MultivariateGaussianTest.C File Reference

Detailed Description

Comparison of MCMC and PLC in a multi-variate gaussian problem

This tutorial produces an N-dimensional multivariate Gaussian with a non-trivial covariance matrix. By default N=4 (called "dim").

A subset of these are considered parameters of interest. This problem is tractable analytically.

We use this mainly as a test of Markov Chain Monte Carlo and we compare the result to the profile likelihood ratio.

We use the proposal helper to create a customized proposal function for this problem.

For N=4 and 2 parameters of interest it takes about 10-20 seconds and the acceptance rate is 37%

Processing /mnt/build/workspace/root-makedoc-v608/rootspi/rdoc/src/v6-08-00-patches/tutorials/roostats/MultivariateGaussianTest.C...

#include "RooGlobalFunc.h"
#include <stdlib.h>
#include "TMatrixDSym.h"
#include "RooMultiVarGaussian.h"
#include "RooArgList.h"
#include "RooRealVar.h"
#include "TH2F.h"
#include "TCanvas.h"
#include "RooAbsReal.h"
#include "RooFitResult.h"
#include "TStopwatch.h"
#include "RooStats/MCMCCalculator.h"
#include "RooStats/MetropolisHastings.h"
#include "RooStats/MarkovChain.h"
#include "RooStats/ConfInterval.h"
#include "RooStats/MCMCInterval.h"
#include "RooStats/MCMCIntervalPlot.h"
#include "RooStats/ModelConfig.h"
#include "RooStats/ProposalHelper.h"
#include "RooStats/ProposalFunction.h"
#include "RooStats/PdfProposal.h"
#include "RooStats/ProfileLikelihoodCalculator.h"
#include "RooStats/LikelihoodIntervalPlot.h"
#include "RooStats/LikelihoodInterval.h"

using namespace std;
using namespace RooFit;
using namespace RooStats;


void MultivariateGaussianTest(Int_t dim = 4, Int_t nPOI = 2)
{
  // let's time this challenging example
  TStopwatch t;
  t.Start();

   RooArgList xVec;
   RooArgList muVec;
   RooArgSet poi;

   // make the observable and means
   Int_t i,j;
   RooRealVar* x;
   RooRealVar* mu_x;
   for (i = 0; i < dim; i++) {
      char* name = Form("x%d", i);
      x = new RooRealVar(name, name, 0, -3,3);
      xVec.add(*x);

      char* mu_name = Form("mu_x%d",i);
      mu_x = new RooRealVar(mu_name, mu_name, 0, -2,2);
      muVec.add(*mu_x);
   }

   // put them into the list of parameters of interest
   for (i = 0; i < nPOI; i++) {
      poi.add(*muVec.at(i));
   }

   // make a covariance matrix that is all 1's
   TMatrixDSym cov(dim);
   for (i = 0; i < dim; i++) {
      for (j = 0; j < dim; j++) {
         if (i == j) cov(i,j) = 3.;
         else        cov(i,j) = 1.0;
      }
   }

   // now make the multivariate Gaussian
   RooMultiVarGaussian mvg("mvg", "mvg", xVec, muVec, cov);

   // --------------------
   // make a toy dataset
   RooDataSet* data = mvg.generate(xVec, 100);

   // now create the model config for this problem
   RooWorkspace* w = new RooWorkspace("MVG");
   ModelConfig modelConfig(w);
   modelConfig.SetPdf(mvg);
   modelConfig.SetParametersOfInterest(poi);

   // -------------------------------------------------------
   // Setup calculators

   // MCMC
   // we want to setup an efficient proposal function
   // using the covariance matrix from a fit to the data
   RooFitResult* fit = mvg.fitTo(*data, Save(true));
   ProposalHelper ph;
   ph.SetVariables((RooArgSet&)fit->floatParsFinal());
   ph.SetCovMatrix(fit->covarianceMatrix());
   ph.SetUpdateProposalParameters(true);
   ph.SetCacheSize(100);
   ProposalFunction* pdfProp = ph.GetProposalFunction();

   // now create the calculator
   MCMCCalculator mc(*data, modelConfig);
   mc.SetConfidenceLevel(0.95);
   mc.SetNumBurnInSteps(100);
   mc.SetNumIters(10000);
   mc.SetNumBins(50);
   mc.SetProposalFunction(*pdfProp);

   MCMCInterval* mcInt = mc.GetInterval();
   RooArgList* poiList = mcInt->GetAxes();

   // now setup the profile likelihood calculator
   ProfileLikelihoodCalculator plc(*data, modelConfig);
   plc.SetConfidenceLevel(0.95);
   LikelihoodInterval* plInt = (LikelihoodInterval*)plc.GetInterval();


   // make some plots
   MCMCIntervalPlot mcPlot(*mcInt);

   TCanvas* c1 = new TCanvas();
   mcPlot.SetLineColor(kGreen);
   mcPlot.SetLineWidth(2);
   mcPlot.Draw();

   LikelihoodIntervalPlot plPlot(plInt);
   plPlot.Draw("same");

   if (poiList->getSize() == 1) {
      RooRealVar* p = (RooRealVar*)poiList->at(0);
      Double_t ll = mcInt->LowerLimit(*p);
      Double_t ul = mcInt->UpperLimit(*p);
      cout << "MCMC interval: [" << ll << ", " << ul << "]" << endl;
   }

   if (poiList->getSize() == 2) {
      RooRealVar* p0 = (RooRealVar*)poiList->at(0);
      RooRealVar* p1 = (RooRealVar*)poiList->at(1);
      TCanvas* scatter = new TCanvas();
      Double_t ll = mcInt->LowerLimit(*p0);
      Double_t ul = mcInt->UpperLimit(*p0);
      cout << "MCMC interval on p0: [" << ll << ", " << ul << "]" << endl;
      ll = mcInt->LowerLimit(*p0);
      ul = mcInt->UpperLimit(*p0);
      cout << "MCMC interval on p1: [" << ll << ", " << ul << "]" << endl;

      //MCMC interval on p0: [-0.2, 0.6]
      //MCMC interval on p1: [-0.2, 0.6]

      mcPlot.DrawChainScatter(*p0, *p1);
      scatter->Update();
   }

  t.Print();

}

Authors

Kevin Belasco and Kyle Cranmer

Definition in file MultivariateGaussianTest.C.