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:
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
Author: Kyle Cranmer
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Tuesday, March 19, 2024 at 07:18 PM.
%%cpp -d
#include "TFile.h"
#include "TROOT.h"
#include "RooWorkspace.h"
#include "RooAbsData.h"
#include "RooRealVar.h"
#include "RooUniform.h"
#include "RooStats/ModelConfig.h"
#include "RooStats/BayesianCalculator.h"
#include "RooStats/SimpleInterval.h"
#include "RooStats/RooStatsUtils.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;
Arguments are defined.
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) {
// 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;
}
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);
std::unique_ptr<RooFitResult> res{
pdf->fitTo(*data, Save(true), Minimizer(ROOT::Math::MinimizerOptions::DefaultMinimizerType().c_str()),
Hesse(true), PrintLevel(ROOT::Math::MinimizerOptions::DefaultPrintLevel() - 1))};
res->Print();
RooArgList nuisPar(*mc->GetNuisanceParameters());
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);
RooRealVar *poi = (RooRealVar *)mc->GetParametersOfInterest()->first();
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
RooAbsReal::setEvalErrorLoggingMode(RooAbsReal::Ignore);
cout << "\nDrawing plot of posterior function....." << endl;
always plot using number of scan points
bayesianCalc.SetScanOfPosterior(nScanPoints);
RooPlot *plot = bayesianCalc.GetPosteriorPlot();
plot->Draw();
Draw all canvases
%jsroot on
gROOT->GetListOfCanvases()->Draw()