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Higgs analysis at ATLAS using RooStats

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This page contains basic information on getting started with Higgs analysis at ATLAS using RooStats.
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This page contains basic information on getting started with Higgs analysis at ATLAS using RooStats. Only the most meager of attempts is made to keep this documentation current.

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RooStats is a project to create statistical tools built on top of the RooFit library, which is a data-modelling toolkit. It is distributed in ROOT. Specifically, it has been distributed in the ROOT release since version 5.22 (December 2008). The latest version of ROOT is recommended as the RooStats project develops quickly.
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using ROOT on the Glasgow PPELX network

There are instructions on how to use the different versions of ROOT at Glasgow here.

Execute commands something like the following in order to set up ROOT version 5.32.00 on PPELX:

%CODE{"bash"}% export ROOTSYS=/data/ppe01/sl5x/x86_64/root/5.32.00 export PATH=$ROOTSYS/bin:$PATH export LD_LIBRARY_PATH=$ROOTSYS/lib/root:$LD_LIBRARY_PATH %ENDCODE%

using ROOT on the CERN LXPLUS network

Execute commands something like the following in order to set up ROOT version 5.32.00 on LXPLUS:

%CODE{"bash"}% . /afs/cern.ch/sw/lcg/external/gcc/4.3.2/x86_64-slc5/setup.sh cd /afs/cern.ch/sw/lcg/app/releases/ROOT/5.32.00/x86_64-slc5-gcc43-opt/root/ . bin/thisroot.sh %ENDCODE%

setting up RooStats

There are three main options available for acquiring ROOT with RooStats included.

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%CODE{"c++"}% // general form for defining a RooFit variable:
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RooRealVar x(<object name>, <object title>, <value>, <minimum value>, <maximum value>)
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RooRealVar x(
// specific example for defining a RooFit variable x with the value 5: RooRealVar x("x", "x observable", 5, -10, 10) %ENDCODE%
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What is the value of this? In a nutshell, it allows one to do Bayesian stuff very easily.
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Bayes' theorem holds that the probability of b given a is related to the probability of a given b. Normally, one might say that the mean of a Gaussian is 1 and that then gives a distribution for x. However, if one had a dataset for x, one might want to know the posterior for the mean. The RooFit ability to switch what the probability density function is of is very useful for Bayesian stuff. Because RooFit allows this composition, the thing that acts as x in the Gaussian could actually be a function of, say, x^{2}. A Jacobian factor is picked up in going from x to x^{2}, so the normalisation no longer makes sense. Sometimes RooFit can figure out what the Jacobian factor should be and sometimes it resorts to numerical integration.
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Bayes' theorem holds that the probability of b given a is related to the probability of a given b. Normally, one might say that the mean of a Gaussian is 1 and that then gives a distribution for x. However, if one had a dataset for x, one might want to know the posterior for the mean. The RooFit ability to switch what the probability density function is of is very useful for Bayesian stuff. Because RooFit allows this composition, the thing that acts as x in the Gaussian could actually be a function of, say, x^{2}. A Jacobian factor is picked up in going from x to x^{2}, so the normalisation no longer makes sense. Sometimes RooFit can figure out what the Jacobian factor should be and sometimes it resorts to numerical integration.

example code: create a Gaussian PDF using RooStats and plot it using the RooPlot class

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// Plot the PDF. RooPlot* xframe = x.frame(); gauss.plotOn(xframe);
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} %ENDCODE%
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%CODE{"c++"}% RooPlot* myFrame = x.frame() ; myData.plotOn(myFrame, Binning(25)) ;
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%ENDCODE%

importing data from ROOT trees (how to populate RooDataSets from TTrees)
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// Access the file. TFile* myFile = new TFile("myFile.root"); // Load the histogram.
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TH1* myHistogram = (TH1*) myFile->Get("myHistogram");
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TH1* myHistogram = (TH1*) myFile->Get("myHistogram");
// Draw the loaded histogram. myHistogram.Draw();
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%CODE{"c++"}% // Create a Gaussian PDF using the Workspace Factory (this is essentially the shorthand for creating a Gaussian). RooWorkspace* myWorkspace = new RooWorkspace("myWorkspace");
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myWorkspace->factory("Gaussian::g(x[-5, 5], mu[0], sigma[1]");
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myWorkspace->factory("Gaussian::g(x[-5, 5], mu[0], sigma[1]");
%ENDCODE%

What's in the RooFit workspace?

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// Open the appropriate ROOT file. root -l myFile.root // Import the workspace.
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myWorkspace = (RooWorkspace*) _file0->Get("myWorkspace");
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myWorkspace = (RooWorkspace*) _file0->Get("myWorkspace");
// Print the workspace contents. myWorkspace.Print(); // Example printout:
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// myFileName = "BR5_MSSM_signal90_combined_datastat_model.root" // TFile *myFile = TFile::Open(myFileName); // Import the workspace.
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RooWorkspace* myWorkspace = (RooWorkspace*) _file0->Get("combined");
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RooWorkspace* myWorkspace = (RooWorkspace*) _file0->Get("combined");
// Print the workspace contents.
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myWorkspace->Print();
// Import the PDF.
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RooAbsPdf* myPDF = myWorkspace->pdf("model_BR5_MSSM_signal90");
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RooAbsPdf* myPDF = myWorkspace->pdf("model_BR5_MSSM_signal90");
// Import the variable representing the observable.
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RooRealVar* myObservable = myWorkspace->var("obs");
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RooRealVar* myObservable = myWorkspace->var("obs");
// Create a RooPlot frame using the imported variable.. RooPlot* myFrame = myObservable.frame(); // Plot the PDF on the created RooPlot frame. myPDF.plotOn(myFrame); // Draw the RooPlot.
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%ENDCODE%

example code: accessing both data and PDF from a workspace stored in a file
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TFile myFile("myResults.root") ; RooWorkspace* myWorkspace = f.Get("myWorkspace") ; // Plot the data and PDF
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RooPlot* xframe = w->var("x")->frame() ; w->data("d")->plotOn(xframe) ; w->pdf("g")->plotOn(xframe) ;
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RooPlot* xframe = w->var("x")->frame() ; w->data("d")->plotOn(xframe) ; w->pdf("g")->plotOn(xframe) ;
// Construct a likelihood and profile likelihood
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RooNLLVar nll("nll","nll",*myWorkspace->pdf("g"),*w->data("d")) ; RooProfileLL pll("pll","pll", nll,*myWorkspace->var("m")) ; RooPlot* myFrame = w->var("m")->frame(-1,1) ;
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RooNLLVar nll("nll","nll",*myWorkspace->pdf("g"),*w->data("d")) ; RooProfileLL pll("pll","pll", nll,*myWorkspace->var("m")) ; RooPlot* myFrame = w->var("m")->frame(-1,1) ;
pll.plotOn(myFrame) ;
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myFrame->Draw()
%ENDCODE%

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// A 95% confidence interval test is run using the ProfileLikelihoodCalculator of RooStats.

// Define a RooFit random seed in order to produce reproducible results.

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RooRandom::randomGenerator()->SetSeed(271);
// Make a simple model using the Workspace Factory.

// Create a new workspace. RooWorkspace* myWorkspace = new RooWorkspace(); // Create the PDF G(x|mu,1) and the variables x, mu and sigma in one command using the factory syntax.

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myWorkspace->factory("Gaussian::normal(x[-10,10], mu[-1,1], sigma[1])");
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myWorkspace->factory("Gaussian::normal(x[-10,10], mu[-1,1], sigma[1])");
// Define parameter sets for observables and parameters of interest.
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myWorkspace->defineSet("poi","mu"); myWorkspace->defineSet("obs","x");
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myWorkspace->defineSet("poi","mu"); myWorkspace->defineSet("obs","x");
// Print the workspace contents.
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myWorkspace->Print() ;
// Specify for the statistical tools the components of the defined model. // Create a new ModelConfig. ModelConfig* myModelConfig = new ModelConfig("my G(x|mu,1)"); // Specify the workspace.
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myModelConfig->SetWorkspace(*myWorkspace);
// Specify the PDF.
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myModelConfig->SetPdf(*myWorkspace->pdf("normal"));
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myModelConfig->SetParametersOfInterest(*myWorkspace->set("poi"));
// Specify the observables.
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myModelConfig->SetObservables(*myWorkspace->set("obs"));
// Create a toy dataset.

// Create a toy dataset of 100 measurements of the observables (x).

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RooDataSet* myData = myWorkspace->pdf("normal")->generate(*myWorkspace->set("obs"), 100); //myData->print();
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RooDataSet* myData = myWorkspace->pdf("normal")->generate(*myWorkspace->set("obs"), 100); //myData->print();
// Use the ProfileLikelihoodCalculator to obtain a 95% confidence interval.
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LikelihoodInterval* myProfileLikelihoodInterval = myProfileLikelihoodCalculator.GetInterval(); // Use this interval result. In this case, it makes sense to say what the lower and upper limits are. // Define the object variables for the purposes of the confidence interval.
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RooRealVar* x = myWorkspace->var("x"); RooRealVar* mu = myWorkspace->var("mu"); cout << "The profile likelihood calculator interval is [ "<< myProfileLikelihoodInterval->LowerLimit(*mu) << ", " << myProfileLikelihoodInterval->UpperLimit(*mu) << "] " << endl;
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RooRealVar* x = myWorkspace->var("x"); RooRealVar* mu = myWorkspace->var("mu"); cout << "The profile likelihood calculator interval is [ "<< myProfileLikelihoodInterval->LowerLimit(*mu) << ", " << myProfileLikelihoodInterval->UpperLimit(*mu) << "] " << endl;
// Set mu equal to zero.
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mu->setVal(0);
// Is mu in the interval?
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cout << "Is mu = 0 in the interval?" << endl; if (myProfileLikelihoodInterval->IsInInterval(*mu) == 1){ cout << "Yes" << endl;
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cout << "Is mu = 0 in the interval?" << endl; if (myProfileLikelihoodInterval->IsInInterval(*mu) == 1){ cout << "Yes" << endl;
} else{
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cout << "No" << endl;
} } %ENDCODE%
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example (early in project development): creation of the Measurement and a Channel and, thence, creation of the channel samples, including signal and backgrounds

%CODE{"c++"}%

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// Create the Measurement and a channel.
std::string myInputFile = "./data/myData.root"; std::string myChannel1Path = "";
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details on the object measurement
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A measurement has several methods to configure its options, each of which are equivalent to their XML equivalents.
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A measurement has several methods to configure its options, each of which is equivalent to their XML equivalents.

objective code
set the prefix for output files void SetOutputFilePrefix(const std::string& prefix);
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void AddShapeSys(std::string Name, Constraint::Type ConstraintType, std::string HistoName, std::string HistoFile, std::string HistoPath=""); %ENDCODE%
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A sample can be included in a channel's bin-by-bin statistical uncertainty fluctuations by "activating" the sample. There are two ways to do this. The first way is to use the default errors that are stored in the histogram's uncertainty array. The second way is to supply the errors using an external histogram (in the case where the desired errors differ from those stored by the HT1 histogram). These can be achieved using thw following methods:
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A sample can be included in a channel's bin-by-bin statistical uncertainty fluctuations by "activating" the sample. There are two ways to do this. The first way is to use the default errors that are stored in the histogram's uncertainty array. The second way is to supply the errors using an external histogram (in the case where the desired errors differ from those stored by the HT1 histogram). These can be achieved using the following methods:
%CODE{"c++"}% void ActivateStatError();
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Model Inspector
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The Model Inspector is a GUI for examining the model contained in the RooFit workspace. The function and it's parameters are as follows:
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The Model Inspector is a GUI for examining the model contained in the RooFit workspace. The function and its parameters are as follows:
%CODE{"c++"}% void ModelInspector(const char* infile = "", const char* workspaceName = "combined", const char* modelConfigName = "ModelConfig", const char* dataName = "obsData")

