Logo ROOT  
Reference Guide
rf204a_extendedLikelihood.C
Go to the documentation of this file.
1 /// \file
2 /// \ingroup tutorial_roofit
3 /// \notebook -js
4 /// Extended maximum likelihood fit in multiple ranges.
5 ///
6 /// When an extended pdf and multiple ranges are used, the
7 /// RooExtendPdf cannot correctly interpret the coefficients
8 /// used for extension.
9 /// This can be solved by using a RooAddPdf for extending the model.
10 ///
11 /// \macro_output
12 /// \macro_code
13 ///
14 /// \date December 2018
15 /// \author Stephan Hageboeck
16 
17 
18 #include "RooRealVar.h"
19 #include "RooDataSet.h"
20 #include "RooGaussian.h"
21 #include "RooChebychev.h"
22 #include "RooAddPdf.h"
23 #include "RooExtendPdf.h"
24 #include "RooFitResult.h"
25 #include "TCanvas.h"
26 #include "TAxis.h"
27 #include "RooPlot.h"
28 using namespace RooFit ;
29 
30 
31 void rf204a_extendedLikelihood()
32 {
33 
34 
35  // S e t u p c o m p o n e n t p d f s
36  // ---------------------------------------
37 
38  // Declare observable x
39  RooRealVar x("x","x",0,11) ;
40 
41  // Create two Gaussian PDFs g1(x,mean1,sigma) anf g2(x,mean2,sigma) and their parameters
42  RooRealVar mean("mean","mean of gaussians",5) ;
43  RooRealVar sigma1("sigma1","width of gaussians",0.5) ;
44  RooRealVar sigma2("sigma2","width of gaussians",1) ;
45 
46  RooGaussian sig1("sig1","Signal component 1",x,mean,sigma1) ;
47  RooGaussian sig2("sig2","Signal component 2",x,mean,sigma2) ;
48 
49  // Build Chebychev polynomial pdf
50  RooRealVar a0("a0","a0",0.5,0.,1.) ;
51  RooRealVar a1("a1","a1",0.2,0.,1.) ;
52  RooChebychev bkg("bkg","Background",x,RooArgSet(a0,a1)) ;
53 
54  // Sum the signal components into a composite signal pdf
55  RooRealVar sig1frac("sig1frac","fraction of component 1 in signal",0.8,0.,1.) ;
56  RooAddPdf sig("sig","Signal",RooArgList(sig1,sig2),sig1frac) ;
57 
58 
59  // E x t e n d t h e p d f s
60  // -----------------------------
61 
62 
63  // Define signal range in which events counts are to be defined
64  x.setRange("signalRange",4,6) ;
65 
66  // Associated nsig/nbkg as expected number of events with sig/bkg _in_the_range_ "signalRange"
67  RooRealVar nsig("nsig","number of signal events in signalRange",500,0.,10000) ;
68  RooRealVar nbkg("nbkg","number of background events in signalRange",500,0,10000) ;
69 
70  // Use AddPdf to extend the model. Giving as many coefficients as pdfs switches
71  // on extension.
