IntervalExamples.C File Reference

Detailed Description

Example showing confidence intervals with four techniques.

An example that shows confidence intervals with four techniques. The model is a Normal Gaussian G(x|mu,sigma) with 100 samples of x. The answer is known analytically, so this is a good example to validate the RooStats tools.

• expected interval is [-0.162917, 0.229075]
• plc interval is [-0.162917, 0.229075]
• fc interval is [-0.17 , 0.23] // stepsize is 0.01
• bc interval is [-0.162918, 0.229076]
• mcmc interval is [-0.166999, 0.230224]

Processing /mnt/build/workspace/root-makedoc-v610/rootspi/rdoc/src/v6-10-00-patches/tutorials/roostats/IntervalExamples.C...

#include "RooStats/ConfInterval.h"
#include "RooStats/PointSetInterval.h"
#include "RooStats/ConfidenceBelt.h"
#include "RooStats/FeldmanCousins.h"
#include "RooStats/ProfileLikelihoodCalculator.h"
#include "RooStats/MCMCCalculator.h"
#include "RooStats/BayesianCalculator.h"
#include "RooStats/MCMCIntervalPlot.h"
#include "RooStats/LikelihoodIntervalPlot.h"

#include "RooStats/ProofConfig.h"
#include "RooStats/ToyMCSampler.h"

#include "RooRandom.h"
#include "RooDataSet.h"
#include "RooRealVar.h"
#include "RooConstVar.h"
#include "RooAddition.h"
#include "RooDataHist.h"
#include "RooPoisson.h"
#include "RooPlot.h"

#include "TCanvas.h"
#include "TTree.h"
#include "TStyle.h"
#include "TMath.h"
#include"Math/DistFunc.h"
#include "TH1F.h"
#include "TMarker.h"
#include "TStopwatch.h"

#include <iostream>

// use this order for safety on library loading
using namespace RooFit;
using namespace RooStats;


void IntervalExamples()
{

   // Time this macro
   TStopwatch t;
   t.Start();


   // set RooFit random seed for reproducible results
   RooRandom::randomGenerator()->SetSeed(3001);

   // make a simple model via the workspace factory
   RooWorkspace* wspace = new RooWorkspace();
   wspace->factory("Gaussian::normal(x[-10,10],mu[-1,1],sigma[1])");
   wspace->defineSet("poi","mu");
   wspace->defineSet("obs","x");

   // specify components of model for statistical tools
   ModelConfig* modelConfig = new ModelConfig("Example G(x|mu,1)");
   modelConfig->SetWorkspace(*wspace);
   modelConfig->SetPdf( *wspace->pdf("normal") );
   modelConfig->SetParametersOfInterest( *wspace->set("poi") );
   modelConfig->SetObservables( *wspace->set("obs") );

   // create a toy dataset
   RooDataSet* data = wspace->pdf("normal")->generate(*wspace->set("obs"),100);
   data->Print();

   // for convenience later on
   RooRealVar* x = wspace->var("x");
   RooRealVar* mu = wspace->var("mu");

   // set confidence level
   double confidenceLevel = 0.95;

   // example use profile likelihood calculator
   ProfileLikelihoodCalculator plc(*data, *modelConfig);
   plc.SetConfidenceLevel( confidenceLevel);
   LikelihoodInterval* plInt = plc.GetInterval();

   // example use of Feldman-Cousins
   FeldmanCousins fc(*data, *modelConfig);
   fc.SetConfidenceLevel( confidenceLevel);
   fc.SetNBins(100); // number of points to test per parameter
   fc.UseAdaptiveSampling(true); // make it go faster

   // Here, we consider only ensembles with 100 events
   // The PDF could be extended and this could be removed
   fc.FluctuateNumDataEntries(false);