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Run some code such as the following. For fun, we will create a simulated data signal at about 126 GeV at about three times the number of events of that which was expected.
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example file: make_test_histograms.cxx
%CODE{"c++"}%
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#include #include #include #include <stdio.h> #include <string.h> #include #include "TStyle.h" #include "TROOT.h" #include "TPluginManager.h" #include "TSystem.h" #include "TFile.h" #include "TGaxis.h" #include "TCanvas.h" #include "TH1.h" #include "TF1.h" #include "TLine.h" #include "TSpline.h" #include "RooAbsData.h" #include "RooDataHist.h" #include "RooCategory.h" #include "RooDataSet.h" #include "RooRealVar.h" #include "RooAbsPdf.h" #include "RooSimultaneous.h" #include "RooProdPdf.h" #include "RooNLLVar.h" #include "RooProfileLL.h" #include "RooFitResult.h" #include "RooPlot.h" #include "RooRandom.h" #include "RooMinuit.h" #include "TRandom3.h" #include "RooWorkspace.h" #include "RooStats/RooStatsUtils.h" #include "RooStats/ModelConfig.h" #include "RooStats/ProfileLikelihoodCalculator.h" #include "RooStats/LikelihoodInterval.h" #include "RooStats/LikelihoodIntervalPlot.h" #include "TStopwatch.h" using namespace std; using namespace RooFit; using namespace RooStats;

int main() {

// Create the expected signal histogram.
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// Create the function used to describe the signal shape (a simple Gaussian shape). TF1 mySignalFunction("mySignalFunction", "(1/sqrt(2*pi*0.5^2))*2.718^(-(x-126)^2/(2*0.5^2))", 120, 130); // Create the histogram with 100 bins between 120 and 130 GeV.
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TH1F myBackground("myBackground", "myBackground", 100, 120, 130); // Fill the histogram using the background function. myBackground.FillRandom("myBackgroundFunction", 100000000000);
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// Create the (simulated) data histogram. This histogram represents what one might have as real data.
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// Create the histogram using by combining the signal histogram multiplied by 3 with the background histogram. TH1F myData=3*mySignal+myBackground; // Set the name of the histogram.
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myData.SetName("myData");
// Save the histograms created to a ROOT file. TFile myFile("test_histograms.root", "RECREATE");
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mySignal->Write(); myBackground->Write(); myData->Write();
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mySignal.Write(); myBackground.Write(); myData.Write();
myFile.Close();
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return 0;
} %ENDCODE%
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<-- workspace output file prefix -->
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OutputFilePrefix="./workspaces/test_workspace" Mode="comb" >
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OutputFilePrefix="./workspaces/test_workspace">

<-- channel XML file(s) -->
./config/test_channel.xml
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Create a C++ program such as the following:
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example file: ProfileLikeliHoodCalculator_confidence_level.cxx
%CODE{"c++"}% #include
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using namespace RooStats;

int main(){

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// Access the inputs.
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// Open the ROOT workspace file. TString myInputFileName = "workspaces/test_workspace_combined_datastat_model.root";
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cout << "open file " << myInputFileName << endl;
TFile *_file0 = TFile::Open(myInputFileName); // Access the workspace.
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cout << "access workspace" << endl;
RooWorkspace* myWorkspace = (RooWorkspace*) _file0->Get("combined");
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// Access the ModelConfig cout << "Accessing ModelConfig..." << endl;
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// Access the ModelConfig. cout << "access ModelConfig..." << endl;
ModelConfig* myModelConfig = (ModelConfig*) myWorkspace->obj("ModelConfig"); // Access the data.
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cout << "accessing data" << endl;
RooAbsData* myData = myWorkspace->data("obsData");
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// Use the ProfileLikelihoodCalculator to calculate the 95% confidence interval on the parameter of interest as specified in the ModelConfig. cout << "Calculating profile likelihood...\n" << endl;
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// Use the ProfileLikelihoodCalculator to calculate the 95% confidence // interval on the parameter of interest as specified in the ModelConfig. cout << "calculate profile likelihood" << endl;
ProfileLikelihoodCalculator myProfileLikelihood(*myData, *myModelConfig); myProfileLikelihood.SetConfidenceLevel(0.95); LikelihoodInterval* myConfidenceInterval = myProfileLikelihood.GetInterval(); // Access the confidence interval on the parameter of interest (POI). RooRealVar* myPOI = (RooRealVar*) myModelConfig->GetParametersOfInterest()->first();
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// Print the results. cout << "Printing results..." << endl;
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// Print results. cout << "print results" << endl;
// Print the confidence interval on the POI.
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cout << "\n95% confidence interval on the point of interest " << myPOI->GetName()<<": ["<<
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cout << "\n95% confidence interval on the point of interest " << myPOI->GetName()<<": ["<<
myConfidenceInterval->LowerLimit(*myPOI) << ", "<< myConfidenceInterval->UpperLimit(*myPOI) <<"]\n"<<endl; return 0;
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example file: Makefile

%CODE{"bash"}%

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ProfileLikeliHoodCalculator_confidence_level.cpp : ProfileLikeliHoodCalculator_confidence_level.cpp g++ -g -O2 -fPIC -Wno-deprecated -o ProfileLikeliHoodCalculator_confidence_level.cpp ProfileLikeliHoodCalculator_confidence_level.cpp root-config --cflags --libs --ldflags -lHistFactory -lXMLParser -lRooStats -lRooFit -lRooFitCore -lThread -lMinuit -lFoam -lHtml -lMathMore -I$ROOTSYS/include -L$ROOTSYS/lib
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ProfileLikeliHoodCalculator_confidence_level : ProfileLikeliHoodCalculator_confidence_level.cxx g++ -g -O2 -fPIC -Wno-deprecated -o ProfileLikeliHoodCalculator_confidence_level ProfileLikeliHoodCalculator_confidence_level.cxx root-config --cflags --libs --ldflags -lHistFactory -lXMLParser -lRooStats -lRooFit -lRooFitCore -lThread -lMinuit -lFoam -lHtml -lMathMore
%ENDCODE%

Compile the code.

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HistoNameHigh="myShapeSystematic_1_high" HistoNameLow="myShapeSystematic_1_low" />
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Note that the order in which the various classes of systematics should be specified is overall systematics followed by shape systematics.

