ROOT   Reference Guide
Zbi_Zgamma.C
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1 /// \file
2 /// \ingroup tutorial_roostats
3 /// \notebook -js
4 /// \brief Demonstrate Z_Bi = Z_Gamma
5 ///
6 /// \macro_image
7 /// \macro_output
8 /// \macro_code
9 ///
10 /// \author Kyle Cranmer & Wouter Verkerke
11
12 #include "RooRealVar.h"
13 #include "RooProdPdf.h"
14 #include "RooWorkspace.h"
15 #include "RooDataSet.h"
16 #include "TCanvas.h"
17 #include "TH1.h"
18
19 using namespace RooFit;
20 using namespace RooStats;
21
22 void Zbi_Zgamma()
23 {
24
25  // Make model for prototype on/off problem
26  // Pois(x | s+b) * Pois(y | tau b )
27  // for Z_Gamma, use uniform prior on b.
28  RooWorkspace *w1 = new RooWorkspace("w", true);
29  w1->factory("Poisson::px(x[150,0,500],sum::splusb(s[0,0,100],b[100,0,300]))");
30  w1->factory("Poisson::py(y[100,0,500],prod::taub(tau[1.],b))");
31  w1->factory("Uniform::prior_b(b)");
32
33  // construct the Bayesian-averaged model (eg. a projection pdf)
34  // p'(x|s) = \int db p(x|s+b) * [ p(y|b) * prior(b) ]
35  w1->factory("PROJ::averagedModel(PROD::foo(px|b,py,prior_b),b)");
36
37  // plot it, blue is averaged model, red is b known exactly
38  RooPlot *frame = w1->var("x")->frame();
39  w1->pdf("averagedModel")->plotOn(frame);
40  w1->pdf("px")->plotOn(frame, LineColor(kRed));
41  frame->Draw();
42
43  // compare analytic calculation of Z_Bi
44  // with the numerical RooFit implementation of Z_Gamma
45  // for an example with x = 150, y = 100
46
47  // numeric RooFit Z_Gamma
48  w1->var("y")->setVal(100);
49  w1->var("x")->setVal(150);
50  RooAbsReal *cdf = w1->pdf("averagedModel")->createCdf(*w1->var("x"));
51  cdf->getVal(); // get ugly print messages out of the way
52
53  cout << "Hybrid p-value = " << cdf->getVal() << endl;
54  cout << "Z_Gamma Significance = " << PValueToSignificance(1 - cdf->getVal()) << endl;
55
56  // analytic Z_Bi
57  double Z_Bi = NumberCountingUtils::BinomialWithTauObsZ(150, 100, 1);
58  std::cout << "Z_Bi significance estimation: " << Z_Bi << std::endl;
59
60  // OUTPUT
61  // Hybrid p-value = 0.999058
62  // Z_Gamma Significance = 3.10804
63  // Z_Bi significance estimation: 3.10804
64 }
RooAbsRealLValue::frame
RooPlot * frame(const RooCmdArg &arg1, 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
Create a new RooPlot on the heap with a drawing frame initialized for this object,...
Definition: RooAbsRealLValue.cxx:199
RooWorkspace.h
RooPlot::Draw
virtual void Draw(Option_t *options=0)
Draw this plot and all of the elements it contains.
Definition: RooPlot.cxx:691
RooRealVar::setVal
virtual void setVal(Double_t value)
Set value of variable to 'value'.
Definition: RooRealVar.cxx:216
RooAbsPdf::createCdf
RooAbsReal * createCdf(const RooArgSet &iset, const RooArgSet &nset=RooArgSet())
Create a cumulative distribution function of this p.d.f in terms of the observables listed in iset.
Definition: RooAbsPdf.cxx:3420
RooAbsReal::getVal
Double_t getVal(const RooArgSet *normalisationSet=nullptr) const
Evaluate object.
Definition: RooAbsReal.h:91
RooAbsReal
RooAbsReal is the common abstract base class for objects that represent a real value and implements f...
Definition: RooAbsReal.h:61
TCanvas.h
RooDataSet.h
RooAbsPdf::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 RooCmdArg &arg9=RooCmdArg::none(), const RooCmdArg &arg10=RooCmdArg::none()) const
Definition: RooAbsPdf.h:118
RooWorkspace::factory
RooFactoryWSTool & factory()
Return instance to factory tool.
Definition: RooWorkspace.cxx:2166
RooStats::NumberCountingUtils::BinomialWithTauObsZ
Double_t BinomialWithTauObsZ(Double_t nObs, Double_t bExp, Double_t tau)
Definition: NumberCountingUtils.cxx:138
RooStats::PValueToSignificance
Double_t PValueToSignificance(Double_t pvalue)
returns one-sided significance corresponding to a p-value
Definition: RooStatsUtils.h:51
RooProdPdf.h
RooFit
The namespace RooFit contains mostly switches that change the behaviour of functions of PDFs (or othe...
Definition: RooCFunction1Binding.h:29
RooPlot
A RooPlot is a plot frame and a container for graphics objects within that frame.
Definition: RooPlot.h:44
RooWorkspace::pdf
RooAbsPdf * pdf(const char *name) const
Retrieve p.d.f (RooAbsPdf) with given name. A null pointer is returned if not found.
Definition: RooWorkspace.cxx:1277
RooRealVar.h
kRed
@ kRed
Definition: Rtypes.h:66
RooWorkspace
The RooWorkspace is a persistable container for RooFit projects.
Definition: RooWorkspace.h:43
RooFit::LineColor
RooCmdArg LineColor(Color_t color)
Definition: RooGlobalFunc.cxx:56
RooStats
Namespace for the RooStats classes.
Definition: Asimov.h:19
RooWorkspace::var
RooRealVar * var(const char *name) const
Retrieve real-valued variable (RooRealVar) with given name. A null pointer is returned if not found.
Definition: RooWorkspace.cxx:1295
TH1.h