rf316_llratioplot.C

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/// \file
/// \ingroup tutorial_roofit
/// \notebook -js
///  'MULTIDIMENSIONAL MODELS' RooFit tutorial macro #316
///
///  Using the likelihood ratio technique to construct a signal enhanced
///  one-dimensional projection of a multi-dimensional p.d.f.
///
/// \macro_image
/// \macro_output
/// \macro_code
/// \author 07/2008 - Wouter Verkerke


#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() ;



}