rf202_extendedmlfit.C File Reference

Detailed Description

Setting up an extended maximum likelihood fit.

 
#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 pdf
   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 pdf
   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
   std::unique_ptr<RooDataSet> data{model.generate(x)};
 
   // Fit model to data, extended ML term automatically included
   model.fitTo(*data, PrintLevel(-1));
 
   // Plot data and PDF overlaid, use expected number of events for pdf 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 pdf
   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 pdf", sig, nsig);
   RooExtendPdf ebkg("ebkg", "extended background pdf", 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 pdf (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();
}

 
[#0] WARNING:InputArguments -- The parameter 'sigma1' with range [-inf, inf] of the RooGaussian 'sig1' exceeds the safe range of (0, inf). Advise to limit its range.
[#0] WARNING:InputArguments -- The parameter 'sigma2' with range [-inf, inf] of the RooGaussian 'sig2' exceeds the safe range of (0, inf). Advise to limit its range.
[#1] INFO:Minimization -- p.d.f. provides expected number of events, including extended term in likelihood.
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization
[#1] INFO:Minimization --  The following expressions have been identified as constant and will be precalculated and cached: (sig1,sig2)
[#1] INFO:Minimization --  The following expressions will be evaluated in cache-and-track mode: (bkg)
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) directly selected PDF components: (bkg)
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) indirectly selected PDF components: ()
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) directly selected PDF components: (bkg,sig2)
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) indirectly selected PDF components: (sig)
0x7ffd780c2ea0 RooAddPdf::model = 0.898614/1 [Auto,Clean] 
  0x7ffd780c2588/V- RooChebychev::bkg = 0.798919 [Auto,Dirty] 
    0x7ffd780c2ab8/V- RooRealVar::x = 5
    0x7ffd780c06f8/V- RooRealVar::a0 = 0.441701 +/- 0.073185
    0x7ffd780c0ae0/V- RooRealVar::a1 = 0.201081 +/- 0.117613
  0x7ffd780c21a0/V- RooRealVar::nbkg = 504.206 +/- 39.3107
  0x7ffd780c12b0/V- RooAddPdf::sig = 1/1 [Auto,Clean] 
    0x7ffd780bf478/V- RooGaussian::sig1 = 1 [Auto,Dirty] 
      0x7ffd780c2ab8/V- RooRealVar::x = 5
      0x7ffd780c19d0/V- RooRealVar::mean = 5
      0x7ffd780bff28/V- RooRealVar::sigma1 = 0.5
    0x7ffd780c0ec8/V- RooRealVar::sig1frac = 0.837341 +/- 0.116841
    0x7ffd780bf9d0/V- RooGaussian::sig2 = 1 [Auto,Dirty] 
      0x7ffd780c2ab8/V- RooRealVar::x = 5
      0x7ffd780c19d0/V- RooRealVar::mean = 5
      0x7ffd780c0310/V- RooRealVar::sigma2 = 1
  0x7ffd780c1db8/V- RooRealVar::nsig = 495.799 +/- 39.2054

Date

July 2008

Author

Wouter Verkerke

Definition in file rf202_extendedmlfit.C.