rs_numberCountingCombination.C: 'Number Counting Example' RooStats tutorial macro #100

/////////////////////////////////////////////////////////////////////////
//
// 'Number Counting Example' RooStats tutorial macro #100
// author: Kyle Cranmer
// date Nov. 2008 
//
// This tutorial shows an example of a combination of 
// two searches using number counting with background uncertainty.
//
// The macro uses a RooStats "factory" to construct a PDF
// that represents the two number counting analyses with background 
// uncertainties.  The uncertainties are taken into account by 
// considering a sideband measurement of a size that corresponds to the
// background uncertainty.  The problem has been studied in these references:
//   http://arxiv.org/abs/physics/0511028
//   http://arxiv.org/abs/physics/0702156
//   http://cdsweb.cern.ch/record/1099969?ln=en
//
// After using the factory to make the model, we use a RooStats 
// ProfileLikelihoodCalculator for a Hypothesis test and a confidence interval.
// The calculator takes into account systematics by eliminating nuisance parameters
// with the profile likelihood.  This is equivalent to the method of MINOS.
//
/////////////////////////////////////////////////////////////////////////

#ifndef __CINT__
#include "RooGlobalFunc.h"
#endif
#include "RooStats/ProfileLikelihoodCalculator.h"
#include "RooStats/NumberCountingPdfFactory.h"
#include "RooStats/ConfInterval.h"
#include "RooStats/HypoTestResult.h"
#include "RooStats/LikelihoodIntervalPlot.h"
#include "RooRealVar.h"

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


// declare three variations on the same tutorial
void rs_numberCountingCombination_expected();
void rs_numberCountingCombination_observed();
void rs_numberCountingCombination_observedWithTau();

////////////////////////////////////////////
// main driver to choose one
void rs_numberCountingCombination(int flag=1)
{
  if(flag==1) 
    rs_numberCountingCombination_expected();
  if(flag==2) 
    rs_numberCountingCombination_observed();
  if(flag==3) 
    rs_numberCountingCombination_observedWithTau();
}

/////////////////////////////////////////////
void rs_numberCountingCombination_expected()
{

  /////////////////////////////////////////
  // An example of a number counting combination with two channels.
  // We consider both hypothesis testing and the equivalent confidence interval.
  /////////////////////////////////////////


  /////////////////////////////////////////
  // The Model building stage
  /////////////////////////////////////////

  // Step 1, define arrays with signal & bkg expectations and background uncertainties
  Double_t s[2] = {20.,10.};           // expected signal
  Double_t b[2] = {100.,100.};         // expected background
  Double_t db[2] = {.0100,.0100};      // fractional background uncertainty

  
  // Step 2, use a RooStats factory to build a PDF for a 
  // number counting combination and add it to the workspace.
  // We need to give the signal expectation to relate the masterSignal
  // to the signal contribution in the individual channels.
  // The model neglects correlations in background uncertainty, 
  // but they could be added without much change to the example.
  NumberCountingPdfFactory f;
  RooWorkspace* wspace = new RooWorkspace();
  f.AddModel(s,2,wspace,"TopLevelPdf", "masterSignal"); 

  // Step 3, use a RooStats factory to add datasets to the workspace.
  // Step 3a.
  // Add the expected data to the workspace
  f.AddExpData(s, b, db, 2, wspace, "ExpectedNumberCountingData");

  // see below for a printout of the workspace
  //  wspace->Print();  //uncomment to see structure of workspace

  /////////////////////////////////////////
  // The Hypothesis testing stage:
  /////////////////////////////////////////
  // Step 4, Define the null hypothesis for the calculator
  // Here you need to know the name of the variables corresponding to hypothesis.
  RooRealVar* mu = wspace->var("masterSignal"); 
  RooArgSet* nullParams = new RooArgSet("nullParams");
  nullParams->addClone(*mu);
  // here we explicitly set the value of the parameters for the null
  nullParams->setRealValue("masterSignal",0); 

  // Step 5, Create a calculator for doing the hypothesis test.
  // because this is a 
  ProfileLikelihoodCalculator plc( *wspace->data("ExpectedNumberCountingData"),
				   *wspace->pdf("TopLevelPdf"), *nullParams);
				  