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createXMLFiles ${originalMass} 115 #userSet createXMLFiles${originalMass} 120 #userSet createXMLFiles ${originalMass} 125 #userSet createXMLFiles${originalMass} 130 #userSet createXMLFiles ${originalMass} 140 #userSet %ENDCODE% C++ approach to HistFactory Line: 1219 to 1226 links for HistFactory Changed: < < HistFactory user guide, June 2012 (draft, under development) > > analysis! Line: 1362 to 1362 HistoName="myData" /> <-- signal --> Changed: < < <Sample Name="signal" HistoName="mySignal" NormalizeByTheory="True" > > > HistoName="mySignal" NormalizeByTheory="True" > Line: 1506 to 1505 links for ROOT Changed: < < ROOT User's Guide > > Revision 462015-06-16 - WilliamBreadenMadden Line: 1 to 1  META TOPICPARENT name="WebHome" Changed: < < -- WilliamBreadenMadden - 2013-08-27 > > -- Line: 12 to 12 What is RooStats? Changed: < < RooStats is a project to create statistical tools built on top of the RooFit library, which is a data modelling toolkit. It is distributed in ROOT. Specifically, it has been distributed in the ROOT release since version 5.22 (December 2008). The latest version of ROOT is recommended as the RooStats project developes quickly. > > RooStats is a project to create statistical tools built on top of the RooFit library, which is a data-modelling toolkit. It is distributed in ROOT. Specifically, it has been distributed in the ROOT release since version 5.22 (December 2008). The latest version of ROOT is recommended as the RooStats project develops quickly. using ROOT on the Glasgow PPELX network There are instructions on how to use the different versions of ROOT at Glasgow here. Changed: < < Execute the following commands in order to set up ROOT version 5.32.00 on PPELX: > > Execute commands something like the following in order to set up ROOT version 5.32.00 on PPELX: %CODE{"bash"}% export ROOTSYS=/data/ppe01/sl5x/x86_64/root/5.32.00 Line: 28 to 28 using ROOT on the CERN LXPLUS network Changed: < < Execute the following commands in order to set up ROOT version 5.32.00 on LXPLUS: > > Execute commands something like the following in order to set up ROOT version 5.32.00 on LXPLUS: %CODE{"bash"}% . /afs/cern.ch/sw/lcg/external/gcc/4.3.2/x86_64-slc5/setup.sh Line: 53 to 53 %CODE{"bash"}% #!/bin/bash Changed: < < # This script builds the latest version of ROOT with RooFit and RooStats in Ubuntu. > > ################################################################################ # This script builds the latest version of ROOT in Ubuntu. Specifically, first # the ROOT prerequisites are installed, then the most common ROOT optional # packages are installed. Next, the latest version of ROOT in the CERN Git # repository is checked out. Finally, ROOT is compiled. After compiling is # complete, ROOT environment variables should be set up as necessary. ################################################################################ echo -e "\nstart ROOT installation\n" read -s -n 1 -p "Press any key to continue." echo Changed: < < # First, the ROOT prerequisites are installed, then, the most common ROOT optional packages are # installed. Next, the latest version of ROOT in the CERN Subversion repository is checked out. # Finally, ROOT is compiled. > > # Specify the time. date # Install ROOT prerequisites. Changed: < < sudo apt-get install subversion sudo apt-get install make sudo apt-get install g++ sudo apt-get install gcc sudo apt-get install binutils sudo apt-get install libx11-dev sudo apt-get install libxpm-dev sudo apt-get install libxft-dev sudo apt-get install libxext-dev > > echo "install ROOT prerequisites..." sudo apt-get -y install subversion sudo apt-get -y install dpkg-dev sudo apt-get -y install make sudo apt-get -y install g++ sudo apt-get -y install gcc sudo apt-get -y install binutils sudo apt-get -y install libx11-dev #sudo apt-get -y install libxpm-dev sudo apt-get -y install libgd2-xpm-dev sudo apt-get -y install libxft-dev sudo apt-get -y install libxext-dev # Install optional ROOT packages. Changed: < < sudo apt-get install gfortran sudo apt-get install ncurses-dev sudo apt-get install libpcre3-dev sudo apt-get install xlibmesa-glu-dev sudo apt-get install libglew1.5-dev sudo apt-get install libftgl-dev sudo apt-get install libmysqlclient-dev sudo apt-get install libfftw3-dev sudo apt-get install cfitsio-dev sudo apt-get install graphviz-dev sudo apt-get install libavahi-compat-libdnssd-dev sudo apt-get install libldap-dev sudo apt-get install python-dev sudo apt-get install libxml2-dev sudo apt-get install libssl-dev sudo apt-get install libgsl0-dev # Check out the latest ROOT trunk. svn co http://root.cern.ch/svn/root/trunk /usr/local/root # Configure the build. cd /usr/local/root # Configure for the system architecture and configure to build the libRooFit advanced fitting package as part of the compilation. ./configure linuxx8664gcc --enable-roofit > > echo "install optional ROOT packages..." sudo apt-get -y install gfortran sudo apt-get -y openssl-dev sudo apt-get -y install libssl-dev #sudo apt-get -y install ncurses-dev sudo apt-get -y install libpcre3-dev sudo apt-get -y install xlibmesa-glu-dev sudo apt-get -y install libglew1.5-dev sudo apt-get -y install libftgl-dev sudo apt-get -y install libmysqlclient-dev sudo apt-get -y install libfftw3-dev sudo apt-get -y install cfitsio-dev sudo apt-get -y install graphviz-dev sudo apt-get -y install libavahi-compat-libdnssd-dev #sudo apt-get -y install libldap-dev sudo apt-get -y install libldap2-dev sudo apt-get -y install python-dev sudo apt-get -y install libxml2-dev sudo apt-get -y install libkrb5-dev sudo apt-get -y install libgsl0-dev sudo apt-get -y install libqt4-dev # Check out the latest ROOT trunk. Save the download in the ~/root directory. # This should take only a moment. echo "check out the latest ROOT trunk..." cd ~/ git clone http://root.cern.ch/git/root.git # Configure for the compilation. Specifically, the system architecture is # defined and building of the libRooFit advanced fitting package is enabled. cd ~/root while true; do read -p "Specify the computer bit architecture you want to compile ROOT for (64/32): " computerArchitecture if [ "${computerArchitecture}" == "32" ]; then echo "configure ROOT compile for 32 bit computer architecture..." #./configure linux --enable-roofit --enable-minuit2 ./configure linux --enable-roofit --enable-minuit2 --enable-python --with-python-incdir=/usr/include/python2.6 --with-python-libdir=/usr/lib/i386-linux-gnu break elif [ "${computerArchitecture}" == "64" ]; then echo "configure ROOT compile for 64 bit computer architecture..." #./configure linuxx8664gcc --enable-roofit --enable-minuit2 ./configure linuxx8664gcc --enable-roofit --enable-minuit2 --enable-python --with-python-incdir=/usr/include/python2.6 --with-python-libdir=/usr/lib/x86_64-linux-gnu break fi echo "invalid input" done # See other possible configurations using the following command: ./configure --help Added: > > # Specify the time. date while true; do read -p "Do you want to continue to compile ROOT now? (y/n): " yOrn if [ "$(echo "${yOrn}" | sed 's/$$.*$$/\L\1/')" == "y" ]; then break elif [ "$(echo "${yOrn}" | sed 's/$$.*$$/\L\1/')" == "n" ]; then echo "exit installation script..." exit 0 fi echo "invalid input" done # Compile. Changed: < < make > > echo "compile ROOT..." time make Changed: < < On a MacBook Pro 7, 1 running Ubuntu 11.04, the compilation takes ~ 1 hour. Following the compilation, the ROOT environment variables can be set up. In Ubuntu or Scientific Linux, the following lines could be added to the ~/.bashrc file:  export ROOTSYS=/usr/local/root export PATH=$ROOTSYS/bin:$PATH export LD_LIBRARY_PATH=$ROOTSYS/lib/root:$LD_LIBRARY_PATH  > > # Move ROOT to the install directory (e.g., /usr/local/) and set up ROOT environment variables in the specified configuration file (e.g., /etc/bash.bashrc, ~/.bashrc). installationDirectory="/usr/local" configurationFile="/etc/bash.bashrc" while true; do read -p "Do you want to continue to move ROOT to the directory "${installationDirectory}" and set up the ROOT environment variables in the file "${configurationFile}"? (y/n): " yOrn yOrnLowercase="$(echo "${yOrn}" | sed 's/$$.*$$/\L\1/')" if [ "${yOrnLowercase}" == "y" ]; then break elif [ "${yOrnLowercase}" == "n" ]; then echo "exit installation script..." exit 0 fi echo "invalid input" done echo "move ROOT to the directory "${installationDirectory}"..." sudo mv ~/root "${installationDirectory}" echo "Set up ROOT environment variables in the file "${configurationFile}"..." echo -e "\n# ROOT environment variables" >> "${configurationFile}" echo "export ROOTSYS="${installationDirectory}"/root" >> "${configurationFile}" echo "export PATH=\$PATH:\$ROOTSYS/bin" >> "${configurationFile}" echo "export LD_LIBRARY_PATH=\$LD_LIBRARY_PATH:\$ROOTSYS/lib" >> "${configurationFile}" # Specify the time. date echo -e "\nROOT install complete\n" %ENDCODE% option 3: Build the RooStats branch. Changed: < < Do this if you want the latest development of RooStats (that has not yet been incorporated into a ROOT version). The necessary instructions can be found here. > > The RooStats branch can be built in order to have the latest development of RooStats (that has not yet been incorporated into a ROOT version). Instructions can be found here. RooFit Line: 120 to 188 The RooFit library provides a toolkit for modelling the expected distribution of events in a physics analysis. Models can be used to perform unbinned maximum likelihood fits, produce plots and generate "toy Monte Carlo" samples for various studies. Changed: < < The core functionality of RooFit is to enable the modelling of 'event data' distributions, in which each event is a discrete occurrence in time and has one or more measured observables associated with it. Experiments of this nature result in datasets obeying Poisson (or binomial) statistics. The natural modeling language for such distributions is probability density functions (PDFs), F(x;p), that describe the probability density of the distribution of observables x in terms of the function parameter p. > > The core functionality of RooFit is to enable the modelling of 'event data' distributions, in which each event is a discrete occurrence in time and has one or more measured observables associated with it. Experiments of this nature result in datasets of Poisson (or binomial) statistics. The natural modeling language for such distributions is probability density functions (PDFs), F(x;p), that describe the probability density of the distribution of observables x in terms of the function parameter p. Changed: < < In RooFit, every variable, data point, function and PDF is represented in a C++ object. So, for example, in constructing a RooFit model, the mathematical components of the model map to separate C++ objects. Objects are classified by the data or function type that they represent, not by their respective role in a particular setup. All objects are self-documenting. The name of an object is a unique identifier for the object while the title of an object is a more elaborate description of the object. > > In RooFit, every variable, data point, function and PDF is represented by a C++ object. So, for example, in constructing a RooFit model, the mathematical components of the model map to separate C++ objects. Objects are classified by the data or function type that they represent, not by their respective role in a particular setup. All objects are self-documenting. The name of an object is a unique identifier for the object while the title of an object is a more elaborate description of the object. Here are a few examples of mathematical concepts that correspond to various RooFit classes: Line: 147 to 215 RooPlot Changed: < < A RooPlot is essentially an empty frame that is capable of holding anything plotted verses its variable. > > A RooPlot is essentially an empty frame that is capable of holding anything plotted against its variable. PDFs Changed: < < One of the things that makes the RooFit PDFs nice and flexible (but perhaps counterintuitive) is that they have no idea what is considered the observable. For example, a Gaussian has x, the mean and sigma while the PDF is always normalised to unity. What is one integrating in order to get 1? For the Gaussian, it is x, by convention; the mean and sigma are parameters of the model. RooFit doesn't know that x is special; x, the mean and sigma are all on equal footing. You can tell RooFit that x is the variable to normalise over. > > One of the things that makes the RooFit PDFs nice and flexible (but perhaps counterintuitive) is that they have no idea what is considered the observable. For example, a Gaussian has x, the mean and sigma while the PDF is always normalised to unity. What is one integrating in order to get 1? For the Gaussian, it is x, by convention; the mean and sigma are parameters of the model. RooFit doesn't know that x is special; x, the mean and sigma are all on equal footing. You can tell RooFit that x is the variable to normalise over. So, RooGaussian has no intrinsic notion of distinction between observables and parameters. The choice of observables (for unit normalisation) is always passed to gauss.getVal(). What is the value of this? In a nutshell, it allows one to do Bayesian stuff very easily. Changed: < < Bayes' theorem holds that the probability of b given a is related to the probability of a given b. Normally, one might say that the mean of a Gaussian is 1 and that then gives a distribution for x. However, if one had a dataset for x, one might want to know the posterior for the mean. The RooFit ability to switch what the probability density function is of is very useful for Bayesian stuff. Because RooFit allows this composition, the thing that acts as x in the Gaussian could actually be a function of, say, x^2. A Jacobian factor is picked up in going from x to x^2, so the normalisation no longer makes sense. Sometimes RooFit can figure out what the Jacobian factor should be and sometimes it resorts to numerical integration. > > Bayes' theorem holds that the probability of b given a is related to the probability of a given b. Normally, one might say that the mean of a Gaussian is 1 and that then gives a distribution for x. However, if one had a dataset for x, one might want to know the posterior for the mean. The RooFit ability to switch what the probability density function is of is very useful for Bayesian stuff. Because RooFit allows this composition, the thing that acts as x in the Gaussian could actually be a function of, say, x^{2}. A Jacobian factor is picked up in going from x to x^{2}, so the normalisation no longer makes sense. Sometimes RooFit can figure out what the Jacobian factor should be and sometimes it resorts to numerical integration. example code: create a Gaussian PDF using RooStats and plot it using the RooPlot class Line: 181 to 249 %CODE{"c++"}% // not normalised (i.e., this is not a PDF): gauss.getVal(); Changed: < < // Hey, RooFit! This is the thing to normalise over (i.e., guarantees Int[xmin, xmax] Gauss(x, m, s)dx == 1): > > // Hey, RooFit! This is the thing over which you should normalise (i.e., guarantees Int[xmin, xmax] Gauss(x, m, s)dx == 1): gauss.getVal(x); // What is the value if sigma is considered the observable? (i.e., guarantees Int[smin, smax] Gauss(x, m, s)ds == 1): %ENDCODE% Line: 190 to 258 general description Changed: < < A dataset is a collection of points in N-dimensional space. In RooFit, data can be stored in an unbinned or binned manner. Unbinned data is stored using the RooDataSet class while binned data is stored using the RooDataHist class. The user can define how many bins there are in a variable. For the purposes of plotting using the RooPlot class, a RooDataSet is binned into a histogram. > > A dataset is a collection of points in N-dimensional space. In RooFit, data can be stored in an unbinned or binned manner. Unbinned data is stored using the RooDataSet class while binned data is stored using the RooDataHist class. The user can define how many bins there are in a variable. For the purposes of plotting using the RooPlot class, a RooDataSet is binned into a histogram. In general, working in RooFit with binned and unbinned data is very similar, as both the RooDataSet (for unbinned data) and RooDataHist (for binned data) classes inherit from a common base class, RooAbsData, which defines the interface for a generic abstract data sample. With few exceptions, all RooFit methods take abstract datasets as input arguments, allowing for the interchangeable use of binned and unbinned data. Line: 225 to 293 RooDataHist (binned data) Changed: < < Importing data from ROOT TH histogram objects (take a histogram and map it to a binned data set) (how to populate RooDataHists from histograms) > > importing data from ROOT TH histogram objects (take a histogram and map it to a binned data set) (how to populate RooDataHists from histograms) Changed: < < In RooFit, binned data is represented by the RooDataHist class. The contents of a ROOT histogram can be imported into a RooDataHist object. In importing a ROOT histogram, the binning of the original histogram is imported as well. A RooDataHist associates the histogram with a RooFit variable object of type RooRealVar. In this way it is always known what kind of data is stored in the histogram. > > In RooFit, binned data is represented by the RooDataHist class. The contents of a ROOT histogram can be imported to a RooDataHist object. In importing a ROOT histogram, the binning of the original histogram is imported as well. A RooDataHist associates the histogram with a RooFit variable object of type RooRealVar. In this way it is always known what kind of data is stored in the histogram. In displaying the data, RooFit, by default, shows the 68% confidence interval for Poisson statistics. Line: 259 to 327 fitting a model to data Changed: < < Fitting a model to data can be done in many ways. The most common methods are the χ2 fit and the -log(L) fit. The default fitting method in ROOT is the χ2 method, while the default method in RooFit is the -log(L) method. The -log(L) method is often preferred because it is more robust for low statistics fits and because it can also be performed on unbinned data. > > Fitting a model to data can be done in many ways. The most common methods are the \chi^{2} fit and the -log(L) fit. The default fitting method in ROOT is the \chi^{2} method, while the default method in RooFit is the -log(L) method. The -log(L) method is often preferred because it is more robust for low statistics fits and because it can also be performed on unbinned data. fitting a PDF to unbinned data Line: 334 to 402 RooRealVar mu("mu", "mu", 150); RooRealVar sigma("sigma", "sigma", 5, 0, 20); RooGaussian myGaussianPDF("myGaussianPDF", "Gaussian PDF", x, mu, sigma); Added: > > // Create a Graphviz DOT file with a representation of the object tree. myGaussianPDF.graphVizTree("myGaussianPDFTree.dot"); // This produced DOT file can be converted to some graphical representation: Changed: < < // Convert the DOT file to a 'top-to-bottom graph' using UNIX commands: > > // - Convert the DOT file to a 'top-to-bottom graph' using UNIX commands: // dot -Tgif -o myGaussianPDF_top-to-bottom_graph.gif myGaussianPDFTree.dot Changed: < < // Convert the DOT file to a 'spring-model graph' using UNIX commands: > > // - Convert the DOT file to a 'spring-model graph' using UNIX commands: // fdp -Tgif -o myGaussianPDF_spring-model_graph.gif myGaussianPDFTree.dot Added: > > // Print the PDF contents. myGaussianPDF.Print(); Changed: < < // Example output: > > // example output: // RooGaussian::G[ x=x mean=mu sigma=sigma ] = 1 // sigma.Print() // RooRealVar::sigma = 5 L(0 - 20) Line: 347 to 417 // RooGaussian::G[ x=x mean=mu sigma=sigma ] = 1 // sigma.Print() // RooRealVar::sigma = 5 L(0 - 20) Added: > > // Print the PDF contents in a detailed manner. myGaussianPDF.Print("verbose"); Added: > > // Print the PDF contents to stdout. myGaussianPDF.Print("t"); Changed: < < // Example output: > > // example output: // 0x166eab0 RooGaussian::G = 1 [Auto] // 0x15f7fe0/V- RooRealVar::x = 150 // 0x1487090/V- RooRealVar::mu = 150 Line: 356 to 428 // 0x15f7fe0/V- RooRealVar::x = 150 // 0x1487090/V- RooRealVar::mu = 150 // 0x1487bc0/V- RooRealVar::sigma = 5 Added: > > // Print the PDF contents to a file. myGaussianPDF.printCompactTree("", "myGaussianPDFTree.txt") Changed: < < // Example output file contents: > > // example output file contents: // 0x166eab0 RooGaussian::G = 1 [Auto] // 0x15f7fe0/V- RooRealVar::x = 150 // 0x1487090/V- RooRealVar::mu = 150 Line: 392 to 465 links Changed: < < Video illustrating the usage of the Model Inspector > > accessing the RooFit workspace Line: 402 to 475 // Open the appropriate ROOT file. root -l BR5_MSSM_signal90_combined_datastat_model.root // Alternatively, you could open the file in a manner such as the following: Changed: < < myFileName = "BR5_MSSM_signal90_combined_datastat_model.root" TFile *myFile = TFile::Open(myFileName); > > // myFileName = "BR5_MSSM_signal90_combined_datastat_model.root" // TFile *myFile = TFile::Open(myFileName); // Import the workspace. RooWorkspace* myWorkspace = (RooWorkspace*) _file0->Get("combined"); // Print the workspace contents. Line: 442 to 515 links for RooFit Changed: < < user's manual > > RooStats Line: 520 to 599 links for RooStats Changed: < < wiki E-group for support with ATLAS-sensitive information: atlas-phys-stat-root@cern.ch E-mail support for software issues, bugs etc.: roostats-development@cern.ch > > ModelConfig Revision 452013-12-17 - AndrewPickford Line: 1 to 1  META TOPICPARENT name="WebHome" -- WilliamBreadenMadden - 2013-08-27 Line: 16 to 16 using ROOT on the Glasgow PPELX network Changed: < < There are instructions on how to use the different versions of ROOT at Glasgow here. > > There are instructions on how to use the different versions of ROOT at Glasgow here. Execute the following commands in order to set up ROOT version 5.32.00 on PPELX: Line: 850 to 850 #!/bin/bash # This script is designed for use with the naming conventions described in the following page: Changed: < < # https://ppes8.physics.gla.ac.uk/twiki/bin/view/ATLAS/HiggsAnalysisAtATLASUsingRooStats > > # ATLAS/HiggsAnalysisAtATLASUsingRooStats # The #userSet hashtag is used to indicate places in the script where the user might modify # things. Revision 442013-08-27 - WilliamBreadenMadden Line: 1 to 1  META TOPICPARENT name="WebHome" Changed: < < -- WilliamBreadenMadden - 2013-08-05 > > -- WilliamBreadenMadden - 2013-08-27 Line: 695 to 695 example file:$ROOTSYS/tutorials/histfactory/example_channel.xml
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InputFile="./data/example.root" HistoName="" > HistoName="data" HistoPath="" />
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<-- HistoPathHigh="" HistoPathLow="histForSyst4"/>-->
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caveats
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A slash must be added to the end of the HistoPath string attribute of the Channel, Data and Sample tags when referencing directories other than the root directory in ROOT files, in such a manner as follows:
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HistoName="myDataHistogram" HistoPath="myDirectory/" />
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example file: ttH_m110_channel.xml
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<-- channel name and input file -->
InputFile="data/ttH_histograms.root" HistoName="">
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example file: ttH_m110_top-level.xml
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<-- workspace output file prefix -->
OutputFilePrefix="workspaces/ttH_m110_workspace" Mode="comb" >
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create XML configuration files automatically
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%CODE{"c++"}% void AddPreprocessFunction(std::string name, std::string expression, std::string dependencies);
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create a class representing a preprocess function and add it to a measurement directly using the constructor PreprocessFunction and a method of a measurement object
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PreprocessFunction::PreprocessFunction(std::string Name, std::string Expression, std::string Dependents); void AddPreprocessFunction(const std::string& function); %ENDCODE%
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Make the main directory.
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cd ~ mkdir test cd test
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Make the directory for the XML configuration files.
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mkdir config
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Make the directory for the input histogram ROOT files.
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Make the directory for the workspace.
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Generate input histograms.

