rf202_extendedmlfit.C

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/// \file
/// \ingroup tutorial_roofit
/// \notebook -js
/// Addition and convolution: setting up an extended maximum likelihood fit
///
/// \macro_image
/// \macro_output
/// \macro_code
/// \author 07/2008 - Wouter Verkerke

#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();
}