# Standard Feldman Cousins Demo¶

Standard demo of the Feldman-Cousins calculator StandardFeldmanCousinsDemo

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 FeldmanCousins tools is a classical frequentist calculation based on the Neyman Construction. The test statistic can be generalized for nuisance parameters by using the profile likelihood ratio. But unlike the ProfileLikelihoodCalculator, this tool explicitly builds the sampling distribution of the test statistic via toy Monte Carlo.

Author: Kyle Cranmer
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Thursday, June 30, 2022 at 10:00 AM.

In [ ]:
%%cpp -d
#include "TFile.h"
#include "TROOT.h"
#include "TH1F.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"

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


Arguments are defined.

In [ ]:
const char *infile = "";
const char *workspaceName = "combined";
const char *modelConfigName = "ModelConfig";
const char *dataName = "obsData";


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

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


In [ ]:
if (!file) {
cout << "StandardRooStatsDemoMacro: Input file " << filename << " is not found" << endl;
return;
}


## Tutorial starts here¶

Get the workspace out of the file

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


Get the modelconfig out of the file

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


Get the modelconfig out of the file

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


Make sure ingredients are found

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


create and use the FeldmanCousins tool to find and plot the 95% confidence interval on the parameter of interest as specified in the model config

In [ ]:
FeldmanCousins fc(*data, *mc);
fc.SetConfidenceLevel(0.95); // 95% interval


Fc.additionalntoysfactor(0.1); // to speed up the result

In [ ]:
fc.UseAdaptiveSampling(true); // speed it up a bit
fc.SetNBins(10);              // set how many points per parameter of interest to scan
fc.CreateConfBelt(true);      // save the information in the belt for plotting


Since this tool needs to throw toy mc the pdf needs to be extended or the tool needs to know how many entries in a dataset per pseudo experiment. In the 'number counting form' where the entries in the dataset are counts, and not values of discriminating variables, the datasets typically only have one entry and the PDF is not extended.

In [ ]:
if (!mc->GetPdf()->canBeExtended()) {
if (data->numEntries() == 1)
fc.FluctuateNumDataEntries(false);
else
}


We can use proof to speed things along in parallel ProofConfig pc(w, 1, "workers=4", kFALSE); ToyMCSampler toymcsampler = (ToyMCSampler*) fc.GetTestStatSampler(); toymcsampler->SetProofConfig(&pc); // enable proof

Now get the interval

In [ ]:
PointSetInterval *interval = fc.GetInterval();
ConfidenceBelt *belt = fc.GetConfidenceBelt();


Print out the interval on the first parameter of interest

In [ ]:
RooRealVar *firstPOI = (RooRealVar *)mc->GetParametersOfInterest()->first();
cout << "\n95% interval on " << firstPOI->GetName() << " is : [" << interval->LowerLimit(*firstPOI) << ", "
<< interval->UpperLimit(*firstPOI) << "] " << endl;


No nice plots yet, so plot the belt by hand

Ask the calculator which points were scanned

In [ ]:
RooDataSet *parameterScan = (RooDataSet *)fc.GetPointsToScan();
RooArgSet *tmpPoint;


Make a histogram of parameter vs. threshold

In [ ]:
TH1F *histOfThresholds =
new TH1F("histOfThresholds", "", parameterScan->numEntries(), firstPOI->getMin(), firstPOI->getMax());


Loop through the points that were tested and ask confidence belt what the upper/lower thresholds were. For FeldmanCousins, the lower cut off is always 0

In [ ]:
for (Int_t i = 0; i < parameterScan->numEntries(); ++i) {
tmpPoint = (RooArgSet *)parameterScan->get(i)->clone("temp");
double arMax = belt->GetAcceptanceRegionMax(*tmpPoint);
double arMin = belt->GetAcceptanceRegionMax(*tmpPoint);
double poiVal = tmpPoint->getRealValue(firstPOI->GetName());
histOfThresholds->Fill(poiVal, arMax);
}
histOfThresholds->SetMinimum(0);
histOfThresholds->Draw();


Draw all canvases

In [ ]:
%jsroot on
gROOT->GetListOfCanvases()->Draw()