limit.C: This program demonstrates the computation of 95 % C.L. limits.

#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() {
//This program demonstrates the computation of 95 % C.L. limits.
//It uses a set of randomly created histograms.
//
//Author:  Christophe.Delaere@cern.ch on 21.08.02

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

// Create some histograms
  TH1D* background = new TH1D("background","The expected background",30,-4,4);
  TH1D* signal     = new TH1D("signal","the expected signal",30,-4,4);
  TH1D* data       = new TH1D("data","some fake data points",30,-4,4);
  background->SetFillColor(48);
  signal->SetFillColor(41);
  data->SetMarkerStyle(21);
  data->SetMarkerColor(kBlue);
  background->Sumw2(); // needed for stat uncertainty
  signal->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);
     background->Fill(bg,0.02);
     signal->Fill(sig,0.001);
  }
  for (Int_t i = 0; i < 500; i++) {
     dt = r.Gaus(0,1);
     data->Fill(dt);
  }
  THStack *hs = new THStack("hs","Signal and background compared to data...");
  hs->Add(background);
  hs->Add(signal);
  hs->Draw("hist");
  data->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(signal,background,data);
  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(signal,background,data,&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;
}