limit.C File Reference

Detailed Description

This program demonstrates the computation of 95 % C.L.

limits. It uses a set of randomly created histograms.

Processing /mnt/build/workspace/root-makedoc-v614/rootspi/rdoc/src/v6-14-00-patches/tutorials/math/limit.C...
Computing limits... 
CLs    : 0.0179535
CLsb   : 0.00930313
CLb    : 0.51818
< CLs >  : 0.0165344
< CLsb > : 0.00826754
< CLb >  : 0.50002

Computing limits with stat systematics... 
CLs    : 0.0189723
CLsb   : 0.00989482
CLb    : 0.52154
< CLs >  : 0.0172591
< CLsb > : 0.00862989
< CLb >  : 0.50002

Computing limits with systematics... 
CLs    : 0.0352037
CLsb   : 0.0184327
CLb    : 0.5236
< CLs >  : 0.0328702
< CLsb > : 0.0164358
< CLb >  : 0.50002

#include <iostream>
#include "TH1.h"
#include "THStack.h"
#include "TCanvas.h"
#include "TFrame.h"
#include "TRandom2.h"
#include "TSystem.h"
#include "TVector.h"
#include "TObjArray.h"
#include "TLimit.h"
#include "TLimitDataSource.h"
#include "TConfidenceLevel.h"

using std::cout;
using std::endl;

void limit() {
   // Create a new canvas.
   TCanvas *c1 = new TCanvas("c1","Dynamic Filling Example",200,10,700,500);
   c1->SetFillColor(42);

   // Create some histograms
   TH1D* backgroundHist = new TH1D("background","The expected background",30,-4,4);
   TH1D* signalHist     = new TH1D("signal","the expected signal",30,-4,4);
   TH1D* dataHist       = new TH1D("data","some fake data points",30,-4,4);
   backgroundHist->SetFillColor(48);
   signalHist->SetFillColor(41);
   dataHist->SetMarkerStyle(21);
   dataHist->SetMarkerColor(kBlue);
   backgroundHist->Sumw2(); // needed for stat uncertainty
   signalHist->Sumw2(); // needed for stat uncertainty

   // Fill histograms randomly
   TRandom2 r;
   Float_t bg,sig,dt;
   for (Int_t i = 0; i < 25000; i++) {
      bg  = r.Gaus(0,1);
      sig = r.Gaus(1,.2);
      backgroundHist->Fill(bg,0.02);
      signalHist->Fill(sig,0.001);
   }
   for (Int_t i = 0; i < 500; i++) {
      dt = r.Gaus(0,1);
      dataHist->Fill(dt);
   }
   THStack *hs = new THStack("hs","Signal and background compared to data...");
   hs->Add(backgroundHist);
   hs->Add(signalHist);
   hs->Draw("hist");
   dataHist->Draw("PE1,Same");
   c1->Modified();
   c1->Update();
   c1->GetFrame()->SetFillColor(21);
   c1->GetFrame()->SetBorderSize(6);
   c1->GetFrame()->SetBorderMode(-1);
   c1->Modified();
   c1->Update();
   gSystem->ProcessEvents();

   // Compute the limits
   cout << "Computing limits... " << endl;
   TLimitDataSource* mydatasource = new TLimitDataSource(signalHist,backgroundHist,dataHist);
   TConfidenceLevel *myconfidence = TLimit::ComputeLimit(mydatasource,50000);
   cout << "CLs    : "   << myconfidence->CLs()  << endl;
   cout << "CLsb   : "   << myconfidence->CLsb() << endl;
   cout << "CLb    : "   << myconfidence->CLb()  << endl;
   cout << "< CLs >  : " << myconfidence->GetExpectedCLs_b()  << endl;
   cout << "< CLsb > : " << myconfidence->GetExpectedCLsb_b() << endl;
   cout << "< CLb >  : " << myconfidence->GetExpectedCLb_b()  << endl;

   // Add stat uncertainty
   cout << endl << "Computing limits with stat systematics... " << endl;
   TConfidenceLevel *mystatconfidence = TLimit::ComputeLimit(mydatasource,50000,true);
   cout << "CLs    : "   << mystatconfidence->CLs()  << endl;
   cout << "CLsb   : "   << mystatconfidence->CLsb() << endl;
   cout << "CLb    : "   << mystatconfidence->CLb()  << endl;
   cout << "< CLs >  : " << mystatconfidence->GetExpectedCLs_b()  << endl;
   cout << "< CLsb > : " << mystatconfidence->GetExpectedCLsb_b() << endl;
   cout << "< CLb >  : " << mystatconfidence->GetExpectedCLb_b()  << endl;

   // Add some systematics
   cout << endl << "Computing limits with systematics... " << endl;
   TVectorD errorb(2);
   TVectorD errors(2);
   TObjArray* names = new TObjArray();
   TObjString name1("bg uncertainty");
   TObjString name2("sig uncertainty");
   names->AddLast(&name1);
   names->AddLast(&name2);
   errorb[0]=0.05; // error source 1: 5%
   errorb[1]=0;    // error source 2: 0%
   errors[0]=0;    // error source 1: 0%
   errors[1]=0.01; // error source 2: 1%
   TLimitDataSource* mynewdatasource  = new TLimitDataSource();
   mynewdatasource->AddChannel(signalHist,backgroundHist,dataHist,&errors,&errorb,names);
   TConfidenceLevel *mynewconfidence = TLimit::ComputeLimit(mynewdatasource,50000,true);
   cout << "CLs    : " << mynewconfidence->CLs()  << endl;
   cout << "CLsb   : " << mynewconfidence->CLsb() << endl;
   cout << "CLb    : " << mynewconfidence->CLb()  << endl;
   cout << "< CLs >  : " << mynewconfidence->GetExpectedCLs_b()  << endl;
   cout << "< CLsb > : " << mynewconfidence->GetExpectedCLsb_b() << endl;
   cout << "< CLb >  : " << mynewconfidence->GetExpectedCLb_b()  << endl;

   // show canonical -2lnQ plots in a new canvas
   // - The histogram of -2lnQ for background hypothesis (full)
   // - The histogram of -2lnQ for signal and background hypothesis (dashed)
   TCanvas *c2 = new TCanvas("c2");
   myconfidence->Draw();

   // clean up (except histograms and canvas)
   delete myconfidence;
   delete mydatasource;
   delete mystatconfidence;
   delete mynewconfidence;
   delete mynewdatasource;
}

Author

Christophe Delaere

Definition in file limit.C.