JeffreysPriorDemo.C

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/// \file
/// \ingroup tutorial_roostats
/// \notebook -js
/// tutorial demonstrating and validates the RooJeffreysPrior class
///
/// Jeffreys's prior is an 'objective prior' based on formal rules.
/// It is calculated from the Fisher information matrix.
///
/// Read more:
/// http://en.wikipedia.org/wiki/Jeffreys_prior
///
/// The analytic form is not known for most PDFs, but it is for
/// simple cases like the Poisson mean, Gaussian mean, Gaussian sigma.
///
/// This class uses numerical tricks to calculate the Fisher Information Matrix
/// efficiently.  In particular, it takes advantage of a property of the
/// 'Asimov data' as described in
/// Asymptotic formulae for likelihood-based tests of new physics
/// Glen Cowan, Kyle Cranmer, Eilam Gross, Ofer Vitells
/// http://arxiv.org/abs/arXiv:1007.1727
///
/// This Demo has four parts:
///  1. TestJeffreysPriorDemo -- validates Poisson mean case 1/sqrt(mu)
///  2. TestJeffreysGaussMean -- validates Gaussian mean case
///  3. TestJeffreysGaussSigma -- validates Gaussian sigma case 1/sigma
///  4. TestJeffreysGaussMeanAndSigma -- demonstrates 2-d example
///
/// \macro_image
/// \macro_output
/// \macro_code
///
/// \author Kyle Cranmer
 
#include "RooJeffreysPrior.h"
 
#include "RooWorkspace.h"
#include "RooDataHist.h"
#include "RooGenericPdf.h"
#include "TCanvas.h"
#include "RooPlot.h"
#include "RooFitResult.h"
#include "TMatrixDSym.h"
#include "RooRealVar.h"
#include "RooAbsPdf.h"
#include "RooNumIntConfig.h"
#include "TH1F.h"
 
using namespace RooFit;
 
void JeffreysPriorDemo(){
   RooWorkspace w("w");
   w.factory("Uniform::u(x[0,1])");
   w.factory("mu[100,1,200]");
   w.factory("ExtendPdf::p(u,mu)");
 
   RooDataHist* asimov = w.pdf("p")->generateBinned(*w.var("x"),ExpectedData());
 
   RooFitResult* res = w.pdf("p")->fitTo(*asimov,Save(),SumW2Error(kTRUE));
 
   asimov->Print();
   res->Print();
   TMatrixDSym cov = res->covarianceMatrix();
   cout << "variance = " << (cov.Determinant()) << endl;
   cout << "stdev = " << sqrt(cov.Determinant()) << endl;
   cov.Invert();
   cout << "jeffreys = " << sqrt(cov.Determinant()) << endl;
 
   w.defineSet("poi","mu");
   w.defineSet("obs","x");
 
   RooJeffreysPrior pi("jeffreys","jeffreys",*w.pdf("p"),*w.set("poi"),*w.set("obs"));
 
   RooGenericPdf* test = new RooGenericPdf("test","test","1./sqrt(mu)",*w.set("poi"));
 
   TCanvas* c1 = new TCanvas;
   RooPlot* plot = w.var("mu")->frame();
   pi.plotOn(plot);
   test->plotOn(plot,LineColor(kRed));
   plot->Draw();
 
}
 
//_________________________________________________
void TestJeffreysGaussMean(){
   RooWorkspace w("w");
   w.factory("Gaussian::g(x[0,-20,20],mu[0,-5,5],sigma[1,0,10])");
   w.factory("n[10,.1,200]");
   w.factory("ExtendPdf::p(g,n)");
   w.var("sigma")->setConstant();
   w.var("n")->setConstant();
 
   RooDataHist* asimov = w.pdf("p")->generateBinned(*w.var("x"),ExpectedData());
 
   RooFitResult* res = w.pdf("p")->fitTo(*asimov,Save(),SumW2Error(kTRUE));
 
   asimov->Print();
   res->Print();
   TMatrixDSym cov = res->covarianceMatrix();
   cout << "variance = " << (cov.Determinant()) << endl;
   cout << "stdev = " << sqrt(cov.Determinant()) << endl;
   cov.Invert();
   cout << "jeffreys = " << sqrt(cov.Determinant()) << endl;
 
   w.defineSet("poi","mu");
   w.defineSet("obs","x");
 
   RooJeffreysPrior pi("jeffreys","jeffreys",*w.pdf("p"),*w.set("poi"),*w.set("obs"));
 
   const RooArgSet* temp = w.set("poi");
   pi.getParameters(*temp)->Print();
 