  // Step 6, Use the Calculator to get a HypoTestResult
  HypoTestResult* htr = plc.GetHypoTest();
  cout << "-------------------------------------------------" << endl;
  cout << "The p-value for the null is " << htr->NullPValue() << endl;
  cout << "Corresponding to a signifcance of " << htr->Significance() << endl;
  cout << "-------------------------------------------------\n\n" << endl;

  /* expected case should return:
     -------------------------------------------------
     The p-value for the null is 0.015294
     Corresponding to a signifcance of 2.16239
     -------------------------------------------------
  */

  //////////////////////////////////////////
  // Confidence Interval Stage

  // Step 8, Here we re-use the ProfileLikelihoodCalculator to return a confidence interval.
  // We need to specify what are our parameters of interest
  RooArgSet* paramsOfInterest = nullParams; // they are the same as before in this case
  plc.SetParameters(*paramsOfInterest);
  LikelihoodInterval* lrint = (LikelihoodInterval*) plc.GetInterval();  // that was easy.
  lrint->SetConfidenceLevel(0.95);

  // Step 9, make a plot of the likelihood ratio and the interval obtained
  paramsOfInterest->setRealValue("masterSignal",1.); 
  LikelihoodIntervalPlot lrPlot(lrint);
  lrPlot.Draw();

  // Step 10a. Get upper and lower limits
  cout << "lower limit on master signal = " <<   lrint->LowerLimit(*mu ) << endl;
  cout << "upper limit on master signal = " <<   lrint->UpperLimit(*mu ) << endl;


  // Step 10b, Ask if masterSignal=0 is in the interval.
  // Note, this is equivalent to the question of a 2-sigma hypothesis test: 
  // "is the parameter point masterSignal=0 inside the 95% confidence interval?"
  // Since the signficance of the Hypothesis test was > 2-sigma it should not be: 
  // eg. we exclude masterSignal=0 at 95% confidence.
  paramsOfInterest->setRealValue("masterSignal",0.); 
  cout << "-------------------------------------------------" << endl;
  std::cout << "Consider this parameter point:" << std::endl;
  paramsOfInterest->first()->Print();
  if( lrint->IsInInterval(*paramsOfInterest) )
    std::cout << "It IS in the interval."  << std::endl;
  else
    std::cout << "It is NOT in the interval."  << std::endl;
  cout << "-------------------------------------------------\n\n" << endl;

  // Step 10c, We also ask about the parameter point masterSignal=2, which is inside the interval.
  paramsOfInterest->setRealValue("masterSignal",2.); 
  cout << "-------------------------------------------------" << endl;
  std::cout << "Consider this parameter point:" << std::endl;
  paramsOfInterest->first()->Print();
  if( lrint->IsInInterval(*paramsOfInterest) )
    std::cout << "It IS in the interval."  << std::endl;
  else
    std::cout << "It is NOT in the interval."  << std::endl;
  cout << "-------------------------------------------------\n\n" << endl;
  

  delete lrint;
  delete htr;
  delete wspace;
  delete nullParams;



  /*
  // Here's an example of what is in the workspace 
  //  wspace->Print();
  RooWorkspace(NumberCountingWS) Number Counting WS contents

  variables
  ---------
  (x_0,masterSignal,expected_s_0,b_0,y_0,tau_0,x_1,expected_s_1,b_1,y_1,tau_1)
  
  p.d.f.s
  -------
  RooProdPdf::joint[ pdfs=(sigRegion_0,sideband_0,sigRegion_1,sideband_1) ] = 2.20148e-08
  RooPoisson::sigRegion_0[ x=x_0 mean=splusb_0 ] = 0.036393
  RooPoisson::sideband_0[ x=y_0 mean=bTau_0 ] = 0.00398939
  RooPoisson::sigRegion_1[ x=x_1 mean=splusb_1 ] = 0.0380088
  RooPoisson::sideband_1[ x=y_1 mean=bTau_1 ] = 0.00398939
  
