StandardTestStatDistributionDemo.C File Reference

Detailed Description

StandardTestStatDistributionDemo.C

This simple script plots the sampling distribution of the profile likelihood ratio test statistic based on the input Model File. To do this one needs to specify the value of the parameter of interest that will be used for evaluating the test statistic and the value of the parameters used for generating the toy data. In this case, it uses the upper-limit estimated from the ProfileLikleihoodCalculator, which assumes the asymptotic chi-square distribution for -2 log profile likelihood ratio. Thus, the script is handy for checking to see if the asymptotic approximations are valid. To aid, that comparison, the script overlays a chi-square distribution as well. The most common parameter of interest is a parameter proportional to the signal rate, and often that has a lower-limit of 0, which breaks the standard chi-square distribution. Thus the script allows the parameter to be negative so that the overlay chi-square is the correct asymptotic distribution.

 
 
␛[1mRooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby␛[0m 
                Copyright (C) 2000-2013 NIKHEF, University of California & Stanford University
                All rights reserved, please read http://roofit.sourceforge.net/license.txt
 
 
=== Using the following for ModelConfig ===
Observables:             RooArgSet:: = (obs_x_channel1,weightVar,channelCat)
Parameters of Interest:  RooArgSet:: = (SigXsecOverSM)
Nuisance Parameters:     RooArgSet:: = (alpha_syst2,alpha_syst3,gamma_stat_channel1_bin_0,gamma_stat_channel1_bin_1)
Global Observables:      RooArgSet:: = (nom_alpha_syst2,nom_alpha_syst3,nom_gamma_stat_channel1_bin_0,nom_gamma_stat_channel1_bin_1)
PDF:                     RooSimultaneous::simPdf[ indexCat=channelCat channel1=model_channel1 ] = 0.174888
 
[#1] INFO:Minization -- p.d.f. provides expected number of events, including extended term in likelihood.
[#1] INFO:Minization -- createNLL: caching constraint set under name CONSTR_OF_PDF_simPdf_FOR_OBS_channelCat:obs_x_channel1 with 4 entries
[#1] INFO:Minization --  Including the following constraint terms in minimization: (alpha_syst2Constraint,alpha_syst3Constraint,gamma_stat_channel1_bin_0_constraint,gamma_stat_channel1_bin_1_constraint)
[#1] INFO:Minization -- The following global observables have been defined: (nom_alpha_syst2,nom_alpha_syst3,nom_gamma_stat_channel1_bin_0,nom_gamma_stat_channel1_bin_1)
[#0] PROGRESS:Minization -- ProfileLikelihoodCalcultor::DoGLobalFit - find MLE 
[#0] PROGRESS:Minization -- ProfileLikelihoodCalcultor::DoMinimizeNLL - using Minuit / Migrad with strategy 1
[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_simPdf_obsData_with_constr) Summation contains a RooNLLVar, using its error level
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
RooAbsTestStatistic::initSimMode: creating slave calculator #0 for state channel1 (2 dataset entries)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(channel1_model_Int[obs_x_channel1]) using numeric integrator RooBinIntegrator to calculate Int(obs_x_channel1)
[#1] INFO:Fitting -- RooAbsTestStatistic::initSimMode: created 1 slave calculators.
[#1] INFO:NumericIntegration -- RooRealIntegral::init(channel1_model_Int[obs_x_channel1]) using numeric integrator RooBinIntegrator to calculate Int(obs_x_channel1)
[#1] INFO:Minization --  The following expressions have been identified as constant and will be precalculated and cached: (signal_channel1_nominal,background1_channel1_nominal,background2_channel1_nominal)
[#1] INFO:Minization --  The following expressions will be evaluated in cache-and-track mode: (mc_stat_channel1)
[#1] INFO:Minization -- 
  RooFitResult: minimized FCN value: -1033.78, estimated distance to minimum: 2.39183e-08
                covariance matrix quality: Full, accurate covariance matrix
                Status : MINIMIZE=0 
 