   //  return;
   RooGenericPdf* test = new RooGenericPdf("test","test","1",*w.set("poi"));
 
   TCanvas* c1 = new TCanvas;
   RooPlot* plot = w.var("mu")->frame();
   pi.plotOn(plot);
   test->plotOn(plot,LineColor(kRed),LineStyle(kDotted));
   plot->Draw();
}
 
//_________________________________________________
void TestJeffreysGaussSigma(){
   // this one is VERY sensitive
   // if the Gaussian is narrow ~ range(x)/nbins(x) then the peak isn't resolved
   //   and you get really bizarre shapes
   // if the Gaussian is too wide range(x) ~ sigma then PDF gets renormalized
   //   and the PDF falls off too fast at high sigma
   RooWorkspace w("w");
   w.factory("Gaussian::g(x[0,-20,20],mu[0,-5,5],sigma[1,1,5])");
   w.factory("n[100,.1,2000]");
   w.factory("ExtendPdf::p(g,n)");
   //  w.var("sigma")->setConstant();
   w.var("mu")->setConstant();
   w.var("n")->setConstant();
   w.var("x")->setBins(301);
 
   RooDataHist* asimov = w.pdf("p")->generateBinned(*w.var("x"),ExpectedData());
 
   RooFitResult* res = w.pdf("p")->fitTo(*asimov,Save(),SumW2Error(kTRUE));
 
   asimov->Print();
   res->Print();
   TMatrixDSym cov = res->covarianceMatrix();
   cout << "variance = " << (cov.Determinant()) << endl;
   cout << "stdev = " << sqrt(cov.Determinant()) << endl;
   cov.Invert();
   cout << "jeffreys = " << sqrt(cov.Determinant()) << endl;
 
   w.defineSet("poi","sigma");
   w.defineSet("obs","x");
 
   RooJeffreysPrior pi("jeffreys","jeffreys",*w.pdf("p"),*w.set("poi"),*w.set("obs"));
   pi.specialIntegratorConfig(kTRUE)->getConfigSection("RooIntegrator1D").setRealValue("maxSteps",3);
 
   const RooArgSet* temp = w.set("poi");
   pi.getParameters(*temp)->Print();
 
   RooGenericPdf* test = new RooGenericPdf("test","test","sqrt(2.)/sigma",*w.set("poi"));
 
   TCanvas* c1 = new TCanvas;
   RooPlot* plot = w.var("sigma")->frame();
   pi.plotOn(plot);
   test->plotOn(plot,LineColor(kRed),LineStyle(kDotted));
   plot->Draw();
 
 
}
 
//_________________________________________________
void TestJeffreysGaussMeanAndSigma(){
   // this one is VERY sensitive
   // if the Gaussian is narrow ~ range(x)/nbins(x) then the peak isn't resolved
   //   and you get really bizarre shapes
   // if the Gaussian is too wide range(x) ~ sigma then PDF gets renormalized
   //   and the PDF falls off too fast at high sigma
   RooWorkspace w("w");
   w.factory("Gaussian::g(x[0,-20,20],mu[0,-5,5],sigma[1,1,5])");
   w.factory("n[100,.1,2000]");
   w.factory("ExtendPdf::p(g,n)");
 
   w.var("n")->setConstant();
   w.var("x")->setBins(301);
 
   RooDataHist* asimov = w.pdf("p")->generateBinned(*w.var("x"),ExpectedData());
 
   RooFitResult* res = w.pdf("p")->fitTo(*asimov,Save(),SumW2Error(kTRUE));
 
   asimov->Print();
   res->Print();
   TMatrixDSym cov = res->covarianceMatrix();
   cout << "variance = " << (cov.Determinant()) << endl;
   cout << "stdev = " << sqrt(cov.Determinant()) << endl;
   cov.Invert();
   cout << "jeffreys = " << sqrt(cov.Determinant()) << endl;
 
   w.defineSet("poi","mu,sigma");
   w.defineSet("obs","x");
 
   RooJeffreysPrior pi("jeffreys","jeffreys",*w.pdf("p"),*w.set("poi"),*w.set("obs"));
   pi.specialIntegratorConfig(kTRUE)->getConfigSection("RooIntegrator1D").setRealValue("maxSteps",3);
 
   const RooArgSet* temp = w.set("poi");
   pi.getParameters(*temp)->Print();
   //  return;
 
   TCanvas* c1 = new TCanvas;
   TH1* Jeff2d = pi.createHistogram("2dJeffreys",*w.var("mu"),Binning(10),YVar(*w.var("sigma"),Binning(10)));
   Jeff2d->Draw("surf");
}