   // Proof
   //  ProofConfig pc(*wspace, 4, "workers=4", kFALSE);    // proof-lite
   //ProofConfig pc(w, 8, "localhost");    // proof cluster at "localhost"
   //  ToyMCSampler* toymcsampler = (ToyMCSampler*) fc.GetTestStatSampler();
   //  toymcsampler->SetProofConfig(&pc);     // enable proof

   PointSetInterval* interval = (PointSetInterval*) fc.GetInterval();


   // example use of BayesianCalculator
   // now we also need to specify a prior in the ModelConfig
   wspace->factory("Uniform::prior(mu)");
   modelConfig->SetPriorPdf(*wspace->pdf("prior"));

   // example usage of BayesianCalculator
   BayesianCalculator bc(*data, *modelConfig);
   bc.SetConfidenceLevel( confidenceLevel);
   SimpleInterval* bcInt = bc.GetInterval();

   // example use of MCMCInterval
   MCMCCalculator mc(*data, *modelConfig);
   mc.SetConfidenceLevel( confidenceLevel);
   // special options
   mc.SetNumBins(200);        // bins used internally for representing posterior
   mc.SetNumBurnInSteps(500); // first N steps to be ignored as burn-in
   mc.SetNumIters(100000);    // how long to run chain
   mc.SetLeftSideTailFraction(0.5); // for central interval
   MCMCInterval* mcInt = mc.GetInterval();

   // for this example we know the expected intervals
   double expectedLL = data->mean(*x)
      + ROOT::Math::normal_quantile(  (1-confidenceLevel)/2,1)
      / sqrt(data->numEntries());
   double expectedUL = data->mean(*x)
      + ROOT::Math::normal_quantile_c((1-confidenceLevel)/2,1)
      / sqrt(data->numEntries()) ;

   // Use the intervals
   std::cout << "expected interval is [" <<
      expectedLL << ", " <<
      expectedUL << "]" << endl;

   cout << "plc interval is [" <<
      plInt->LowerLimit(*mu) << ", " <<
      plInt->UpperLimit(*mu) << "]" << endl;

   std::cout << "fc interval is ["<<
      interval->LowerLimit(*mu) << " , "  <<
      interval->UpperLimit(*mu) << "]" << endl;

   cout << "bc interval is [" <<
      bcInt->LowerLimit() << ", " <<
      bcInt->UpperLimit() << "]" << endl;

   cout << "mc interval is [" <<
      mcInt->LowerLimit(*mu) << ", " <<
      mcInt->UpperLimit(*mu) << "]" << endl;

   mu->setVal(0);
   cout << "is mu=0 in the interval? " <<
      plInt->IsInInterval(RooArgSet(*mu)) << endl;


   // make a reasonable style
   gStyle->SetCanvasColor(0);
   gStyle->SetCanvasBorderMode(0);
   gStyle->SetPadBorderMode(0);
   gStyle->SetPadColor(0);
   gStyle->SetCanvasColor(0);
   gStyle->SetTitleFillColor(0);
   gStyle->SetFillColor(0);
   gStyle->SetFrameFillColor(0);
   gStyle->SetStatColor(0);


   // some plots
   TCanvas* canvas = new TCanvas("canvas");
   canvas->Divide(2,2);

   // plot the data
   canvas->cd(1);
   RooPlot* frame = x->frame();
   data->plotOn(frame);
   data->statOn(frame);
   frame->Draw();

   // plot the profile likelihood
   canvas->cd(2);
   LikelihoodIntervalPlot plot(plInt);
   plot.Draw();

   // plot the MCMC interval
   canvas->cd(3);
   MCMCIntervalPlot* mcPlot = new MCMCIntervalPlot(*mcInt);
   mcPlot->SetLineColor(kGreen);
   mcPlot->SetLineWidth(2);
   mcPlot->Draw();

   canvas->cd(4);
   RooPlot * bcPlot = bc.GetPosteriorPlot();
   bcPlot->Draw();

   canvas->Update();

   t.Stop();
   t.Print();

}

Author

Kyle Cranmer

Definition in file IntervalExamples.C.