for (int ievt = 0; ievt < parScanData->numEntries(); ++ievt) {
      const RooArgSet * evt = parScanData->get(ievt);
      double x = evt->getRealValue("ratioBkgEff");
      double y = evt->getRealValue("ratioSigEff");
      double z = evt->getRealValue("s");
      gr->SetPoint(ievt, x,y,z);
      // std::cout << ievt << "  " << x << "  " << y << "  " << z << std::endl;
   }
   gr->SetMarkerStyle(24);
   gr->Draw("P SAME");


   delete wspace;
   delete lrinterval;
   delete mcInt;
   delete fcint;
   delete data;

   // print timing info
   t.Stop();
   t.Print();
}

Author

Kyle Cranmer

Definition in file rs101_limitexample.C.