//////////////////////////////////////////////////////////////////////////
//
// 'ADDITION AND CONVOLUTION' RooFit tutorial macro #202
//
// Setting up an extended maximum likelihood fit
//
//
//
// 07/2008 - Wouter Verkerke
//
/////////////////////////////////////////////////////////////////////////
#ifndef __CINT__
#include "RooGlobalFunc.h"
#endif
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooChebychev.h"
#include "RooAddPdf.h"
#include "RooExtendPdf.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
using namespace RooFit ;
void rf202_extendedmlfit()
{
// S e t u p c o m p o n e n t p d f s
// ---------------------------------------
// Declare observable x
RooRealVar x("x","x",0,10) ;
// Create two Gaussian PDFs g1(x,mean1,sigma) anf g2(x,mean2,sigma) and their parameters
RooRealVar mean("mean","mean of gaussians",5) ;
RooRealVar sigma1("sigma1","width of gaussians",0.5) ;
RooRealVar sigma2("sigma2","width of gaussians",1) ;
RooGaussian sig1("sig1","Signal component 1",x,mean,sigma1) ;
RooGaussian sig2("sig2","Signal component 2",x,mean,sigma2) ;
// Build Chebychev polynomial p.d.f.
RooRealVar a0("a0","a0",0.5,0.,1.) ;
RooRealVar a1("a1","a1",-0.2,0.,1.) ;
RooChebychev bkg("bkg","Background",x,RooArgSet(a0,a1)) ;
// Sum the signal components into a composite signal p.d.f.
RooRealVar sig1frac("sig1frac","fraction of component 1 in signal",0.8,0.,1.) ;
RooAddPdf sig("sig","Signal",RooArgList(sig1,sig2),sig1frac) ;
/////////////////////
// M E T H O D 1 //
/////////////////////
// C o n s t r u c t e x t e n d e d c o m p o s i t e m o d e l
// -------------------------------------------------------------------
// Sum the composite signal and background into an extended pdf nsig*sig+nbkg*bkg
RooRealVar nsig("nsig","number of signal events",500,0.,10000) ;
RooRealVar nbkg("nbkg","number of background events",500,0,10000) ;
RooAddPdf model("model","(g1+g2)+a",RooArgList(bkg,sig),RooArgList(nbkg,nsig)) ;
// S a m p l e , f i t a n d p l o t e x t e n d e d m o d e l
// ---------------------------------------------------------------------
// Generate a data sample of expected number events in x from model
// = model.expectedEvents() = nsig+nbkg
RooDataSet *data = model.generate(x) ;
// Fit model to data, extended ML term automatically included
model.fitTo(*data) ;
// Plot data and PDF overlaid, use expected number of events for p.d.f projection normalization
// rather than observed number of events (==data->numEntries())
RooPlot* xframe = x.frame(Title("extended ML fit example")) ;
data->plotOn(xframe) ;
model.plotOn(xframe,Normalization(1.0,RooAbsReal::RelativeExpected)) ;
// Overlay the background component of model with a dashed line
model.plotOn(xframe,Components(bkg),LineStyle(kDashed),Normalization(1.0,RooAbsReal::RelativeExpected)) ;
// Overlay the background+sig2 components of model with a dotted line
model.plotOn(xframe,Components(RooArgSet(bkg,sig2)),LineStyle(kDotted),Normalization(1.0,RooAbsReal::RelativeExpected)) ;
// Print structure of composite p.d.f.
model.Print("t") ;
/////////////////////
// M E T H O D 2 //
/////////////////////
// C o n s t r u c t e x t e n d e d c o m p o n e n t s f i r s t
// ---------------------------------------------------------------------
// Associated nsig/nbkg as expected number of events with sig/bkg
RooExtendPdf esig("esig","extended signal p.d.f",sig,nsig) ;
RooExtendPdf ebkg("ebkg","extended background p.d.f",bkg,nbkg) ;
// S u m e x t e n d e d c o m p o n e n t s w i t h o u t c o e f s
// -------------------------------------------------------------------------
// Construct sum of two extended p.d.f. (no coefficients required)
RooAddPdf model2("model2","(g1+g2)+a",RooArgList(ebkg,esig)) ;
// Draw the frame on the canvas
new TCanvas("rf202_composite","rf202_composite",600,600) ;
gPad->SetLeftMargin(0.15) ; xframe->GetYaxis()->SetTitleOffset(1.4) ; xframe->Draw() ;
}