  functions
  --------
  RooAddition::splusb_0[ set1=(s_0,b_0) set2=() ] = 120
  RooProduct::s_0[ compRSet=(masterSignal,expected_s_0) compCSet=() ] = 20
  RooProduct::bTau_0[ compRSet=(b_0,tau_0) compCSet=() ] = 10000
  RooAddition::splusb_1[ set1=(s_1,b_1) set2=() ] = 110
  RooProduct::s_1[ compRSet=(masterSignal,expected_s_1) compCSet=() ] = 10
  RooProduct::bTau_1[ compRSet=(b_1,tau_1) compCSet=() ] = 10000
  
  datasets
  --------
  RooDataSet::ExpectedNumberCountingData(x_0,y_0,x_1,y_1)
  
  embedded precalculated expensive components
  -------------------------------------------
  */
  
}



void rs_numberCountingCombination_observed()
{

  /////////////////////////////////////////
  // The same example with observed data in a main
  // measurement and an background-only auxiliary 
  // measurement with a factor tau more background
  // than in the main measurement.

  /////////////////////////////////////////
  // The Model building stage
  /////////////////////////////////////////

  // Step 1, define arrays with signal & bkg expectations and background uncertainties
  // We still need the expectation to relate signal in different channels with the master signal
  Double_t s[2] = {20.,10.};           // expected signal

  
  // Step 2, use a RooStats factory to build a PDF for a 
  // number counting combination and add it to the workspace.
  // We need to give the signal expectation to relate the masterSignal
  // to the signal contribution in the individual channels.
  // The model neglects correlations in background uncertainty, 
  // but they could be added without much change to the example.
  NumberCountingPdfFactory f;
  RooWorkspace* wspace = new RooWorkspace();
  f.AddModel(s,2,wspace,"TopLevelPdf", "masterSignal"); 

  // Step 3, use a RooStats factory to add datasets to the workspace.
  // Add the observed data to the workspace
  Double_t mainMeas[2] = {123.,117.};      // observed main measurement
  Double_t bkgMeas[2] = {111.23,98.76};    // observed background
  Double_t dbMeas[2] = {.011,.0095};       // observed fractional background uncertainty
  f.AddData(mainMeas, bkgMeas, dbMeas, 2, wspace,"ObservedNumberCountingData");

  // see below for a printout of the workspace
  //  wspace->Print();  //uncomment to see structure of workspace

  /////////////////////////////////////////
  // The Hypothesis testing stage:
  /////////////////////////////////////////
  // Step 4, Define the null hypothesis for the calculator
  // Here you need to know the name of the variables corresponding to hypothesis.
  RooRealVar* mu = wspace->var("masterSignal"); 
  RooArgSet* nullParams = new RooArgSet("nullParams");
  nullParams->addClone(*mu);
  // here we explicitly set the value of the parameters for the null
  nullParams->setRealValue("masterSignal",0); 

  // Step 5, Create a calculator for doing the hypothesis test.
  // because this is a 
  ProfileLikelihoodCalculator plc( *wspace->data("ObservedNumberCountingData"),
				   *wspace->pdf("TopLevelPdf"), *nullParams);
	
  wspace->var("tau_0")->Print();
  wspace->var("tau_1")->Print();

  // Step 7, Use the Calculator to get a HypoTestResult
  HypoTestResult* htr = plc.GetHypoTest();
  cout << "-------------------------------------------------" << endl;
  cout << "The p-value for the null is " << htr->NullPValue() << endl;
  cout << "Corresponding to a signifcance of " << htr->Significance() << endl;
  cout << "-------------------------------------------------\n\n" << endl;

  /* observed case should return:
     -------------------------------------------------
     The p-value for the null is 0.0351669
     Corresponding to a signifcance of 1.80975
     -------------------------------------------------
  */


  //////////////////////////////////////////
  // Confidence Interval Stage

  // Step 8, Here we re-use the ProfileLikelihoodCalculator to return a confidence interval.
  // We need to specify what are our parameters of interest
  RooArgSet* paramsOfInterest = nullParams; // they are the same as before in this case
  plc.SetParameters(*paramsOfInterest);
  LikelihoodInterval* lrint = (LikelihoodInterval*) plc.GetInterval();  // that was easy.
  lrint->SetConfidenceLevel(0.95);

  // Step 9c. Get upper and lower limits
  cout << "lower limit on master signal = " <<   lrint->LowerLimit(*mu ) << endl;
  cout << "upper limit on master signal = " <<   lrint->UpperLimit(*mu ) << endl;

  delete lrint;
  delete htr;
  delete wspace;
  delete nullParams;


  
}


void rs_numberCountingCombination_observedWithTau()
{

  /////////////////////////////////////////
  // The same example with observed data in a main
  // measurement and an background-only auxiliary 
  // measurement with a factor tau more background
  // than in the main measurement.