Change to the directory for the input histograms.

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cd data
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Run some code such as the following. For fun, we will create a simulated data signal at about 126 GeV at about three times the number of events of that which was expected.

example file: make_test_histograms.c
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{ // Create the expected signal histogram. // Create the function used to describe the signal shape (a simple Gaussian shape).
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myData->Write(); myFile.Close(); }
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Create the workspace.

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Change to the directory for the configuration XML files.
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cd ~/test/config
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Copy the HistFactory XML schema to the configuration directory.
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cp $ROOTSYS/etc/HistFactorySchema.dtd . Changed: < < > > %ENDCODE% Create XML configuration files in the configuration directory. example file: test_top-level.xml Changed: < <   > > %CODE{"html"}% <-- workspace output file prefix --> Line: 1277 to 1273 Changed: < < > > %ENDCODE% example file: test_channel.xml Changed: < <   > > %CODE{"html"}% <-- channel name and input file --> Line: 1304 to 1299 Changed: < < > > %ENDCODE% As you can see, the model is very simple. There is the expected signal, the expected background and the actual data (in this case, the data is simulated). The point of interest relates to the signal and the expected data will be compared to the actual data. Run hist2workspace. Changed: < < > > %CODE{"bash"}% hist2workspace config/test_top-level.xml Changed: < < > > %ENDCODE% There should now be created 4 files in the workspaces directory: Changed: < < > > %CODE{"bash"}% test_workspace_combined_datastat_model.root test_workspace_datastat.root test_workspace_results.table test_workspace_test_datastat_model.root Changed: < < > > %ENDCODE% The test_workspace_combined_datastat_model.root file is the ROOT file that contains the combined workspace object (is has constraints, weightings etc. properly incorporated). This is the file you are almost certainly interested in. The test_workspace_test_datastat_model.root file contains a workspace object without proper constraints, weightings etc. I don't know what the other two files are. Line: 1331 to 1326 example file: ProfileLikeliHoodCalculator_confidence_level.cpp Changed: < <   > > %CODE{"c++"}% #include #include #include Line: 1408 to 1402 myConfidenceInterval->UpperLimit(*myPOI) <<"]\n"<<endl; return 0; } Changed: < < > > %ENDCODE% Compile this code using a Makefile such as the following: example file: Makefile Changed: < <   > > %CODE{"bash"}% ProfileLikeliHoodCalculator_confidence_level.cpp : ProfileLikeliHoodCalculator_confidence_level.cpp g++ -g -O2 -fPIC -Wno-deprecated -o ProfileLikeliHoodCalculator_confidence_level.cpp ProfileLikeliHoodCalculator_confidence_level.cpp root-config --cflags --libs --ldflags -lHistFactory -lXMLParser -lRooStats -lRooFit -lRooFitCore -lThread -lMinuit -lFoam -lHtml -lMathMore -I$ROOTSYS/include -L$ROOTSYS/lib Changed: < < > > %ENDCODE% Compile the code. Changed: < < > > %CODE{"bash"}% make Changed: < < > > %ENDCODE% results The end result as displayed in the terminal output is the following: Changed: < < > > %CODE{"bash"}% 95% confidence interval on the point of interest SigXsecOverSM: [2.99653, 3.00347] Changed: < < > > %ENDCODE% further information Revision 432013-08-07 - WilliamBreadenMadden Line: 1 to 1  META TOPICPARENT name="WebHome" -- WilliamBreadenMadden - 2013-08-05 Line: 20 to 20 Execute the following commands in order to set up ROOT version 5.32.00 on PPELX: Changed: < < > > %CODE{"bash"}% export ROOTSYS=/data/ppe01/sl5x/x86_64/root/5.32.00 export PATH=$ROOTSYS/bin:$PATH export LD_LIBRARY_PATH=$ROOTSYS/lib/root:$LD_LIBRARY_PATH Changed: < < > > %ENDCODE% using ROOT on the CERN LXPLUS network Execute the following commands in order to set up ROOT version 5.32.00 on LXPLUS: Changed: < < > > %CODE{"bash"}% . /afs/cern.ch/sw/lcg/external/gcc/4.3.2/x86_64-slc5/setup.sh cd /afs/cern.ch/sw/lcg/app/releases/ROOT/5.32.00/x86_64-slc5-gcc43-opt/root/ . bin/thisroot.sh Changed: < < > > %ENDCODE% setting up RooStats Line: 49 to 49 Follow the appropriate instructions here to build the ROOT trunk. shell script: building ROOT with RooFit and RooStats Changed: < <   > > %CODE{"bash"}% #!/bin/bash # This script builds the latest version of ROOT with RooFit and RooStats in Ubuntu. Line: 105 to 106 export ROOTSYS=/usr/local/root export PATH=$ROOTSYS/bin:$PATH export LD_LIBRARY_PATH=$ROOTSYS/lib/root:$LD_LIBRARY_PATH Changed: < < > > %ENDCODE% option 3: Build the RooStats branch. Line: 136 to 137 Composite functions correspond to composite objects. The ArgSet class is dependent on argument order while the ArgList class is not. example code: defining a RooFit variable Changed: < <  general form for defining a RooFit variable:  > > %CODE{"c++"}% // general form for defining a RooFit variable: RooRealVar x(<object name>, <object title>, <value>, <minimum value>, <maximum value>) Changed: < < specific example for defining a RooFit variable x with the value 5: > > // specific example for defining a RooFit variable x with the value 5: RooRealVar x("x", "x observable", 5, -10, 10) Changed: < < > > %ENDCODE% RooPlot Line: 158 to 160 Bayes' theorem holds that the probability of b given a is related to the probability of a given b. Normally, one might say that the mean of a Gaussian is 1 and that then gives a distribution for x. However, if one had a dataset for x, one might want to know the posterior for the mean. The RooFit ability to switch what the probability density function is of is very useful for Bayesian stuff. Because RooFit allows this composition, the thing that acts as x in the Gaussian could actually be a function of, say, x^2. A Jacobian factor is picked up in going from x to x^2, so the normalisation no longer makes sense. Sometimes RooFit can figure out what the Jacobian factor should be and sometimes it resorts to numerical integration. example code: create a Gaussian PDF using RooStats and plot it using the RooPlot class Changed: < <   > > %CODE{"c++"}% { // Build a Gaussian PDF. RooRealVar x("x", "x", -10, 10); Line: 171 to 174 gauss.plotOn(xframe); xframe->Draw(); } Changed: < < > > %ENDCODE% example code: telling a RooFit PDF what to normalise over Changed: < <  not normalised (i.e., this is not a PDF):  > > %CODE{"c++"}% // not normalised (i.e., this is not a PDF): gauss.getVal(); Changed: < < Hey, RooFit! This is the thing to normalise over (i.e., guarantees Int[xmin, xmax] Gauss(x, m, s)dx == 1): > > // Hey, RooFit! This is the thing to normalise over (i.e., guarantees Int[xmin, xmax] Gauss(x, m, s)dx == 1): gauss.getVal(x); Changed: < < What is the value if sigma is considered the observable? (i.e., guarantees Int[smin, smax] Gauss(x, m, s)ds == 1): > > // What is the value if sigma is considered the observable? (i.e., guarantees Int[smin, smax] Gauss(x, m, s)ds == 1): %ENDCODE% datasets Line: 193 to 197 RooDataSet (unbinned data) example code: generating toy Monte Carlo, storing it as unbinned data and then plotting it Changed: < <   > > %CODE{"c++"}% } // Create a RooDataSet and fill it with generated toy Monte Carlo data: RooDataSet* myData = gauss.generate(x, 100); Line: 202 to 207 myData.plotOn()(myFrame); myFrame.Draw(); } Changed: < < > > %ENDCODE% Plotting unbinned data is similar to plotting binned data with the exception that one can display it in some preferred binning. example code: plotting unbinned data (a RooDataSet) using a specified binning Changed: < <   > > %CODE{"c++"}% RooPlot* myFrame = x.frame() ; myData.plotOn(myFrame, Binning(25)) ; myFrame->Draw() Changed: < < > > %ENDCODE% importing data from ROOT trees (how to populate RooDataSets from TTrees) Line: 226 to 232 In displaying the data, RooFit, by default, shows the 68% confidence interval for Poisson statistics. example code: import a ROOT histogram into a RooDataHist (a RooFit binned dataset) Changed: < <   > > %CODE{"c++"}% { // Access the file. TFile* myFile = new TFile("myFile.root"); Line: 246 to 253 myData.plotOn(myFrame) myFrame.Draw() } Changed: < < > > %ENDCODE% fitting Line: 257 to 264 fitting a PDF to unbinned data example code: fit a Gaussian PDF to data Changed: < <   > > %CODE{"c++"}% // Fit gauss to unbinned data gauss.fitTo(*myData); Changed: < < > > %ENDCODE% The RooFit workspace Line: 271 to 279 Consider a Gaussian PDF. One might create this Gaussian PDF and then import it into a workspace. All of the dependencies of the Gaussian would be drawn in and owned by the workspace (there are no nightmarish ownership problems). Alternatively, one might create simply the Gaussian inside the workspace using the "Workspace Factory". example code: using the Workspace Factory to create a Gaussian PDF Changed: < <   > > %CODE{"c++"}% // Create a Gaussian PDF using the Workspace Factory (this is essentially the shorthand for creating a Gaussian). RooWorkspace* myWorkspace = new RooWorkspace("myWorkspace"); myWorkspace->factory("Gaussian::g(x[-5, 5], mu[0], sigma[1]"); Changed: < < > > %ENDCODE% What's in the RooFit workspace? example code: What's in the workspace? Changed: < <   > > %CODE{"c++"}% // Open the appropriate ROOT file. root -l myFile.root // Import the workspace. Line: 309 to 319 RooAbsData* myData = myWorkspace.data("d"); // Import the ModelConfig saved as m. ModelConfig* myModelConfig = (ModelConfig*) myWorkspace.obj("m"); Changed: < < > > %ENDCODE% visual representations of the model/PDF contents Line: 318 to 328 Graphviz consists of a graph description language called the DOT language and a set of tools that can generate and/or process DOT files. example code: examining PDFs and creating graphical representations of them Changed: < <   > > %CODE{"c++"}% // Create variables and a PDF using those variables. RooRealVar mu("mu", "mu", 150); RooRealVar sigma("sigma", "sigma", 5, 0, 20); Line: 352 to 363 // 0x15f7fe0/V- RooRealVar::x = 150 // 0x1487090/V- RooRealVar::mu = 150 // 0x1487bc0/V- RooRealVar::sigma = 5 Changed: < < > > %ENDCODE% Model Inspector The Model Inspector is a GUI for examining the model contained in the RooFit workspace. The function and it's parameters are as follows: Changed: < <   > > %CODE{"c++"}% void ModelInspector(const char* infile = "", const char* workspaceName = "combined", const char* modelConfigName = "ModelConfig", const char* dataName = "obsData") Changed: < < > > %ENDCODE% If the workspace(s) were made using hist2workspace, the names have a standard form (as shown above). using the Model Inspector Changed: < < > > %CODE{"c++"}% // Load the macro. root -L ModelInspector.C++ // Run the macro on the appropriate ROOT workspace file. ModelInspector("results/my_combined_example_model.root") Changed: < < > > %ENDCODE% The Model Inspector GUI should appear. The GUI consists of a number of plots, corresponding to the various channels in the model, and a few sliders, corresponding to the parameters of interest and the nuisance parameters in the model. The initial plots are based on the values of the parameters in the workspace. There is a little "Fit" button which fits the model to the data points (while also printing the standard terminal output detailing the fitting). After fitting, a yellow band is shown around the best fit model indicating the uncertainty from propagating the uncertainty of the fit through the model. On the plots, there is a red line shown (corresponding to the fit for each of the parameters at their nominal value pushed up by 1 sigma). Line: 385 to 397 accessing the RooFit workspace example code: accessing the workspace Changed: < <   > > %CODE{"c++"}% // Open the appropriate ROOT file. root -l BR5_MSSM_signal90_combined_datastat_model.root // Alternatively, you could open the file in a manner such as the following: Line: 405 to 418 myPDF.plotOn(myFrame); // Draw the RooPlot. myFrame->Draw(); Changed: < < > > %ENDCODE% example code: accessing both data and PDF from a workspace stored in a file Changed: < <   > > %CODE{"c++"}% // Note that the following code is independent of actual PDF in the file. So, for example, a full Higgs combination could work with identical code. // Open a file and import the workspace. Line: 424 to 438 RooPlot* myFrame = w->var("m")->frame(-1,1) ; pll.plotOn(myFrame) ; myFrame->Draw() Changed: < < > > %ENDCODE% links for RooFit Line: 441 to 455 The main goal is to standardise the interface for major statistical procedures so that they can work on an arbitrary RooFit model and dataset and handle any parameters of interest and nuisance parameters. Another goal is to implement most accepted techniques from frequentist, Bayesian and likelihood based approaches. A further goal is to provide utilities to perform combined measurements. example code: create a simple model using the RooFit Workspace Factory. Specify parts of the model using ModelConfig. Create a simple dataset. Complete a confidence interval test using the ProfileLikelihoodCalculator of RooStats Changed: < <   > > %CODE{"c++"}% { // In this script, a simple model is created using the Workspace Factory in RooFit. // ModelConfig is used to specify the parts of the model necessary for the statistical tools of RooStats. Line: 501 to 516 cout << "No" << endl; } } Changed: < < > > %ENDCODE% links for RooStats Line: 540 to 554 The hist2workspace executable is run using the top-level XML configuration file as an argument in the following manner: Changed: < < > > %CODE{"bash"}% hist2workspace top_level.xml Changed: < < > > %ENDCODE% hist2workspace builds the model and saves input histograms in the output ROOT file. The measurement's configuration class is made to persist as well. This measurement class has a member function that can write XML configuration files which point to the histograms saved in the (output) ROOT file (e.g.: GaussExample->WriteToXML). Line: 612 to 626 There are several parts in the top-level XML file. Initially, the XML schema is specified. The output is specified next. Specifically, the prefix for any output files (ROOT files containing workspaces) is given. Now, the channel XML files are given for each measurement (e.g., signal, background, systematics information) using the Input tag. Next, the details for each channel are defined using the Measurement tag. Which bins to use are specified inclusively using the Measurement tag attributes BinLow and BinHigh. Within the Measurement tag, the POI tag is used to specify the point of interest for the channel, i.e. the test statistic. example file:$ROOTSYS/tutorials/histfactory/example.xml
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C++ approach to HistFactory

