rf605_profilell.C: 'LIKELIHOOD AND MINIMIZATION' RooFit tutorial macro #605

//////////////////////////////////////////////////////////////////////////
//
// 'LIKELIHOOD AND MINIMIZATION' RooFit tutorial macro #605
// 
// Working with the profile likelihood estimator
//
//
//
// 07/2008 - Wouter Verkerke 
// 
/////////////////////////////////////////////////////////////////////////

#ifndef __CINT__
#include "RooGlobalFunc.h"
#endif
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooConstVar.h"
#include "RooAddPdf.h"
#include "RooMinuit.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
using namespace RooFit ;


void rf605_profilell()
{
  // C r e a t e   m o d e l   a n d   d a t a s e t 
  // -----------------------------------------------

  // Observable
  RooRealVar x("x","x",-20,20) ;

  // Model (intentional strong correlations)
  RooRealVar mean("mean","mean of g1 and g2",0,-10,10) ;
  RooRealVar sigma_g1("sigma_g1","width of g1",3) ;
  RooGaussian g1("g1","g1",x,mean,sigma_g1) ;

  RooRealVar sigma_g2("sigma_g2","width of g2",4,3.0,6.0) ;
  RooGaussian g2("g2","g2",x,mean,sigma_g2) ;

  RooRealVar frac("frac","frac",0.5,0.0,1.0) ;
  RooAddPdf model("model","model",RooArgList(g1,g2),frac) ;

  // Generate 1000 events
  RooDataSet* data = model.generate(x,1000) ;
  


  // C o n s t r u c t   p l a i n   l i k e l i h o o d
  // ---------------------------------------------------

  // Construct unbinned likelihood
  RooAbsReal* nll = model.createNLL(*data,NumCPU(2)) ;

  // Minimize likelihood w.r.t all parameters before making plots
  RooMinuit(*nll).migrad() ;

  // Plot likelihood scan frac 
  RooPlot* frame1 = frac.frame(Bins(10),Range(0.01,0.95),Title("LL and profileLL in frac")) ;
  nll->plotOn(frame1,ShiftToZero()) ;

  // Plot likelihood scan in sigma_g2
  RooPlot* frame2 = sigma_g2.frame(Bins(10),Range(3.3,5.0),Title("LL and profileLL in sigma_g2")) ;
  nll->plotOn(frame2,ShiftToZero()) ;



  // C o n s t r u c t   p r o f i l e   l i k e l i h o o d   i n   f r a c
  // -----------------------------------------------------------------------

  // The profile likelihood estimator on nll for frac will minimize nll w.r.t
  // all floating parameters except frac for each evaluation

  RooAbsReal* pll_frac = nll->createProfile(frac) ;

  // Plot the profile likelihood in frac
  pll_frac->plotOn(frame1,LineColor(kRed)) ;

  // Adjust frame maximum for visual clarity
  frame1->SetMinimum(0) ;
  frame1->SetMaximum(3) ;



  // C o n s t r u c t   p r o f i l e   l i k e l i h o o d   i n   s i g m a _ g 2 
  // -------------------------------------------------------------------------------

  // The profile likelihood estimator on nll for sigma_g2 will minimize nll
  // w.r.t all floating parameters except sigma_g2 for each evaluation
  RooAbsReal* pll_sigmag2 = nll->createProfile(sigma_g2) ;

  // Plot the profile likelihood in sigma_g2
  pll_sigmag2->plotOn(frame2,LineColor(kRed)) ;

  // Adjust frame maximum for visual clarity
  frame2->SetMinimum(0) ;
  frame2->SetMaximum(3) ;



  // Make canvas and draw RooPlots
  TCanvas *c = new TCanvas("rf605_profilell","rf605_profilell",800, 400);
  c->Divide(2);
  c->cd(1) ; gPad->SetLeftMargin(0.15) ; frame1->GetYaxis()->SetTitleOffset(1.4) ; frame1->Draw() ;
  c->cd(2) ; gPad->SetLeftMargin(0.15) ; frame2->GetYaxis()->SetTitleOffset(1.4) ; frame2->Draw() ;

  delete pll_frac ;
  delete pll_sigmag2 ;
  delete nll ;
}