  /////////////////////////////////////////
  // The Model building stage
  /////////////////////////////////////////

  // Step 1, define arrays with signal & bkg expectations and background uncertainties
  // We still need the expectation to relate signal in different channels with the master signal
  Double_t s[2] = {20.,10.};           // expected signal
  
  // Step 2, use a RooStats factory to build a PDF for a 
  // number counting combination and add it to the workspace.
  // We need to give the signal expectation to relate the masterSignal
  // to the signal contribution in the individual channels.
  // The model neglects correlations in background uncertainty, 
  // but they could be added without much change to the example.
  NumberCountingPdfFactory f;
  RooWorkspace* wspace = new RooWorkspace();
  f.AddModel(s,2,wspace,"TopLevelPdf", "masterSignal"); 

  // Step 3, use a RooStats factory to add datasets to the workspace.
  // Add the observed data to the workspace in the on-off problem.
  Double_t mainMeas[2] = {123.,117.};      // observed main measurement
  Double_t sideband[2] = {11123.,9876.};    // observed sideband
  Double_t tau[2] = {100.,100.}; // ratio of bkg in sideband to bkg in main measurement, from experimental design.
  f.AddDataWithSideband(mainMeas, sideband, tau, 2, wspace,"ObservedNumberCountingDataWithSideband");

  // see below for a printout of the workspace
  //  wspace->Print();  //uncomment to see structure of workspace

  /////////////////////////////////////////
  // The Hypothesis testing stage:
  /////////////////////////////////////////
  // Step 4, Define the null hypothesis for the calculator
  // Here you need to know the name of the variables corresponding to hypothesis.
  RooRealVar* mu = wspace->var("masterSignal"); 
  RooArgSet* nullParams = new RooArgSet("nullParams");
  nullParams->addClone(*mu);
  // here we explicitly set the value of the parameters for the null
  nullParams->setRealValue("masterSignal",0); 

  // Step 5, Create a calculator for doing the hypothesis test.
  // because this is a 
  ProfileLikelihoodCalculator plc( *wspace->data("ObservedNumberCountingDataWithSideband"),
				   *wspace->pdf("TopLevelPdf"), *nullParams);
				  


  // Step 7, Use the Calculator to get a HypoTestResult
  HypoTestResult* htr = plc.GetHypoTest();
  cout << "-------------------------------------------------" << endl;
  cout << "The p-value for the null is " << htr->NullPValue() << endl;
  cout << "Corresponding to a signifcance of " << htr->Significance() << endl;
  cout << "-------------------------------------------------\n\n" << endl;

  /* observed case should return:
     -------------------------------------------------
     The p-value for the null is 0.0352035
     Corresponding to a signifcance of 1.80928
     -------------------------------------------------
  */


  //////////////////////////////////////////
  // Confidence Interval Stage

  // Step 8, Here we re-use the ProfileLikelihoodCalculator to return a confidence interval.
  // We need to specify what are our parameters of interest
  RooArgSet* paramsOfInterest = nullParams; // they are the same as before in this case
  plc.SetParameters(*paramsOfInterest);
  LikelihoodInterval* lrint = (LikelihoodInterval*) plc.GetInterval();  // that was easy.
  lrint->SetConfidenceLevel(0.95);

  

  // Step 9c. Get upper and lower limits
  cout << "lower limit on master signal = " <<   lrint->LowerLimit(*mu ) << endl;
  cout << "upper limit on master signal = " <<   lrint->UpperLimit(*mu ) << endl;

  delete lrint;
  delete htr;
  delete wspace;
  delete nullParams;


  
}