This approach has not been committed to the RooStats branch yet, though it soon will be. There are a few stylistic changes to be made to the latest code, though verification of the code is complete (changes reproduce exactly results from ROOT 5.32). Code examples will be written in due course.

The C++ approach to HistFactory allows one to interact with HistFactory (creating models etc.) using C++ and Python code. The configuration part of HistFactory is based on a C++ class structure. Since the configuration state of HistFactory is based on C++, one can bypass XML. All functions used in the executable hist2workspace are available for use in C++ code. These C++ classes mirror the structure of the input XML tags. These classes are automatically saved in the output ROOT file along with the workspace. They can then be browsed in CINT or imported in code.

The main advantage of using the C++ approach to HistFactory is that it allows one to easily create many similar models based on an initial template. In the XML approach, one must create many similar XML configuration files and execute hist2workspace many times (though this can be done in an automated manner).

HistFactory class tree structure

• Measurement
• std::string POI
• double Lumi
• ... etc.
• std:: vector<Channels>
• Channel
• Data
• TH1* Observed
• StatErrorConfig
• std::vector<Samples>
• Sample
• TH1* Nominal
• std::vector<NormFactor>
• std::vector<OverallSys>
• std::vector<HistoSys>

HistFactory configuration in C++

Example: creation of the Measurement and a Channel and, thence, creation of the channel samples, including signal and backgrounds

// Create the Measurement and a channel
std::string myInputFile = "./data/myData.root";
std::string myChannel1Path = "";

// Create the measurement.
Measurement myMeasurement("myMeasurement", "myMeasurement");
myMeasurement.OutputFilePrefix = "./workspaces/myWorkspace";
myMeasurement.POI = "SigXsecOverSM";
myMeasurement.constantParams.push_back("alpha_syst1");
myMeasurement.constantParams.push_back("Lumi");
myMeasurement.Lumi = 1.0;
myMeasurement.LumiRelErr = 0.10;
myMeasurement.ExportOnly = false;
myMeasurement.BinHigh = 2;

// Create a channel.
Channel myChannel("myChannel1");
myChannel.SetData("myData", myInputFile);
myChannel.SetStatErrorConfig(0.05, "Poisson");

// Create the channel samples, including signal and background.
// Create the signal sample.
Sample mySignal("mySignal", "mySignal", myInputFile);
myChannel.samples.push_back(mySignal);
// Create the background 1 sample.
Sample myBackground1("myBackground1", "myBackground1", myInputFile);
myBackground1.ActivateStatError("myBackground1StatisticalUncertainty", myInputFile);
myChannel.samples.push_back(myBackground1);
// Create the background 2 sample.
Sample myBackground2("myBackground2", "myBackground2", myInputFile);
myBackground2.ActivateStatError();
myChannel.samples.push_back(myBackground2);
// Add the samples to the measurement.
myMeasurement.channels.push_back(myChannel);


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Early description of C++ approach to HistFactory

Analysis!

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<-- signal -->
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There are instructions on how to use the different versions of ROOT at Glasgow here.
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Using ROOT on the CERN LXPLUS network

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RooStats is a project to create statistical tools built on top of the RooFit library, which is a data modelling toolkit. It is distributed in ROOT. Specifically, it has been distributed in the ROOT release since version 5.22 (December 2008). The latest version of ROOT is recommended as the RooStats project developes quickly.
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Setting up RooStats

There are three main options available for acquiring ROOT with RooStats included.

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ATLAS recommends the use of the profile likelihood as a test statistic.
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Full significance calculation example, from histogram creation to model production (using hist2workspace), to RooStats calculations

Prepare a working area.

Make the main directory.

cd ~
mkdir test
cd test


Make the directory for the XML configuration files.

mkdir config


Make the directory for the input histogram ROOT files.

mkdir data


Make the directory for the workspace.

mkdir workspaces


Generate input histograms.

Change to the directory for the input histograms.

cd data


Run some code such as the following. For fun, we will create a simulated data signal at about 126 GeV at about three times the number of events of that which was expected.

Example file: make_test_histograms.c

{
// Create the expected signal histogram.
// Create the function used to describe the signal shape (a simple Gaussian shape).
TF1 mySignalFunction("mySignalFunction", "(1/sqrt(2*pi*0.5^2))*2.718^(-(x-126)^2/(2*0.5^2))", 120, 130);
// Create the histogram with 100 bins between 120 and 130 GeV.
TH1F mySignal("mySignal", "mySignal", 100, 120, 130);
// Fill the histogram using the signal function.
mySignal.FillRandom("mySignalFunction", 10000000);
// Create the background histogram.
// Create the function used to describe the signal shape (a simple polynomial of the second order).
TF1 myBackgroundFunction("myBackgroundFunction", "-2.3*10^(-6)*x^2+0.0007*x+0.4", 120, 130);
// Create the histogram with 100 bins between 120 and 130 GeV.
TH1F myBackground("myBackground", "myBackground", 100, 120, 130);
// Fill the histogram using the background function.
myBackground.FillRandom("myBackgroundFunction", 100000000000);
// Create the (simulated) data histogram. This histogram represents what one might have as real data.
// Create the histogram using by combining the signal histogram multiplied by 3 with the background histogram.
TH1F myData=3*mySignal+myBackground;
// Set the name of the histogram.
myData->SetName("myData");
// Save the histograms created to a ROOT file.
TFile myFile("test_histograms.root", "RECREATE");
mySignal->Write();
myBackground->Write();
myData->Write();
myFile.Close();
}


Create the workspace.

There are two approaches which might be used to create the RooFit workspace. The first method uses the hist2workspace program to run on XML configuration files and input histogram files. The second method explicitly builds the workspace using RooFit code. In general, most should opt for the first, XML-based approach. If you wish to understand the process of specifying the specifics of the models you want to create, you might take a look at the second approach.

Option 1: Create the workspace using hist2workspace and XML configuration files.

Change to the directory for the configuration XML files.

cd ~/test/config


Copy the HistFactory XML schema to the configuration directory.

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The ROOT release ships with a script called prepareHistFactory in the $ROOTSYS/bin directory. The prepareHistFactory script prepares a working area. Specifically, it creates results/, data/ and config/ directories. It then copies the HistFactorySchema.dtd and example XML files from the ROOT tutorials directory into the config/ directory. It also copies a ROOT file into the data/ directory for use with the example XML configuration files. HistFactorySchema.dtd Changed: < < This file, located in$ROOTSYS/etc/, specifies the XML schema. It is typically placed in the config/ directory of a working area together with the top-level XML file and the individual channel XML files. The user should not modify this file. The HistFactorySchema.dtd is commented to specify exactly the meaning of the various options.
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The HistFactorySchema.dtd file, located in $ROOTSYS/etc/, specifies the XML schema. It is typically placed in the config/ directory of a working area together with the top-level XML file and the individual channel XML files. The user should not modify this file. The HistFactorySchema.dtd is commented to specify exactly the meaning of the various options. hist2workspace Line: 589 to 589 Val allows for the specification of the specific value. Changed: < < Const: this has a specific value, not set here, but where the param is defined > > Const: this has a specific value, not set here, but where the param is defined. Specific instructions Line: 697 to 697 The input histogram names are of no special significance, however, it is often preferable to have a good naming convention devised. One might consider the order in which one has information in the XML and aim to have histogram names appear in a similar order when listed alphabetically. Changed: < < Generic example: > > Generic example Type of histogram Histogram naming convention Phenomenon histogram <phenomenon name>_m<mass point> Phenomenon upward systematic histogram <phenomenon name>_m<mass point>_sys_<systematic name>_up Line: 706 to 705 The reason for having an "m" character preceding the mass point is that it allows for easy search and replace of the mass point value when automatically producing multiple XML configuration files corresponding to multiple mass points. Changed: < < Specific example: > > Specific example Type of histogram <-- --> Histogram name ttH histogram ttH_m110 ttH upward luminosity systematic histogram ttH_m110_sys_Lumi_up Line: 719 to 717  WW Herwig 105987 upward JES systematic histogram WW_Herwig_105987_m110_sys_JES_up WW Herwig 105987 downward JES systematic histogram WW_Herwig_105987_m110_sys_JES_do Changed: < < Samples > > Samples The sample names are of no special significance, however, it is often preferable to have very short names (e.g., signal1) for the purposes of clarity when, for example, printing the contents of the workspace. The NormalizedByTheory attribute should be "True" (as opposed to "TRUE" or "true") for all non-data-driven backgrounds. If the Data tag is removed, expected data shall be used in calculations. Changed: < < The signal(s) are specified as such through the use of the POI tag. > > The signal(s) are specified as such through the use of the POI tag (in the channel XML configuration files). Example file: ttH_m110_channel.xml Line: 796 to 794 Added: > > Create XML configuration files automatically Once the XML configuration files for a certain mass point are written, these files can be used to automatically create further XML configuration files for all remaining mass points. If the described naming convention is used (i.e., mass points are prefixed with an "m"), the following shell script might be used to create all required XML configuration files for all mass points. Example file: createXMLFiles.sh #!/bin/bash # This script is designed for use with the naming conventions described in the following page: # https://ppes8.physics.gla.ac.uk/twiki/bin/view/ATLAS/HiggsAnalysisAtATLASUsingRooStats # The #userInput hashtag is used to indicate places in the script where the user might modify # things. createXMLFiles() # Arguments: originalMass { originalMass=$1
newMass=$2 # Set/specify the original XML configuration file names. originalChannelXMLFileName=ttH_m${originalMass}_channel.xml
originalTopLevelXMLFileName=ttH_m${originalMass}_top-level.xml # Set/specify the new XML configuration file names. newChannelXMLFileName=ttH_m${newMass}_channel.xml
newTopLevelXMLFileName=ttH_m${newMass}_top-level.xml # Duplicate the original XML configuration files while substituting the original mass # points with the new mass points in the new resulting file. # Here, the program sed is used to replace all occurrances of a specified pattern in # a specified file with another specified pattern. # The "s" correspondes to "substitute". # The "g" corresponds to "globally" (all instances in a line). sed "s/m$originalMass/m$newMass/g"$originalChannelXMLFileName > $newChannelXMLFileName sed "s/m$originalMass/m$newMass/g"$originalTopLevelXMLFileName > $newTopLevelXMLFileName } # Specify the original mass point. originalMass=110 #userInput # Execute the function for creation of new XML configuration files for all required mass points. createXMLFiles$originalMass 115 #userInput
createXMLFiles $originalMass 120 #userInput createXMLFiles$originalMass 125 #userInput
createXMLFiles $originalMass 130 #userInput createXMLFiles$originalMass 140 #userInput


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General description

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E-group for support with ATLAS-sensitive information: atlas-phys-stat-root@cern.ch

E-mail support for software issues, bugs etc.: roostats-development@cern.ch

ModelConfig

The ModelConfig RooStats class encapsulates the configuration of a model to define a particular hypothesis. It is now used extensively by the calculator tools. ModelConfig always contains a reference to an external workspace that manages all of the objects that are a part of the model (PDFs and parameter sets). So, in order to use ModelConfig, the user must specify a workspace pointer before creating the various objects of the model.

