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Zbi_Zgamma.C File Reference

Detailed Description

Demonstrate Z_Bi = Z_Gamma.

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RooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby
Copyright (C) 2000-2013 NIKHEF, University of California & Stanford University
All rights reserved, please read http://roofit.sourceforge.net/license.txt
[#1] INFO:ObjectHandling -- RooWorkspace::exportToCint(w) INFO: references to all objects in this workspace will be created in CINT in 'namespace w'
[#1] INFO:NumericIntegration -- RooRealIntegral::init([py_X_prior_b]_Norm[b]_denominator_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)
[#1] INFO:NumericIntegration -- RooRealIntegral::init([py_X_prior_b]_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)
[#1] INFO:NumericIntegration -- RooRealIntegral::init([py_X_prior_b]_Norm[b]_denominator_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)
[#1] INFO:NumericIntegration -- RooRealIntegral::init([[py_X_prior_b]_Norm[b]_X_px_NORM[x]]_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)
[#1] INFO:NumericIntegration -- RooRealIntegral::init([py_X_prior_b]_Norm[b]_denominator_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)
[#1] INFO:NumericIntegration -- RooRealIntegral::init([py_X_prior_b]_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)
[#1] INFO:NumericIntegration -- RooRealIntegral::init([py_X_prior_b]_Norm[b]_denominator_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)
[#1] INFO:NumericIntegration -- RooRealIntegral::init([py_X_prior_b_X_px]_Norm[b]_denominator_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)
[#1] INFO:NumericIntegration -- RooRealIntegral::init([py_X_prior_b]_Norm[b]_denominator_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)
[#1] INFO:NumericIntegration -- RooRealIntegral::init([py_X_prior_b]_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)
[#1] INFO:NumericIntegration -- RooRealIntegral::init([py_X_prior_b]_Norm[b]_denominator_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)
[#1] INFO:NumericIntegration -- RooRealIntegral::init([py_X_prior_b]_Norm[b]_denominator_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)
[#1] INFO:NumericIntegration -- RooRealIntegral::init([py_X_prior_b]_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)
[#1] INFO:NumericIntegration -- RooRealIntegral::init([[py_X_prior_b]_Norm[b]_X_px_cdf_NORM[x_prime]]_Int[b]) using numeric integrator RooIntegrator1D to calculate Int(b)
[#1] INFO:NumericIntegration -- RooRealIntegral::init([[py_X_prior_b]_Norm[b]_X_px_cdf_Int[x_prime|CDF]_Norm[x_prime]]_Int[b|CDF]) using numeric integrator RooIntegrator1D to calculate Int(b)
Hybrid p-value = 0.999226
Z_Gamma Significance = 3.1655
Z_Bi significance estimation: 3.10804
#include "RooRealVar.h"
#include "RooProdPdf.h"
#include "RooWorkspace.h"
#include "RooDataSet.h"
#include "TCanvas.h"
#include "TH1.h"
using namespace RooFit;
using namespace RooStats;
void Zbi_Zgamma()
{
// Make model for prototype on/off problem
// Pois(x | s+b) * Pois(y | tau b )
// for Z_Gamma, use uniform prior on b.
RooWorkspace *w1 = new RooWorkspace("w", true);
w1->factory("Poisson::px(x[150,0,500],sum::splusb(s[0,0,100],b[100,0,300]))");
w1->factory("Poisson::py(y[100,0,500],prod::taub(tau[1.],b))");
w1->factory("Uniform::prior_b(b)");
// construct the Bayesian-averaged model (eg. a projection pdf)
// p'(x|s) = \int db p(x|s+b) * [ p(y|b) * prior(b) ]
w1->factory("PROJ::averagedModel(PROD::foo(px|b,py,prior_b),b)");
// plot it, blue is averaged model, red is b known exactly
RooPlot *frame = w1->var("x")->frame();
w1->pdf("averagedModel")->plotOn(frame);
w1->pdf("px")->plotOn(frame, LineColor(kRed));
frame->Draw();
// compare analytic calculation of Z_Bi
// with the numerical RooFit implementation of Z_Gamma
// for an example with x = 150, y = 100
// numeric RooFit Z_Gamma
w1->var("y")->setVal(100);
w1->var("x")->setVal(150);
RooAbsReal *cdf = w1->pdf("averagedModel")->createCdf(*w1->var("x"));
cdf->getVal(); // get ugly print messages out of the way
cout << "Hybrid p-value = " << cdf->getVal() << endl;
cout << "Z_Gamma Significance = " << PValueToSignificance(1 - cdf->getVal()) << endl;
// analytic Z_Bi
double Z_Bi = NumberCountingUtils::BinomialWithTauObsZ(150, 100, 1);
std::cout << "Z_Bi significance estimation: " << Z_Bi << std::endl;
// OUTPUT
// Hybrid p-value = 0.999058
// Z_Gamma Significance = 3.10804
// Z_Bi significance estimation: 3.10804
}
Author
Kyle Cranmer & Wouter Verkerke

Definition in file Zbi_Zgamma.C.

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:3406
RooAbsReal::getVal
Double_t getVal(const RooArgSet *normalisationSet=nullptr) const
Evaluate object.
Definition: RooAbsReal.h:91
RooAbsReal
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
Helper calling plotOn(RooPlot*, RooLinkedList&) 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
Definition: RooCFunction1Binding.h:29
RooPlot
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
Definition: RooWorkspace.h:43
RooFit::LineColor
RooCmdArg LineColor(Color_t color)
Definition: RooGlobalFunc.cxx:56
RooStats
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