# Standard Test Stat Distribution Demo¶

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.

Author: Kyle Cranmer
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Monday, February 24, 2020 at 03:34 AM.

In [1]:
%%cpp -d
#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"

In [2]:
%%cpp -d
// This is a workaround to make sure the namespace is used inside functions
using namespace RooFit;
using namespace RooStats;

In [3]:
bool useProof = false; // flag to control whether to use Proof
int nworkers = 0;      // number of workers (default use all available cores)


The actual macro

Arguments are defined.

In [4]:
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

In [5]:
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

In [6]:
bool allowNegativeMu = true;


First part is just to access a user-defined file or create the standard example file if it doesn't exist

In [7]:
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

In [8]:
TFile *file = TFile::Open(filename);

RooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby
Copyright (C) 2000-2013 NIKHEF, University of California & Stanford University



In [9]:
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

In [10]:
RooWorkspace *w = (RooWorkspace *)file->Get(workspaceName);
if (!w) {
return;
}


Get the modelconfig out of the file

In [11]:
ModelConfig *mc = (ModelConfig *)w->obj(modelConfigName);


Get the modelconfig out of the file

In [12]:
RooAbsData *data = w->data(dataName);


Make sure ingredients are found

In [13]:
if (!data || !mc) {
w->Print();
return;
}

mc->Print();

=== 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



Now find the upper limit based on the asymptotic results

In [14]:
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");
}

[#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


create the test stat sampler

In [15]:
ProfileLikelihoodTestStat ts(*mc->GetPdf());


To avoid effects from boundary and simplify asymptotic comparison, set min=-max

In [16]:
if (allowNegativeMu)
firstPOI->setMin(-1 * firstPOI->getMax());


Temporary rooargset

In [17]:
RooArgSet poi;


Create and configure the toymcsampler

In [18]:
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.Print("v");

SamplingDistribution *sampDist = sampler.GetSamplingDistribution(allParameters);
SamplingDistPlot plot;
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");

  1) 0x7f909ce89090 RooRealVar::             SigXsecOverSM = 2.32744 +/- 0.586082  L(-3 - 3)  "SigXsecOverSM"
2) 0x7f909ce85530 RooRealVar::               alpha_syst2 = 0.710796 +/- 0.982182  L(-5 - 5)  "alpha_syst2"
3) 0x7f909ce8c710 RooRealVar::               alpha_syst3 = 0.260222 +/- 0.947589  L(-5 - 5)  "alpha_syst3"
4) 0x7f909c122110 RooRealVar:: gamma_stat_channel1_bin_0 = 1.03668 +/- 0.0493173  L(0 - 1.25)  "gamma_stat_channel1_bin_0"
5) 0x7f909c10dc70 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

Info in <TCanvas::Print>: pdf file standard_test_stat_distribution.pdf has been created


Draw all canvases

In [19]:
gROOT->GetListOfCanvases()->Draw()