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Analysis!

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Guidance in writing the XML configuration files

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Units

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The units of the input histogram and the luminosity specified in the top-level XML configuration file should be compatible; for example, input histograms might be in pb while the luminosity might be in pb^{-1} or input histograms might be in fb while the luminosity might be in fb^{-1}.

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Type of histogram Histogram naming convention
Phenomenon histogram <phenomenon name>_m<mass point>
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Phenomenon downward systematic histogram <phenomenon name>_m<mass point>_sys_<systematic name>_do

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ttH histogram ttH_m110
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ttH downward luminosity systematic histogram ttH_m110_sys_Lumi_do
ttH upward JES systematic histogram ttH_m110_sys_JES_up
ttH downward JES systematic histogram ttH_m110_sys_JES_do
WW Herwig 105987 upward luminosity systematic histogram WW_Herwig_105987_m110_sys_Lumi_up
WW Herwig 105987 downward luminosity systematic histogram WW_Herwig_105987_m110_sys_Lumi_do
WW Herwig 105987 upward JES systematic histogram WW_Herwig_105987_m110_sys_JES_up
WW Herwig 105987 downward JES systematic histogram WW_Herwig_105987_m110_sys_JES_do

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Samples

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Example file: ttH_m110_channel.xml

<!DOCTYPE Channel SYSTEM 'HistFactorySchema.dtd'>

<!-- channel name and input file -->
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<HistoSys Name="Lumi" HistoNameHigh="ttH_m110_sys_Lumi_up" HistoNameLow="ttH_m110_sys_Lumi_do" /> <HistoSys Name="JES" HistoNameHigh="ttH_m110_sys_JES_up" HistoNameLow="ttH_m110_sys_JES_do" />

<-- backgrounds -->

<-- WW_Herwig_105987 -->
NormalizeByTheory="True" HistoName="WW_Herwig_105987_m110">

<-- Wplusjets -->
NormalizeByTheory="False" HistoName="Wplusjets_m110">
<-- systematics -->
<HistoSys Name="Lumi" HistoNameHigh="Wplusjets_m110_sys_Lumi_up" HistoNameLow="Wplusjets_m110_sys_Lumi_do" /> <HistoSys Name="JES" HistoNameHigh="Wplusjets_m110_sys_JES_up" HistoNameLow="Wplusjets_m110_sys_JES_do" />

Example file: ttH_m110_top-level.xml

<!DOCTYPE Combination SYSTEM 'HistFactorySchema.dtd'>

<!-- workspace output file prefix -->
<Combination OutputFilePrefix="workspaces/ttH_m110_workspace" Mode="comb" >

<!-- channel XML file(s) -->
<Input>config/ttH_m110_channel.xml</Input>

<!-- measurement and bin range -->
<Measurement Name="datastat" Lumi="1" LumiRelErr="0.037" BinLow="0" BinHigh="21" Mode="comb" ExportOnly="True">
<POI>SigXsecOverSM</POI>
</Measurement>

</Combination>


Exotics Working Group statistics tutorial XML reference
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XML example
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Analysis!

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HistFactory XML reference
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ATLAS recommends the use of the profile likelihood as a test statistic.

Further information

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prepareHistFactory

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The ROOT release ships with a script called prepareHistFactory and a binary file called hist2workspace in the $ROOTSYS/bin directory. The prepareHistFactory script prepares a working area. Specifically, it creates the results/, data/ and config/ directories. It copies the HistFactorySchema.dtd and example XML files into the config/ directory. Also, it copies a ROOT file into the data/ directory for use with the examples. > > The ROOT release ships with a script called prepareHistFactory and a binary file called hist2workspace in the$ROOTSYS/bin directory. The prepareHistFactory script prepares a working area. Specifically, it creates results/, data/ and config/ directories. It then copies the HistFactorySchema.dtd and example XML files from the ROOT tutorials directory into the config/ directory. It also copies a ROOT file into the data/ directory for use with the example XML configuration files.

HistFactorySchema.dtd

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HistFactorySchema.dtd: This file, located in $ROOTSYS/etc/, specifies the XML schema. It is typically placed in the config/ directory of a working area together with the top-level XML file and the individual channel XML files. The user should not modify this file. The HistFactorySchema.dtd is commented to specify exactly the meaning of the various options. > > This file, located in$ROOTSYS/etc/, specifies the XML schema. It is typically placed in the config/ directory of a working area together with the top-level XML file and the individual channel XML files. The user should not modify this file. The HistFactorySchema.dtd is commented to specify exactly the meaning of the various options.

hist2workspace

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The hist2workspace executable is used in the following manner:
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The hist2workspace executable is run using the top-level XML configuration file as an argument in the following manner:

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hist2workspace input.xml
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hist2workspace top_level.xml

XML files

General description

Changed:
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A minimum of two XML files are required for configuration. The "top-level" XML file defines the measurement and contains a list of channels that contribute to this measurement. "channel" XML files are used to describe each channel in detail. For each contributing channel, there is a separate XML file.
>
>
A minimum of two XML files are required for configuration. The "top-level" XML configuration file defines the measurement and contains a list of channels that contribute to this measurement. The "channel" XML configuration files are used to describe each channel in detail. For each contributing channel, there is a separate XML configuration file.

Conventions

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The nominal and variational histograms should all have the same normalization convention. There are a few conventions possible:
>
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The nominal and variational histograms should all have the same normalisation convention. There are a few conventions possible:

• Option 1:
Changed:
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• Lumi="XXX" in thee main XML's element, where XX is in fb^-1
• Histograms are in fb / bin
• Some samples have NormFactors that are all relative to prediction (eg. 1 is the nominal prediction)
>
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• Lumi="XXX" is in the main XML's element, where XXX is in fb^-1.
• Histograms have units of fb/bin.
• Some samples have NormFactors that are all relative to prediction (e.g. 1 is the nominal prediction).

• Option 2:
Changed:
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• Lumi="1" in thee main XML's element
• Histograms are normalized to unity
• each sample has a NormFactor that is the expected numbers of events in data
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• Lumi="1" is in the main XML's element.
• Histograms are normalized to unity.
• Each sample has a NormFactor that is the expected numbers of events in data.

• Option 3:
Changed:
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• Lumi="1" in thee main XML's element
• Histograms are in numbers of events / bin expected in data
• Some samples have NormFactors that are all relative to prediction (eg. 1 is the nominal prediction)
• It's up to you. In the end, the expected number is the product of them: N=Lumi*BinContent*NormFactor(s) See the PDF user's guide for more precise equations.
>
>
• Lumi="1" is in the main XML's element.
• Histograms have units of (numbers of events)/bin expected in data.
• Some samples have NormFactors that are all relative to prediction (e.g. 1 is the nominal prediction).
• It's up to you. In the end, the expected number is a product: N=Lumi*BinContent*NormFactor(s). See the user's guide for more precise equations.

Top-Level XML file

General description

This file specifies a top level 'Combination' that is composed of:

Changed:
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• several 'Channels', which are described in separate XML files.
>
>
• several 'Channels', which are described in separate XML configuration files.

• several 'Measurements' (corresponding to a full fit of the model), each of which specifies
• Name, a name for this measurement to be used in tables and files.
Changed:
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• Lumi, the integrated luminosity associated with the measurement in picobarns
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• Lumi, the integrated luminosity associated with the measurement in picobarns.

• LumiRelErr, the relative error of the luminosity measurement.
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• which bins of the histogram should be used.
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• the histogram bins to be used:

• BinLow specifies the lowest bin number used for the measurement (inclusive).
• BinHigh specifies the highest bin number used for the measurement (exclusive).
Changed:
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• what the relative uncertainty on the luminosity is.
>
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• relative uncertainty on the luminosity.

• what is(/are) the parameter(/s) of interest that will be measured.
• Use POI to specify this.
• which parameter(/s) should be fixed/floating (e.g., nuisance parameters)
Line: 561 to 561

• whether the tool should export the model only and skip the default fit.
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• ExportOnly: if "True", skip the fit (only export the model; don't perform the initial fit).
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• ExportOnly: if "True", skip the fit (export only the model; don't perform the initial fit).
OutputFilePrefix is a prefix for the output ROOT file to be created.
>
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Mode represents the type of analysis. Use "comb".

ParamSetting allows for the specification of which parameters are fixed. If a parameter is included here, it is neither a nuisance parameter nor a POI, but a fixed parameter of the mode.

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void ModelInspector(const char* infile = "", const char* workspaceName = "combined", const char* modelConfigName = "ModelConfig", const char* dataName = "obsData")

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If the worspace(s) were made using hist2workspace, the names have a standard form (as shown above).
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If the workspace(s) were made using hist2workspace, the names have a standard form (as shown above).

Using the Model Inspector

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 META TOPICPARENT name="WebHome"
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This file specifies a top level 'Combination' that is composed of:
• several 'Channels', which are described in separate XML files.
• several 'Measurements' (corresponding to a full fit of the model), each of which specifies
Changed:
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• a name for this measurement to be used in tables and files.
• the luminosity associated with the measurement in picobarns.
>
>
• Name, a name for this measurement to be used in tables and files.
• Lumi, the integrated luminosity associated with the measurement in picobarns
• LumiRelErr, the relative error of the luminosity measurement.

• which bins of the histogram should be used.
>
>
• BinLow specifies the lowest bin number used for the measurement (inclusive).
• BinHigh specifies the highest bin number used for the measurement (exclusive).

• what the relative uncertainty on the luminosity is.
• what is(/are) the parameter(/s) of interest that will be measured.
>
>
• Use POI to specify this.

• which parameter(/s) should be fixed/floating (e.g., nuisance parameters)
• which type of constriants are desired:
>
>

• default: Gaussian
Changed:
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>
>

• whether the tool should export the model only and skip the default fit.
>
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• ExportOnly: if "True", skip the fit (only export the model; don't perform the initial fit).

OutputFilePrefix is a prefix for the output ROOT file to be created. Mode represents the type of analysis. Use "comb".

ParamSetting allows for the specification of which parameters are fixed. If a parameter is included here, it is neither a nuisance parameter nor a POI, but a fixed parameter of the mode. Val allows for the specification of the specific value. Const: this has a specific value, not set here, but where the param is defined

Line: 601 to 614

General description

These files specify for each channel

>
>
• Name, a name for the channel.
• InputFile, the input file in which the histogram can be found. If this is not specified, it must be specified for each sample and data.
• HistoPath, the path (within the ROOT file) at which the histogram can be found.
• HistoName (optional), the name of the histogram to be used, unless overridden for specific samples and data.

• observed data (if absent, the tool will use the expectation, which is useful for expected sensitivity)
• several 'Samples' (e.g., signal, bkg1, bkg2 etc.), each of which specifies
Changed:
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• a name.
>
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• Name, a name

• whether the sample is normalized by theory (e.g., N = L * sigma) or whether the sample is data driven.
• a nominal expectation histogram.
• a named 'Normalization Factor' (which can be fixed or allowed to float in a fit).
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XML example
>
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HistFactory XML reference

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A minimum of two XML files are required for configuration. The "top-level" XML file defines the measurement and contains a list of channels that contribute to this measurement. "channel" XML files are used to describe each channel in detail. For each contributing channel, there is a separate XML file.
>
>

Conventions

The nominal and variational histograms should all have the same normalization convention. There are a few conventions possible:

• Option 1:
• Lumi="XXX" in thee main XML's element, where XX is in fb^-1
• Histograms are in fb / bin
• Some samples have NormFactors that are all relative to prediction (eg. 1 is the nominal prediction)

• Option 2:
• Lumi="1" in thee main XML's element
• Histograms are normalized to unity
• each sample has a NormFactor that is the expected numbers of events in data

• Option 3:
• Lumi="1" in thee main XML's element
• Histograms are in numbers of events / bin expected in data
• Some samples have NormFactors that are all relative to prediction (eg. 1 is the nominal prediction)
• It's up to you. In the end, the expected number is the product of them: N=Lumi*BinContent*NormFactor(s) See the PDF user's guide for more precise equations.