    Floating Parameter    FinalValue +/-  Error   
  --------------------  --------------------------
         SigXsecOverSM    1.1153e+00 +/-  5.86e-01
           alpha_syst2   -8.9016e-03 +/-  9.82e-01
           alpha_syst3    1.7918e-02 +/-  9.48e-01
  gamma_stat_channel1_bin_0    9.9955e-01 +/-  4.93e-02
  gamma_stat_channel1_bin_1    1.0036e+00 +/-  8.01e-02
 
Warning: lower value for SigXsecOverSM is at limit 0
 
 
--------------------------------------
Will generate sampling distribution at SigXsecOverSM = 2.32744
  1) 0x560536ca1180 RooRealVar::             SigXsecOverSM = 2.32744 +/- 0.586082  L(-3 - 3)  "SigXsecOverSM"
  2) 0x560536c9e6a0 RooRealVar::               alpha_syst2 = 0.710796 +/- 0.982182  L(-5 - 5)  "alpha_syst2"
  3) 0x560536ca4470 RooRealVar::               alpha_syst3 = 0.260222 +/- 0.947589  L(-5 - 5)  "alpha_syst3"
  4) 0x5605353349a0 RooRealVar:: gamma_stat_channel1_bin_0 = 1.03668 +/- 0.0493173  L(0 - 1.25)  "gamma_stat_channel1_bin_0"
  5) 0x560534d2e900 RooRealVar:: gamma_stat_channel1_bin_1 = 1.05157 +/- 0.080065  L(0 - 1.5)  "gamma_stat_channel1_bin_1"
[#0] PROGRESS:Generation -- generated toys: 500 / 1000

 
#include "TFile.h"
#include "TROOT.h"
#include "TH1F.h"
#include "TCanvas.h"
#include "TSystem.h"
#include "TF1.h"
#include "TSystem.h"
 
#include "RooWorkspace.h"
#include "RooAbsData.h"
 
#include "RooStats/ModelConfig.h"
#include "RooStats/FeldmanCousins.h"
#include "RooStats/ToyMCSampler.h"
#include "RooStats/PointSetInterval.h"
#include "RooStats/ConfidenceBelt.h"
 
#include "RooStats/ProfileLikelihoodCalculator.h"
#include "RooStats/LikelihoodInterval.h"
#include "RooStats/ProfileLikelihoodTestStat.h"
#include "RooStats/SamplingDistribution.h"
#include "RooStats/SamplingDistPlot.h"
 
using namespace RooFit;
using namespace RooStats;
 
bool useProof = false; // flag to control whether to use Proof
int nworkers = 0;      // number of workers (default use all available cores)
 
// -------------------------------------------------------
// The actual macro
 
void StandardTestStatDistributionDemo(const char *infile = "", const char *workspaceName = "combined",
                                      const char *modelConfigName = "ModelConfig", const char *dataName = "obsData")
{
 
   // the number of toy MC used to generate the distribution
   int nToyMC = 1000;
   // The parameter below is needed for asymptotic distribution to be chi-square,
   // but set to false if your model is not numerically stable if mu<0
   bool allowNegativeMu = true;
 
   // -------------------------------------------------------
   // First part is just to access a user-defined file
   // or create the standard example file if it doesn't exist
   const char *filename = "";
   if (!strcmp(infile, "")) {
      filename = "results/example_combined_GaussExample_model.root";
      bool fileExist = !gSystem->AccessPathName(filename); // note opposite return code
      // if file does not exists generate with histfactory
      if (!fileExist) {
#ifdef _WIN32
         cout << "HistFactory file cannot be generated on Windows - exit" << endl;
         return;
#endif
         // Normally this would be run on the command line
         cout << "will run standard hist2workspace example" << endl;
         gROOT->ProcessLine(".! prepareHistFactory .");
         gROOT->ProcessLine(".! hist2workspace config/example.xml");
         cout << "\n\n---------------------" << endl;
         cout << "Done creating example input" << endl;
         cout << "---------------------\n\n" << endl;
      }
 
   } else
      filename = infile;
 
   // Try to open the file
   TFile *file = TFile::Open(filename);
 
   // if input file was specified byt not found, quit
   if (!file) {
      cout << "StandardRooStatsDemoMacro: Input file " << filename << " is not found" << endl;
      return;
   }
 
