rs401c_FeldmanCousins.C: Produces an interval on the mean signal in a number counting

/////////////////////////////////////////////////////////////////////////
//
// Produces an interval on the mean signal in a number counting
// experiment with known background using the Feldman-Cousins technique.
// date Jan. 2009
// updated June 2010
//
// Using the RooStats FeldmanCousins tool with 200 bins 
// it takes 1 min and the interval is [0.2625, 10.6125] 
// with a step size of 0.075.
// The interval in Feldman & Cousins's original paper is [.29, 10.81]
//  Phys.Rev.D57:3873-3889,1998. 
/////////////////////////////////////////////////////////////////////////

#include "RooGlobalFunc.h"
#include "RooStats/ConfInterval.h"
#include "RooStats/PointSetInterval.h"
#include "RooStats/ConfidenceBelt.h"
#include "RooStats/FeldmanCousins.h"
#include "RooStats/ModelConfig.h"

#include "RooWorkspace.h"
#include "RooDataSet.h"
#include "RooRealVar.h"
#include "RooConstVar.h"
#include "RooAddition.h"

#include "RooDataHist.h"

#include "RooPoisson.h"
#include "RooPlot.h"

#include "TCanvas.h"
#include "TTree.h"
#include "TH1F.h"
#include "TMarker.h"
#include "TStopwatch.h"

#include <iostream>

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


void rs401c_FeldmanCousins()
{
  // to time the macro... about 30 s
  TStopwatch t;
  t.Start();

  // make a simple model
  RooRealVar x("x","", 1,0,50);
  RooRealVar mu("mu","", 2.5,0, 15); // with a limit on mu>=0
  RooConstVar b("b","", 3.);
  RooAddition mean("mean","",RooArgList(mu,b));
  RooPoisson pois("pois", "", x, mean);
  RooArgSet parameters(mu);

  // create a toy dataset
  RooDataSet* data = pois.generate(RooArgSet(x), 1);
  data->Print("v");
  
  TCanvas* dataCanvas = new TCanvas("dataCanvas");
  RooPlot* frame = x.frame();
  data->plotOn(frame);
  frame->Draw();
  dataCanvas->Update();

  RooWorkspace* w = new RooWorkspace();
  ModelConfig modelConfig("poissonProblem",w);
  modelConfig.SetPdf(pois);
  modelConfig.SetParametersOfInterest(parameters);
  modelConfig.SetObservables(RooArgSet(x));
  w->Print();

  //////// show use of Feldman-Cousins
  RooStats::FeldmanCousins fc(*data,modelConfig);
  fc.SetTestSize(.05); // set size of test
  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

  // use the Feldman-Cousins tool
  PointSetInterval* interval = (PointSetInterval*)fc.GetInterval();

  // make a canvas for plots
  TCanvas* intervalCanvas =  new TCanvas("intervalCanvas");
  
  std::cout << "is this point in the interval? " << 
    interval->IsInInterval(parameters) << std::endl;

  std::cout << "interval is ["<<  
    interval->LowerLimit(mu)  << ", "  <<
    interval->UpperLimit(mu) << "]" << endl;

  // using 200 bins it takes 1 min and the answer is
  // interval is [0.2625, 10.6125] with a step size of .075
  // The interval in Feldman & Cousins's original paper is [.29, 10.81]
  //  Phys.Rev.D57:3873-3889,1998. 

  // No dedicated plotting class yet, so do it by hand:

  RooDataHist* parameterScan = (RooDataHist*) fc.GetPointsToScan();
  TH1F* hist = (TH1F*) parameterScan->createHistogram("mu",30);
  hist->Draw();

 
  RooArgSet* tmpPoint;
  // loop over points to test
  for(Int_t i=0; i<parameterScan->numEntries(); ++i){
    //    cout << "on parameter point " << i << " out of " << parameterScan->numEntries() << endl;
     // get a parameter point from the list of points to test.
    tmpPoint = (RooArgSet*) parameterScan->get(i)->clone("temp");

    TMarker* mark = new TMarker(tmpPoint->getRealValue("mu"), 1, 25);
    if (interval->IsInInterval( *tmpPoint ) ) 
      mark->SetMarkerColor(kBlue);
    else
      mark->SetMarkerColor(kRed);

    mark->Draw("s");
    //delete tmpPoint;
    //    delete mark;
  }
  t.Stop();
  t.Print();
    

}