Top-Level XML file

General description

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 META TOPICPARENT name="WebHome"
Line: 170 to 168
Hey, RooFit! This is the thing to normalise over (i.e., guarantees Int[xmin, xmax] Gauss(x, m, s)dx == 1): gauss.getVal(x); What is the value if sigma is considered the observable? (i.e., guarantees Int[smin, smax] Gauss(x, m, s)ds == 1):
Deleted:
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Datasets

General description

Changed:
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In RooFit, data can be stored in an unbinned or binned manner. Unbinned data is stored using the RooDataSet class while binned data is stored using the RooDataHist class. The user can define how many bins there are in a variable. For the purposes of plotting using the RooPlot class, a RooDataSet is binned into a histogram.
>
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A dataset is a collection of points in N-dimensional space. In RooFit, data can be stored in an unbinned or binned manner. Unbinned data is stored using the RooDataSet class while binned data is stored using the RooDataHist class. The user can define how many bins there are in a variable. For the purposes of plotting using the RooPlot class, a RooDataSet is binned into a histogram.

Changed:
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In general, working in RooFit with binned and unbinned data is very similar, as both class RooDataSet (for unbinned data) and class RooDataHist (for binned data) inherit from a common base class, RooAbsData, which defines the interface for a generic abstract data sample. With few exceptions, all RooFit methods take abstract datasets as input arguments, allowing for the interchangeable use of binned and unbinned data.
>
>
In general, working in RooFit with binned and unbinned data is very similar, as both the RooDataSet (for unbinned data) and RooDataHist (for binned data) classes inherit from a common base class, RooAbsData, which defines the interface for a generic abstract data sample. With few exceptions, all RooFit methods take abstract datasets as input arguments, allowing for the interchangeable use of binned and unbinned data.

RooDataSet (unbinned data)

Line: 193 to 190
myData.plotOn()(myFrame); myFrame.Draw(); }
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Plotting unbinned data is similar to plotting binned data with the exception that one can show it in some preferred binning.
>
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Plotting unbinned data is similar to plotting binned data with the exception that one can display it in some preferred binning.

Example code: plotting unbinned data (a RooDataSet) using a specified binning



Line: 203 to 199
RooPlot* myFrame = x.frame() ; myData.plotOn(myFrame, Binning(25)) ; myFrame->Draw()
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Importing data from ROOT trees (how to populate RooDataSets from TTrees)
Changed:
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* Put stuff here, Will. *
>
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* to be completed *

RooDataHist (binned data)

Line: 263 to 256
The RooFit "workspace" provides the ability to store the full likelihood model, any desired priors and the minimal data necessary to reproduce the likelihood function in a ROOT file. Thus, the workspace is needed for combinations and has potential for digitally publishing results (PhyStats agreed to publish likelihood functions). The RooFit workspace can be used for this.
Changed:
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One might create a Gaussian PDF and then import it into a workspace. All of the dependencies of the Gaussian shall be drawn in and owned by the workspace. There are no nightmarish ownership problems. Alternatively, one might create simply the Gaussian inside the workspace using the "Workspace Factory".
>
>
Consider a Gaussian PDF. One might create this Gaussian PDF and then import it into a workspace. All of the dependencies of the Gaussian would be drawn in and owned by the workspace (there are no nightmarish ownership problems). Alternatively, one might create simply the Gaussian inside the workspace using the "Workspace Factory".

Example code: using the Workspace Factory to create a Gaussian PDF




Line: 285 to 277
myWorkspace.Print(); // Example printout:
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variables --------- (x,m,s)

p.d.f.s ------- RooGaussian::g[ x=x mean=m sigma=s ] = 0

datasets -------- RooDataSet::d(x)

>
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// variables // --------- // (x,m,s) // // p.d.f.s // ------- // RooGaussian::g[ x=x mean=m sigma=s ] = 0 // // datasets // -------- // RooDataSet::d(x)
// Import the variable saved as x. RooRealVar* myVariable = myWorkspace.var("x");
Line: 349 to 340
// 0x15f7fe0/V- RooRealVar::x = 150 // 0x1487090/V- RooRealVar::mu = 150 // 0x1487bc0/V- RooRealVar::sigma = 5
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Model Inspector

The Model Inspector is a GUI for examining the model contained in the RooFit workspace. The function and it's parameters are as follows:

Changed:
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void ModelInspector(const char* infile = "", const char* workspaceName = "combined", const char* modelConfigName = "ModelConfig", const char* dataName = "obsData")
>
>

Changed:
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If the worspace(/s) were made using hist2workspace, the names have a standard form (as shown above).
>
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If the worspace(s) were made using hist2workspace, the names have a standard form (as shown above).

Line: 505 to 494

General description

Changed:
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The HistFactory can be used to run an analysis without being a RooFit/RooStats expert. In a nutshell, ROOT files containing input histograms are set up and XML files are set up for those input ROOT files. The XML files specify details on the histograms and specify how RooFit should interpret the information in the files. An little executable contained in ROOT called hist2workspace is used to import the histograms into a RooFit workspace appropriately.
>
>
The HistFactory can be used to run an analysis without being a RooFit/RooStats expert. In a nutshell, ROOT files containing input histograms are set up and XML files are set up for those input ROOT files. The XML files specify details on the histograms and specify how RooFit should interpret the information in the files. A little executable contained in ROOT called hist2workspace is used to import the histograms into a RooFit workspace appropriately.

prepareHistFactory

Changed:
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The ROOT release ships with a script called prepareHistFactory and a binary file called hist2workspace in the $ROOTSYS/bin directories. prepareHistFactory prepares a working area. It creates results/, data/ and config/ directories. It copies the HistFactorySchema.dtd and example XML files into the config/ directory. Also, it copies a ROOT file into the data/ directory for use with the examples. > > The ROOT release ships with a script called prepareHistFactory and a binary file called hist2workspace in the$ROOTSYS/bin directory. The prepareHistFactory script prepares a working area. Specifically, it creates the results/, data/ and config/ directories. It copies the HistFactorySchema.dtd and example XML files into the config/ directory. Also, it copies a ROOT file into the data/ directory for use with the examples.

HistFactorySchema.dtd

Changed:
<
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HistFactorySchema.dtd: This file is located in $ROOTSYS/etc/ specifies the XML schema. It is typically placed in the config/ directory of a working area together with the top-level XML file and the individual channel XML files. The user should not modify this file. The HistFactorySchema.dtd is commented to specify exactly the meaning of the various options. > > HistFactorySchema.dtd: This file, located in$ROOTSYS/etc/, specifies the XML schema. It is typically placed in the config/ directory of a working area together with the top-level XML file and the individual channel XML files. The user should not modify this file. The HistFactorySchema.dtd is commented to specify exactly the meaning of the various options.

hist2workspace

Changed:
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The hist2workspace executable is used in the following manner: hist2workspace input.xml
>
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The hist2workspace executable is used in the following manner:

   hist2workspace input.xml


XML files

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Higgs analysis at ATLAS using RooStats

Deleted:
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This page contains basic information on getting started with Higgs analysis at ATLAS using RooStats.

Deleted:
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A note on code and formatting

Example code is generally indented and given highlighting. Explanatory code and text directly relating to it has yellow highlighting while example code that one might run directly in ROOT is given a classical green-text-on-black-background console style. Scripts are given grey highlighting. File contents are given the golden verbatim colouring. So, in a nutshell, code segments are in yellow, full ROOT scripts are in terminal, general scripts are in grey and file contents are in gold. In code examples given, user-created objects are generally prefaced with "my", for example, "myData", for the purposes of clarity.

What is RooStats?

Changed:
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RooStats is a project to create statistical tools built on top of the RooFit library, which is a data modelling toolkit. It is distributed in ROOT. Specifically, it has been distributed in the ROOT release since version 5.22 (December 2008). The latest version of ROOT is recommended as the RooStats project is developing quickly.
>
>
RooStats is a project to create statistical tools built on top of the RooFit library, which is a data modelling toolkit. It is distributed in ROOT. Specifically, it has been distributed in the ROOT release since version 5.22 (December 2008). The latest version of ROOT is recommended as the RooStats project developes quickly.

Using the appropriate version of ROOT at Glasgow

There are instructions on how to use the different versions of ROOT at Glasgow here.

To check what version of ROOT is running, use the following command:

Changed:
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root -v -b
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root -v -b


Setting up RooStats

Line: 51 to 46
# Next, the latest version of ROOT in the CERN Subversion repository is checked out. # Finally, ROOT is compiled.
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# Install the ROOT prerequisites.
>
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# Install ROOT prerequisites.
sudo apt-get install subversion sudo apt-get install make sudo apt-get install g++
Line: 62 to 57
sudo apt-get install libxft-dev sudo apt-get install libxext-dev
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# Install the optional ROOT packages.
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sudo apt-get install gfortran sudo apt-get install ncurses-dev sudo apt-get install libpcre3-dev
Line: 80 to 75
sudo apt-get install libssl-dev sudo apt-get install libgsl0-dev
Changed:
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# Check out latest ROOT trunk. svn co http://root.cern.ch/svn/root/trunk ~/root
>
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# Check out the latest ROOT trunk. svn co http://root.cern.ch/svn/root/trunk /usr/local/root

Changed:
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# The configuration for the build is set. cd ~/root # Run this to define the system architecture and to enable building of the libRooFit advanced fitting package:
>
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# Configure the build. cd /usr/local/root # Configure for the system architecture and configure to build the libRooFit advanced fitting package as part of the compilation.
./configure linuxx8664gcc --enable-roofit # See other possible configurations using the following command: ./configure --help
Changed:
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# Start compiling.
>
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# Compile.
make
>
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Changed:
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# Upon completion, ROOT is run by executing ~/root/bin/root.

Changed:
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Option 3: Build the RooStats branch.

Line: 130 to 127
Composite functions correspond to composite objects. The ArgSet class is dependent on argument order while the ArgList class is not.
Deleted:
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Example code: defining a RooFit variable

Changed:
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General form for defining a RooFit variable: RooRealVar x(<object name>, <object title>, <value>, <minimum value>, <maximum value>) Specific example for defining a RooFit variable x with the value 5: RooRealVar x("x", "x observable", 5, -10, 10)
Changed:
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RooPlot

Line: 154 to 150
Bayes' theorem holds that the probability of b given a is related to the probability of a given b. Normally, one might say that the mean of a Gaussian is 1 and that then gives a distribution for x. However, if one had a dataset for x, one might want to know the posterior for the mean. The RooFit ability to switch what the probability density function is of is very useful for Bayesian stuff. Because RooFit allows this composition, the thing that acts as x in the Gaussian could actually be a function of, say, x^2. A Jacobian factor is picked up in going from x to x^2, so the normalisation no longer makes sense. Sometimes RooFit can figure out what the Jacobian factor should be and sometimes it resorts to numerical integration.
Deleted:
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Example code: create a Gaussian PDF using RooStats and plot it using the RooPlot class

Changed:
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>
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{ // Build a Gaussian PDF. RooRealVar x("x", "x", -10, 10);
Line: 168 to 163
// Plot the PDF. RooPlot* xframe = x.frame(); gauss.plotOn(xframe);
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xframe->Draw();
>
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xframe->Draw();
}
Changed:
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>
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Deleted:
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Example code: telling a RooFit PDF what to normalise over

Changed:
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>
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Not normalised (i.e., this is not a PDF): gauss.getVal(); Hey, RooFit! This is the thing to normalise over (i.e., guarantees Int[xmin, xmax] Gauss(x, m, s)dx == 1): gauss.getVal(x); What is the value if sigma is considered the observable? (i.e., guarantees Int[smin, smax] Gauss(x, m, s)ds == 1):
Changed:
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Datasets

Line: 194 to 188

RooDataSet (unbinned data)

Deleted:
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Example code: generating toy Monte Carlo, storing it as unbinned data and then plotting it
Changed:
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>
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} // Create a RooDataSet and fill it with generated toy Monte Carlo data: RooDataSet* myData = gauss.generate(x, 100);
Line: 206 to 199
myFrame.Draw(); }
Changed:
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>
>

Plotting unbinned data is similar to plotting binned data with the exception that one can show it in some preferred binning.
Deleted:
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Example code: plotting unbinned data (a RooDataSet) using a specified binning
Changed:
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>
>



RooPlot* myFrame = x.frame() ; myData.plotOn(myFrame, Binning(25)) ;
Changed:
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myFrame->Draw()
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myFrame->Draw()

Changed:
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Importing data from ROOT trees (how to populate RooDataSets from TTrees)
Line: 231 to 223
In displaying the data, RooFit, by default, shows the 68% confidence interval for Poisson statistics.
Deleted:
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Example code: import a ROOT histogram into a RooDataHist (a RooFit binned dataset)
Changed:
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>
>



{ // Access the file. TFile* myFile = new TFile("myFile.root"); // Load the histogram.
Changed:
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TH1* myHistogram = (TH1*) myFile->Get("myHistogram");
>
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TH1* myHistogram = (TH1*) myFile->Get("myHistogram");
// Draw the loaded histogram. myHistogram.Draw();
Line: 254 to 245
myFrame.Draw() }
Changed:
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>
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Fitting

Fitting a model to data

Changed:
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Fitting a model to data can be done in many ways. The most common methods are the χ2 fit and the -log(L) fit. The default fitting method in ROOT is the χ2 method, while the default method in RooFit is the -log(L) method. The -log(L) method is often preferred because it is more robust for low statistics fits and because it can also be performed on unbinned data.
>
>
Fitting a model to data can be done in many ways. The most common methods are the χ2 fit and the -log(L) fit. The default fitting method in ROOT is the χ2 method, while the default method in RooFit is the -log(L) method. The -log(L) method is often preferred because it is more robust for low statistics fits and because it can also be performed on unbinned data.

