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Reference Guide
StandardBayesianNumericalDemo.C File Reference

Detailed Description

View in nbviewer Open in SWAN Standard demo of the numerical Bayesian calculator

This is a standard demo that can be used with any ROOT file prepared in the standard way. You specify:

  • name for input ROOT file
  • name of workspace inside ROOT file that holds model and data
  • name of ModelConfig that specifies details for calculator tools
  • name of dataset

With default parameters the macro will attempt to run the standard hist2workspace example and read the ROOT file that it produces.

The actual heart of the demo is only about 10 lines long.

The BayesianCalculator is based on Bayes's theorem and performs the integration using ROOT's numeric integration utilities

RooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby
Copyright (C) 2000-2013 NIKHEF, University of California & Stanford University
All rights reserved, please read http://roofit.sourceforge.net/license.txt
[#1] INFO:ObjectHandling -- RooWorkspace::import(combined) importing RooUniform::prior
[#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)
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:Eval -- BayesianCalculator::GetPosteriorFunction : nll value -1033.75 poi value = 1
[#1] INFO:Eval -- BayesianCalculator::GetPosteriorFunction : minimum of NLL vs POI for POI = 1.12121 min NLL = -1033.78
[#1] INFO:InputArguments -- BayesianCalculator:GetInterval Compute the interval from the posterior cdf
[#1] INFO:NumericIntegration -- PosteriorCdfFunction - integral of posterior = 0.0560849 +/- 0.000423427
[#0] WARNING:Eval -- BayesianCalculator::GetInterval : 315 errors reported in evaluating log-likelihood function
[#1] INFO:Eval -- BayesianCalculator::GetInterval - found a valid interval : [0.170773 , 2.33979 ]
>>>> RESULT : 95% interval on SigXsecOverSM is : [0.170773, 2.33979]
#include "TFile.h"
#include "TROOT.h"
#include "RooWorkspace.h"
#include "RooAbsData.h"
#include "RooRealVar.h"
#include "RooUniform.h"
#include "RooPlot.h"
#include "TSystem.h"
#include <cassert>
using namespace RooFit;
using namespace RooStats;
struct BayesianNumericalOptions {
double confLevel = 0.95; // interval CL
TString integrationType = ""; // integration Type (default is adaptive (numerical integration)
// possible values are "TOYMC" (toy MC integration, work when nuisances have a constraints pdf)
// "VEGAS" , "MISER", or "PLAIN" (these are all possible MC integration)
int nToys =
10000; // number of toys used for the MC integrations - for Vegas should be probably set to an higher value
bool scanPosterior =
false; // flag to compute interval by scanning posterior (it is more robust but maybe less precise)
bool plotPosterior = false; // plot posterior function after having computed the interval
int nScanPoints = 50; // number of points for scanning the posterior (if scanPosterior = false it is used only for
// plotting). Use by default a low value to speed-up tutorial
int intervalType = 1; // type of interval (0 is shortest, 1 central, 2 upper limit)
double maxPOI = -999; // force a different value of POI for doing the scan (default is given value)
double nSigmaNuisance = -1; // force integration of nuisance parameters to be within nSigma of their error (do first
// a model fit to find nuisance error)
};
BayesianNumericalOptions optBayes;
void StandardBayesianNumericalDemo(const char *infile = "", const char *workspaceName = "combined",
const char *modelConfigName = "ModelConfig", const char *dataName = "obsData")
{
// option definitions
double confLevel = optBayes.confLevel;
TString integrationType = optBayes.integrationType;
int nToys = optBayes.nToys;
bool scanPosterior = optBayes.scanPosterior;
bool plotPosterior = optBayes.plotPosterior;
int nScanPoints = optBayes.nScanPoints;
int intervalType = optBayes.intervalType;
int maxPOI = optBayes.maxPOI;
double nSigmaNuisance = optBayes.nSigmaNuisance;
// -------------------------------------------------------
// 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;
}
// -------------------------------------------------------
// Tutorial starts here
// -------------------------------------------------------
// 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;
}
// ------------------------------------------
// create and use the BayesianCalculator
// to find and plot the 95% credible interval
// on the parameter of interest as specified
// in the model config
// before we do that, we must specify our prior
// it belongs in the model config, but it may not have
// been specified
RooUniform prior("prior", "", *mc->GetParametersOfInterest());
w->import(prior);
mc->SetPriorPdf(*w->pdf("prior"));
// do without systematics
// mc->SetNuisanceParameters(RooArgSet() );
if (nSigmaNuisance > 0) {
RooAbsPdf *pdf = mc->GetPdf();
assert(pdf);
RooFitResult *res =
res->Print();
for (int i = 0; i < nuisPar.getSize(); ++i) {
RooRealVar *v = dynamic_cast<RooRealVar *>(&nuisPar[i]);
assert(v);
v->setMin(TMath::Max(v->getMin(), v->getVal() - nSigmaNuisance * v->getError()));
v->setMax(TMath::Min(v->getMax(), v->getVal() + nSigmaNuisance * v->getError()));
std::cout << "setting interval for nuisance " << v->GetName() << " : [ " << v->getMin() << " , "
<< v->getMax() << " ]" << std::endl;
}
}
BayesianCalculator bayesianCalc(*data, *mc);
bayesianCalc.SetConfidenceLevel(confLevel); // 95% interval
// default of the calculator is central interval. here use shortest , central or upper limit depending on input
// doing a shortest interval might require a longer time since it requires a scan of the posterior function
if (intervalType == 0)
bayesianCalc.SetShortestInterval(); // for shortest interval
if (intervalType == 1)
bayesianCalc.SetLeftSideTailFraction(0.5); // for central interval
if (intervalType == 2)
bayesianCalc.SetLeftSideTailFraction(0.); // for upper limit
if (!integrationType.IsNull()) {
bayesianCalc.SetIntegrationType(integrationType); // set integrationType
bayesianCalc.SetNumIters(nToys); // set number of iterations (i.e. number of toys for MC integrations)
}
// in case of toyMC make a nuisance pdf
if (integrationType.Contains("TOYMC")) {
RooAbsPdf *nuisPdf = RooStats::MakeNuisancePdf(*mc, "nuisance_pdf");
cout << "using TOYMC integration: make nuisance pdf from the model " << std::endl;
nuisPdf->Print();
bayesianCalc.ForceNuisancePdf(*nuisPdf);
scanPosterior = true; // for ToyMC the posterior is scanned anyway so used given points
}
// compute interval by scanning the posterior function
if (scanPosterior)
bayesianCalc.SetScanOfPosterior(nScanPoints);
if (maxPOI != -999 && maxPOI > poi->getMin())
poi->setMax(maxPOI);
SimpleInterval *interval = bayesianCalc.GetInterval();
// print out the interval on the first Parameter of Interest
cout << "\n>>>> RESULT : " << confLevel * 100 << "% interval on " << poi->GetName() << " is : ["
<< interval->LowerLimit() << ", " << interval->UpperLimit() << "] " << endl;
// end in case plotting is not requested
if (!plotPosterior)
return;
// make a plot
// since plotting may take a long time (it requires evaluating
// the posterior in many points) this command will speed up
// by reducing the number of points to plot - do 50
// ignore errors of PDF if is zero
cout << "\nDrawing plot of posterior function....." << endl;
// always plot using numer of scan points
bayesianCalc.SetScanOfPosterior(nScanPoints);
RooPlot *plot = bayesianCalc.GetPosteriorPlot();
plot->Draw();
}
Author
Kyle Cranmer

Definition in file StandardBayesianNumericalDemo.C.