rf316_llratioplot.C: 'MULTIDIMENSIONAL MODELS' RooFit tutorial macro #316

//////////////////////////////////////////////////////////////////////////
//
// 'MULTIDIMENSIONAL MODELS' RooFit tutorial macro #316
// 
// Using the likelihood ratio techique to construct a signal enhanced
// one-dimensional projection of a multi-dimensional p.d.f.
//
//
//
// 07/2008 - Wouter Verkerke 
// 
/////////////////////////////////////////////////////////////////////////

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


void rf316_llratioplot()
{

  // C r e a t e   3 D   p d f   a n d   d a t a 
  // -------------------------------------------

  // Create observables
  RooRealVar x("x","x",-5,5) ;
  RooRealVar y("y","y",-5,5) ;
  RooRealVar z("z","z",-5,5) ;

  // Create signal pdf gauss(x)*gauss(y)*gauss(z) 
  RooGaussian gx("gx","gx",x,RooConst(0),RooConst(1)) ;
  RooGaussian gy("gy","gy",y,RooConst(0),RooConst(1)) ;
  RooGaussian gz("gz","gz",z,RooConst(0),RooConst(1)) ;
  RooProdPdf sig("sig","sig",RooArgSet(gx,gy,gz)) ;

  // Create background pdf poly(x)*poly(y)*poly(z) 
  RooPolynomial px("px","px",x,RooArgSet(RooConst(-0.1),RooConst(0.004))) ;
  RooPolynomial py("py","py",y,RooArgSet(RooConst(0.1),RooConst(-0.004))) ;
  RooPolynomial pz("pz","pz",z) ;
  RooProdPdf bkg("bkg","bkg",RooArgSet(px,py,pz)) ;

  // Create composite pdf sig+bkg
  RooRealVar fsig("fsig","signal fraction",0.1,0.,1.) ;
  RooAddPdf model("model","model",RooArgList(sig,bkg),fsig) ;

  RooDataSet* data = model.generate(RooArgSet(x,y,z),20000) ;



  // P r o j e c t   p d f   a n d   d a t a   o n   x
  // -------------------------------------------------

  // Make plain projection of data and pdf on x observable
  RooPlot* frame = x.frame(Title("Projection of 3D data and pdf on X"),Bins(40)) ;
  data->plotOn(frame) ;
  model.plotOn(frame) ;
  


  // D e f i n e   p r o j e c t e d   s i g n a l   l i k e l i h o o d   r a t i o
  // ----------------------------------------------------------------------------------

  // Calculate projection of signal and total likelihood on (y,z) observables
  // i.e. integrate signal and composite model over x
  RooAbsPdf* sigyz = sig.createProjection(x) ;
  RooAbsPdf* totyz = model.createProjection(x) ;

  // Construct the log of the signal / signal+background probability 
  RooFormulaVar llratio_func("llratio","log10(@0)-log10(@1)",RooArgList(*sigyz,*totyz)) ;



  // P l o t   d a t a   w i t h   a   L L r a t i o   c u t 
  // -------------------------------------------------------

  // Calculate the llratio value for each event in the dataset
  data->addColumn(llratio_func) ;

  // Extract the subset of data with large signal likelihood
  RooDataSet* dataSel = (RooDataSet*) data->reduce(Cut("llratio>0.7")) ;

  // Make plot frame
  RooPlot* frame2 = x.frame(Title("Same projection on X with LLratio(y,z)>0.7"),Bins(40)) ;

  // Plot select data on frame
  dataSel->plotOn(frame2) ;



  // M a k e   M C   p r o j e c t i o n   o f   p d f   w i t h   s a m e   L L r a t i o   c u t 
  // ---------------------------------------------------------------------------------------------

  // Generate large number of events for MC integration of pdf projection
  RooDataSet* mcprojData = model.generate(RooArgSet(x,y,z),10000) ;

  // Calculate LL ratio for each generated event and select MC events with llratio)0.7
  mcprojData->addColumn(llratio_func) ;
  RooDataSet* mcprojDataSel = (RooDataSet*) mcprojData->reduce(Cut("llratio>0.7")) ;
    
  // Project model on x, integrating projected observables (y,z) with Monte Carlo technique
  // on set of events with the same llratio cut as was applied to data
  model.plotOn(frame2,ProjWData(*mcprojDataSel)) ;



  TCanvas* c = new TCanvas("rf316_llratioplot","rf316_llratioplot",800,400) ;
  c->Divide(2) ;
  c->cd(1) ; gPad->SetLeftMargin(0.15) ; frame->GetYaxis()->SetTitleOffset(1.4) ; frame->Draw() ;
  c->cd(2) ; gPad->SetLeftMargin(0.15) ; frame2->GetYaxis()->SetTitleOffset(1.4) ; frame2->Draw() ;


  
}