ROOT   Reference Guide
rf202_extendedmlfit.C
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1/// \file
2/// \ingroup tutorial_roofit
3/// \notebook -js
4///
5/// Addition and convolution: setting up an extended maximum likelihood fit
6///
7/// \macro_image
8/// \macro_output
9/// \macro_code
10///
11/// \date 07/2008
12/// \author Wouter Verkerke
13
14#include "RooRealVar.h"
15#include "RooDataSet.h"
16#include "RooGaussian.h"
17#include "RooChebychev.h"
19#include "RooExtendPdf.h"
20#include "TCanvas.h"
21#include "TAxis.h"
22#include "RooPlot.h"
23using namespace RooFit;
24
26{
27
28 // S e t u p c o m p o n e n t p d f s
29 // ---------------------------------------
30
31 // Declare observable x
32 RooRealVar x("x", "x", 0, 10);
33
34 // Create two Gaussian PDFs g1(x,mean1,sigma) anf g2(x,mean2,sigma) and their parameters
35 RooRealVar mean("mean", "mean of gaussians", 5);
36 RooRealVar sigma1("sigma1", "width of gaussians", 0.5);
37 RooRealVar sigma2("sigma2", "width of gaussians", 1);
38
39 RooGaussian sig1("sig1", "Signal component 1", x, mean, sigma1);
40 RooGaussian sig2("sig2", "Signal component 2", x, mean, sigma2);
41
42 // Build Chebychev polynomial p.d.f.
43 RooRealVar a0("a0", "a0", 0.5, 0., 1.);
44 RooRealVar a1("a1", "a1", 0.2, 0., 1.);
45 RooChebychev bkg("bkg", "Background", x, RooArgSet(a0, a1));
46
47 // Sum the signal components into a composite signal p.d.f.
48 RooRealVar sig1frac("sig1frac", "fraction of component 1 in signal", 0.8, 0., 1.);
49 RooAddPdf sig("sig", "Signal", RooArgList(sig1, sig2), sig1frac);
50
51 //----------------
52 // M E T H O D 1
53 //================
54
55 // 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
56 // -------------------------------------------------------------------
57
58 // Sum the composite signal and background into an extended pdf nsig*sig+nbkg*bkg
59 RooRealVar nsig("nsig", "number of signal events", 500, 0., 10000);
60 RooRealVar nbkg("nbkg", "number of background events", 500, 0, 10000);
61 RooAddPdf model("model", "(g1+g2)+a", RooArgList(bkg, sig), RooArgList(nbkg, nsig));
62
63 // 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
64 // ---------------------------------------------------------------------
65
66 // Generate a data sample of expected number events in x from model
67 // = model.expectedEvents() = nsig+nbkg
68 RooDataSet *data = model.generate(x);
69
70 // Fit model to data, extended ML term automatically included
71 model.fitTo(*data);
72
73 // Plot data and PDF overlaid, use expected number of events for p.d.f projection normalization
74 // rather than observed number of events (==data->numEntries())
75 RooPlot *xframe = x.frame(Title("extended ML fit example"));
76 data->plotOn(xframe);
77 model.plotOn(xframe, Normalization(1.0, RooAbsReal::RelativeExpected));
78
79 // Overlay the background component of model with a dashed line
80 model.plotOn(xframe, Components(bkg), LineStyle(kDashed), Normalization(1.0, RooAbsReal::RelativeExpected));
81
82 // Overlay the background+sig2 components of model with a dotted line
83 model.plotOn(xframe, Components(RooArgSet(bkg, sig2)), LineStyle(kDotted),
85
86 // Print structure of composite p.d.f.
87 model.Print("t");
88
89 //----------------
90 // M E T H O D 2
91 //================
92
93 // 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
94 // ---------------------------------------------------------------------
95
96 // Associated nsig/nbkg as expected number of events with sig/bkg
97 RooExtendPdf esig("esig", "extended signal p.d.f", sig, nsig);
98 RooExtendPdf ebkg("ebkg", "extended background p.d.f", bkg, nbkg);
99
100 // 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
101 // -------------------------------------------------------------------------
102
103 // Construct sum of two extended p.d.f. (no coefficients required)
104 RooAddPdf model2("model2", "(g1+g2)+a", RooArgList(ebkg, esig));
105
106 // Draw the frame on the canvas
107 new TCanvas("rf202_composite", "rf202_composite", 600, 600);
109 xframe->GetYaxis()->SetTitleOffset(1.4);
110 xframe->Draw();
111}
@ kDashed
Definition: TAttLine.h:48
@ kDotted
Definition: TAttLine.h:48
virtual RooPlot * plotOn(RooPlot *frame, const RooCmdArg &arg1=RooCmdArg::none(), const RooCmdArg &arg2=RooCmdArg::none(), const RooCmdArg &arg3=RooCmdArg::none(), const RooCmdArg &arg4=RooCmdArg::none(), const RooCmdArg &arg5=RooCmdArg::none(), const RooCmdArg &arg6=RooCmdArg::none(), const RooCmdArg &arg7=RooCmdArg::none(), const RooCmdArg &arg8=RooCmdArg::none()) const
Calls RooPlot* plotOn(RooPlot* frame, const RooLinkedList& cmdList) const ;.
Definition: RooAbsData.cxx:546
@ RelativeExpected
Definition: RooAbsReal.h:252
RooAddPdf is an efficient implementation of a sum of PDFs of the form.
RooArgList is a container object that can hold multiple RooAbsArg objects.
Definition: RooArgList.h:21
RooArgSet is a container object that can hold multiple RooAbsArg objects.
Definition: RooArgSet.h:28
Chebychev polynomial p.d.f.
Definition: RooChebychev.h:25
RooDataSet is a container class to hold unbinned data.
Definition: RooDataSet.h:33
RooExtendPdf is a wrapper around an existing PDF that adds a parameteric extended likelihood term to ...
Definition: RooExtendPdf.h:22
Plain Gaussian p.d.f.
Definition: RooGaussian.h:25
A RooPlot is a plot frame and a container for graphics objects within that frame.
Definition: RooPlot.h:44
TAxis * GetYaxis() const
Definition: RooPlot.cxx:1277
virtual void Print(Option_t *options=0) const
Print TNamed name and title.
Definition: RooPlot.h:134
virtual void Draw(Option_t *options=0)
Draw this plot and all of the elements it contains.
Definition: RooPlot.cxx:712
RooRealVar represents a variable that can be changed from the outside.
Definition: RooRealVar.h:35
virtual void SetTitleOffset(Float_t offset=1)
Set distance between the axis and the axis title.
Definition: TAttAxis.cxx:294
The Canvas class.
Definition: TCanvas.h:27
RooCmdArg Components(const RooArgSet &compSet)
RooCmdArg Normalization(Double_t scaleFactor)
RooCmdArg LineStyle(Style_t style)
Double_t x[n]
Definition: legend1.C:17
The namespace RooFit contains mostly switches that change the behaviour of functions of PDFs (or othe...
const char * Title
Definition: TXMLSetup.cxx:67