72  RooAddPdf model("model","(g1+g2)+a", RooArgList(bkg,sig), RooArgList(nbkg,nsig)) ;
73 
74 
75  // S a m p l e d a t a , f i t m o d e l
76  // -------------------------------------------
77 
78  // Generate 1000 events from model so that nsig,nbkg come out to numbers <<500 in fit
79  RooDataSet *data = model.generate(x,1000) ;
80 
81 
82 
83  auto canv = new TCanvas("Canvas", "Canvas", 1500, 600);
84  canv->Divide(3,1);
85 
86  // Fit full range
87  // -------------------------------------------
88 
89  canv->cd(1);
90 
91  // Perform unbinned ML fit to data, full range
92 
93  // IMPORTANT:
94  // The model needs to be copied when fitting with different ranges because
95  // the interpretation of the coefficients is tied to the fit range
96  // that's used in the first fit
97  RooAddPdf model1(model);
98  RooFitResult* r = model1.fitTo(*data,Save()) ;
99  r->Print() ;
100 
101  RooPlot * frame = x.frame(Title("Full range fitted"));
102  data->plotOn(frame);
103  model1.plotOn(frame, VisualizeError(*r));
104  model1.plotOn(frame);
105  model1.paramOn(frame);
106  frame->Draw();
107 
108 
109  // Fit in two regions
110  // -------------------------------------------
111 
112  canv->cd(2);
113  x.setRange("left", 0., 4.);
114  x.setRange("right", 6., 10.);
115 
116  RooAddPdf model2(model);
117  RooFitResult* r2 = model2.fitTo(*data,
118  Range("left,right"),
119  Save()) ;
120  r2->Print();
121 
122 
123  RooPlot * frame2 = x.frame(Title("Fit in left/right sideband"));
124  data->plotOn(frame2);
125  model2.plotOn(frame2, VisualizeError(*r2));
126  model2.plotOn(frame2);
127  model2.paramOn(frame2);
128  frame2->Draw();
129 
130 
131  // Fit in one region
132  // -------------------------------------------
133  // Note how restricting the region to only the left tail increases
134  // the fit uncertainty
135 
136  canv->cd(3);
137  x.setRange("leftToMiddle", 0., 5.);
138 
139  RooAddPdf model3(model);
140  RooFitResult* r3 = model3.fitTo(*data,
141  Range("leftToMiddle"),
142  Save()) ;
143  r3->Print();
144 
145 
146  RooPlot * frame3 = x.frame(Title("Fit from left to middle"));
147  data->plotOn(frame3);
148  model3.plotOn(frame3, VisualizeError(*r3));
149  model3.plotOn(frame3);
150  model3.paramOn(frame3);
151  frame3->Draw();
152 
153  canv->Draw();
154 }
RooPlot::Draw
virtual void Draw(Option_t *options=0)
Draw this plot and all of the elements it contains.
Definition: RooPlot.cxx:691
RooChebychev.h
RooAddPdf
RooAddPdf is an efficient implementation of a sum of PDFs of the form.
Definition: RooAddPdf.h:32
RooExtendPdf.h
TObject::Print
virtual void Print(Option_t *option="") const
This method must be overridden when a class wants to print itself.
Definition: TObject.cxx:552
RooFit::VisualizeError
RooCmdArg VisualizeError(const RooDataSet &paramData, Double_t Z=1)
Definition: RooGlobalFunc.cxx:71
RooChebychev
Chebychev polynomial p.d.f.
Definition: RooChebychev.h:25
r
ROOT::R::TRInterface & r
Definition: Object.C:4
RooArgList
RooArgList is a container object that can hold multiple RooAbsArg objects.
Definition: RooArgList.h:21
RooGaussian.h
x
Double_t x[n]
Definition: legend1.C:17
RooGaussian
Plain Gaussian p.d.f.
Definition: RooGaussian.h:24
RooAddPdf.h
TCanvas.h
RooDataSet.h
RooFitResult
RooFitResult is a container class to hold the input and output of a PDF fit to a dataset.
Definition: RooFitResult.h:40
RooFit
The namespace RooFit contains mostly switches that change the behaviour of functions of PDFs (or othe...
Definition: RooCFunction1Binding.h:29
RooAbsData::plotOn
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
Definition: RooAbsData.cxx:547
RooPlot.h
RooPlot
A RooPlot is a plot frame and a container for graphics objects within that frame.
Definition: RooPlot.h:44
RooRealVar.h
RooFitResult.h
TCanvas
The Canvas class.
Definition: TCanvas.h:23
TAxis.h
RooFit::Range
RooCmdArg Range(const char *rangeName, Bool_t adjustNorm=kTRUE)
Definition: RooGlobalFunc.cxx:53
RooFitResult::Print
virtual void Print(Option_t *options=0) const
Print TNamed name and title.
Definition: RooFitResult.h:66
RooDataSet
RooDataSet is a container class to hold unbinned data.
Definition: RooDataSet.h:33
make_cnn_model.model
model
Definition: make_cnn_model.py:6
RooRealVar
RooRealVar represents a variable that can be changed from the outside.
Definition: RooRealVar.h:37
RooFit::Save
RooCmdArg Save(Bool_t flag=kTRUE)
Definition: RooGlobalFunc.cxx:190
RooFit::Title
RooCmdArg Title(const char *name)
Definition: RooGlobalFunc.cxx:176
RooArgSet
RooArgSet is a container object that can hold multiple RooAbsArg objects.
Definition: RooArgSet.h:29