   // -------------------------------------------------------
   // Now get the data and workspace
 
   // get the workspace out of the file
   RooWorkspace *w = (RooWorkspace *)file->Get(workspaceName);
   if (!w) {
      cout << "workspace not found" << endl;
      return;
   }
 
   // get the modelConfig out of the file
   ModelConfig *mc = (ModelConfig *)w->obj(modelConfigName);
 
   // get the modelConfig out of the file
   RooAbsData *data = w->data(dataName);
 
   // make sure ingredients are found
   if (!data || !mc) {
      w->Print();
      cout << "data or ModelConfig was not found" << endl;
      return;
   }
 
   mc->Print();
   // -------------------------------------------------------
   // Now find the upper limit based on the asymptotic results
   RooRealVar *firstPOI = (RooRealVar *)mc->GetParametersOfInterest()->first();
   ProfileLikelihoodCalculator plc(*data, *mc);
   LikelihoodInterval *interval = plc.GetInterval();
   double plcUpperLimit = interval->UpperLimit(*firstPOI);
   delete interval;
   cout << "\n\n--------------------------------------" << endl;
   cout << "Will generate sampling distribution at " << firstPOI->GetName() << " = " << plcUpperLimit << endl;
   int nPOI = mc->GetParametersOfInterest()->getSize();
   if (nPOI > 1) {
      cout << "not sure what to do with other parameters of interest, but here are their values" << endl;
      mc->GetParametersOfInterest()->Print("v");
   }
 
   // -------------------------------------------------------
   // create the test stat sampler
   ProfileLikelihoodTestStat ts(*mc->GetPdf());
 
   // to avoid effects from boundary and simplify asymptotic comparison, set min=-max
   if (allowNegativeMu)
      firstPOI->setMin(-1 * firstPOI->getMax());
 
   // temporary RooArgSet
   RooArgSet poi;
   poi.add(*mc->GetParametersOfInterest());
 
   // create and configure the ToyMCSampler
   ToyMCSampler sampler(ts, nToyMC);
   sampler.SetPdf(*mc->GetPdf());
   sampler.SetObservables(*mc->GetObservables());
   sampler.SetGlobalObservables(*mc->GetGlobalObservables());
   if (!mc->GetPdf()->canBeExtended() && (data->numEntries() == 1)) {
      cout << "tell it to use 1 event" << endl;
      sampler.SetNEventsPerToy(1);
   }
   firstPOI->setVal(plcUpperLimit);                                  // set POI value for generation
   sampler.SetParametersForTestStat(*mc->GetParametersOfInterest()); // set POI value for evaluation
 
   if (useProof) {
      ProofConfig pc(*w, nworkers, "", false);
      sampler.SetProofConfig(&pc); // enable proof
   }
 
   firstPOI->setVal(plcUpperLimit);
   RooArgSet allParameters;
   allParameters.add(*mc->GetParametersOfInterest());
   allParameters.add(*mc->GetNuisanceParameters());
   allParameters.Print("v");
 
   SamplingDistribution *sampDist = sampler.GetSamplingDistribution(allParameters);
   SamplingDistPlot plot;
   plot.AddSamplingDistribution(sampDist);
   plot.GetTH1F(sampDist)->GetYaxis()->SetTitle(
      Form("f(-log #lambda(#mu=%.2f) | #mu=%.2f)", plcUpperLimit, plcUpperLimit));
   plot.SetAxisTitle(Form("-log #lambda(#mu=%.2f)", plcUpperLimit));
 
   TCanvas *c1 = new TCanvas("c1");
   c1->SetLogy();
   plot.Draw();
   double min = plot.GetTH1F(sampDist)->GetXaxis()->GetXmin();
   double max = plot.GetTH1F(sampDist)->GetXaxis()->GetXmax();
 
   TF1 *f = new TF1("f", Form("2*ROOT::Math::chisquared_pdf(2*x,%d,0)", nPOI), min, max);
   f->Draw("same");
   c1->SaveAs("standard_test_stat_distribution.pdf");
}

Author

Kyle Cranmer

Definition in file StandardTestStatDistributionDemo.C.