Fitting a PDF to unbinned data

Deleted:
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Example code: fit a Gaussian PDF to data
Changed:
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>
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// Fit gauss to unbinned data gauss.fitTo(*myData);
Changed:
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The RooFit workspace

Line: 280 to 270
One might create a Gaussian PDF and then import it into a workspace. All of the dependencies of the Gaussian shall be drawn in and owned by the workspace. There are no nightmarish ownership problems. Alternatively, one might create simply the Gaussian inside the workspace using the "Workspace Factory".
Deleted:
<
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Example code: using the Workspace Factory to create a Gaussian PDF

Changed:
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// Create a Gaussian PDF using the Workspace Factory (this is essentially the shorthand for creating a Gaussian). RooWorkspace* myWorkspace = new RooWorkspace("myWorkspace");
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myWorkspace->factory("Gaussian::g(x[-5, 5], mu[0], sigma[1]");
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myWorkspace->factory("Gaussian::g(x[-5, 5], mu[0], sigma[1]");

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What's in the RooFit workspace?

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Example code: What's in the workspace?

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// Open the appropriate ROOT file. root -l myFile.root // Import the workspace.
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myWorkspace = (RooWorkspace*) _file0->Get("myWorkspace");
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myWorkspace = (RooWorkspace*) _file0->Get("myWorkspace");
// Print the workspace contents. myWorkspace.Print(); // Example printout:
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// Import the ModelConfig saved as m. ModelConfig* myModelConfig = (ModelConfig*) myWorkspace.obj("m");
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Visual representations of the model/PDF contents

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Graphviz consists of a graph description language called the DOT language and a set of tools that can generate and/or process DOT files.
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Example code: examining PDFs and creating graphical representations of them
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// Create variables and a PDF using those variables. RooRealVar mu("mu", "mu", 150); RooRealVar sigma("sigma", "sigma", 5, 0, 20);
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// 0x1487090/V- RooRealVar::mu = 150 // 0x1487bc0/V- RooRealVar::sigma = 5
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Accessing the RooFit workspace

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Example code: accessing the workspace
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// Open the appropriate ROOT file. root -l BR5_MSSM_signal90_combined_datastat_model.root // Alternatively, you could open the file in a manner such as the following: myFileName = "BR5_MSSM_signal90_combined_datastat_model.root" TFile *myFile = TFile::Open(myFileName); // Import the workspace.
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RooWorkspace* myWorkspace = (RooWorkspace*) _file0->Get("combined");
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RooWorkspace* myWorkspace = (RooWorkspace*) _file0->Get("combined");
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myWorkspace->Print();
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myWorkspace->Print();
// Import the PDF.
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RooAbsPdf* myPDF = myWorkspace->pdf("model_BR5_MSSM_signal90");
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RooAbsPdf* myPDF = myWorkspace->pdf("model_BR5_MSSM_signal90");
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RooRealVar* myObservable = myWorkspace->var("obs");
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RooRealVar* myObservable = myWorkspace->var("obs");
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myFrame->Draw();
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myFrame->Draw();

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Example code: accessing both data and PDF from a workspace stored in a file
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// Note that the following code is independent of actual PDF in the file. So, for example, a full Higgs combination could work with identical code.

// Open a file and import the workspace. TFile myFile("myResults.root") ; RooWorkspace* myWorkspace = f.Get("myWorkspace") ; // Plot the data and PDF

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RooPlot* xframe = w->var("x")->frame() ; w->data("d")->plotOn(xframe) ; w->pdf("g")->plotOn(xframe) ;
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RooNLLVar nll("nll","nll",*myWorkspace->pdf("g"),*w->data("d")) ; RooProfileLL pll("pll","pll", nll,*myWorkspace->var("m")) ; RooPlot* myFrame = w->var("m")->frame(-1,1) ;
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RooNLLVar nll("nll","nll",*myWorkspace->pdf("g"),*w->data("d")) ; RooProfileLL pll("pll","pll", nll,*myWorkspace->var("m")) ; RooPlot* myFrame = w->var("m")->frame(-1,1) ;
pll.plotOn(myFrame) ;
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myFrame->Draw()
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myFrame->Draw()

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RooStats

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The main goal is to standardise the interface for major statistical procedures so that they can work on an arbitrary RooFit model and dataset and handle any parameters of interest and nuisance parameters. Another goal is to implement most accepted techniques from frequentist, Bayesian and likelihood based approaches. A further goal is to provide utilities to perform combined measurements.
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Example code: create a simple model using the RooFit Workspace Factory. Specify parts of the model using ModelConfig. Create a simple dataset. Complete a confidence interval test using the ProfileLikelihoodCalculator of RooStats

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{ // In this script, a simple model is created using the Workspace Factory in RooFit. // ModelConfig is used to specify the parts of the model necessary for the statistical tools of RooStats. // A 95% confidence interval test is run using the ProfileLikelihoodCalculator of RooStats.

// Define a RooFit random seed in order to produce reproducible results.

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RooRandom::randomGenerator()->SetSeed(271);
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RooRandom::randomGenerator()->SetSeed(271);
// Make a simple model using the Workspace Factory. // Create a new workspace. RooWorkspace* myWorkspace = new RooWorkspace(); // Create the PDF G(x|mu,1) and the variables x, mu and sigma in one command using the factory syntax.
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myWorkspace->factory("Gaussian::normal(x[-10,10], mu[-1,1], sigma[1])");
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myWorkspace->factory("Gaussian::normal(x[-10,10], mu[-1,1], sigma[1])");
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myWorkspace->defineSet("poi","mu"); myWorkspace->defineSet("obs","x");
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myWorkspace->defineSet("poi","mu"); myWorkspace->defineSet("obs","x");
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myWorkspace->Print() ;
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myWorkspace->Print() ;
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myModelConfig->SetPdf(*myWorkspace->pdf("normal"));
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myModelConfig->SetObservables(*myWorkspace->set("obs"));
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RooDataSet* myData = myWorkspace->pdf("normal")->generate(*myWorkspace->set("obs"), 100); //myData->print();
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RooDataSet* myData = myWorkspace->pdf("normal")->generate(*myWorkspace->set("obs"), 100); //myData->print();
// Use the ProfileLikelihoodCalculator to obtain a 95% confidence interval. // Specify the confidence level required. double confidenceLevel = 0.95;
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LikelihoodInterval* myProfileLikelihoodInterval = myProfileLikelihoodCalculator.GetInterval(); // Use this interval result. In this case, it makes sense to say what the lower and upper limits are. // Define the object variables for the purposes of the confidence interval.
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RooRealVar* x = myWorkspace->var("x"); RooRealVar* mu = myWorkspace->var("mu"); cout << "The profile likelihood calculator interval is [ "<< myProfileLikelihoodInterval->LowerLimit(*mu) << ", " << myProfileLikelihoodInterval->UpperLimit(*mu) << "] " << endl;
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RooRealVar* x = myWorkspace->var("x"); RooRealVar* mu = myWorkspace->var("mu"); cout << "The profile likelihood calculator interval is [ "<< myProfileLikelihoodInterval->LowerLimit(*mu) << ", " << myProfileLikelihoodInterval->UpperLimit(*mu) << "] " << endl;
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mu->setVal(0);
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cout << "Is mu = 0 in the interval?" << endl; if (myProfileLikelihoodInterval->IsInInterval(*mu) == 1){ cout << "Yes" << endl;
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} }
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ModelConfig

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The ModelConfig RooStats class encapsulates the configuration of a model to define a particular hypothesis. It is now used extensively by the calculator tools. ModelConfig always contains a reference to an external workspace that manages all of the objects that are a part of the model (PDFs and parameter sets). So, in order to use ModelConfig, the user must specify a workspace pointer before creating the various objects of the model.
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The ModelConfig RooStats class encapsulates the configuration of a model to define a particular hypothesis. It is now used extensively by the calculator tools. ModelConfig always contains a reference to an external workspace that manages all of the objects that are a part of the model (PDFs and parameter sets). So, in order to use ModelConfig, the user must specify a workspace pointer before creating the various objects of the model.

HistFactory

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hist2workspace

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The hist2workspace executable is used in the following manner: hist2workspace input.xml
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The hist2workspace executable is used in the following manner: hist2workspace input.xml

XML files

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There are several parts in the top-level XML file. Initially, the XML schema is specified. The output is specified next. Specifically, the prefix for any output files (ROOT files containing workspaces) is given. Now, the channel XML files are given for each measurement (e.g., signal, background, systematics information) using the Input tag. Next, the details for each channel are defined using the Measurement tag. Which bins to use are specified inclusively using the Measurement tag attributes BinLow and BinHigh. Within the Measurement tag, the POI tag is used to specify the point of interest for the channel, i.e. the test statistic.
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Example file: $ROOTSYS/tutorials/histfactory/example.xml Changed: < <   > >   <!DOCTYPE Combination SYSTEM 'HistFactorySchema.dtd'> <Combination OutputFilePrefix="./results/example" Mode="comb" > Line: 578 to 559 Changed: < < > > Channel XML files Line: 610 to 591 HistoNameHigh="myShapeSystematic_1_high" HistoNameLow="myShapeSystematic_1_low" /> Deleted: < < Example file:$ROOTSYS/tutorials/histfactory/example_channel.xml
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<!DOCTYPE Channel  SYSTEM 'HistFactorySchema.dtd'>

<Channel Name="channel1" InputFile="./data/example.root" HistoName="" >
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Analysis!

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HistFactory manual
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E-group for support with ATLAS-sensitive information: atlas-phys-stat-root@cern.ch
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E-group for support with ATLAS-sensitive information: atlas-phys-stat-root@cern.ch

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E-mail support for software issues, bugs etc.: roostats-development@cern.ch
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E-mail support for software issues, bugs etc.: roostats-development@cern.ch

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Analysis!

ATLAS recommends the use of the profile likelihood as a test statistic.

Further information

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There are instructions on how to use the different versions of ROOT at Glasgow here.
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To check what version of ROOT is running, use the following command:

root -v -b

Setting up RooStats

There are three main options available for acquiring ROOT with RooStats included.

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The hist2workspace executable is used in the following manner: hist2workspace input.xml
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XML files

General description

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A minimum of two XML files are required for configuration. The "top-level" XML file defines the measurement and contains a list of channels that contribute to this measurement. "channel" XML files are used to describe each channel in detail. For each contributing channel, there is a separate XML file.

Top-Level XML file

General description
This file specifies a top level 'Combination' that is composed of:
• several 'Channels', which are described in separate XML files.
• several 'Measurements' (corresponding to a full fit of the model), each of which specifies
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• whether the tool should export the model only and skip the default fit.
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Specific instructions

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Specific instructions
There are several parts in the top-level XML file. Initially, the XML schema is specified. The output is specified next. Specifically, the prefix for any output files (ROOT files containing workspaces) is given. Now, the channel XML files are given for each measurement (e.g., signal, background, systematics information) using the Input tag. Next, the details for each channel are defined using the Measurement tag. Which bins to use are specified inclusively using the Measurement tag attributes BinLow and BinHigh. Within the Measurement tag, the POI tag is used to specify the point of interest for the channel, i.e. the test statistic.

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Example file: $ROOTSYS/tutorials/histfactory/example.xml > > Example file:$ROOTSYS/tutorials/histfactory/example.xml


<!DOCTYPE Combination  SYSTEM 'HistFactorySchema.dtd'>


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Channel XML files

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General description

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General description
These files specify for each channel
• observed data (if absent, the tool will use the expectation, which is useful for expected sensitivity)
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• a name (which can be shared with the OverallSyst if correlated).
• +/- 1 sigma variational histograms.
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Specific instructions

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Specific instructions

First, the channel file specifies the XML schema. Then, the channel is defined and named. The location of the data histogram for the channel is defined. For each background, a Sample is defined. It is specified whether it is normalised to luminosity (i.e., the histograms should be per inverse picobarn and will be scaled). To enable normalisation to luminosity, set the tag attribute NormalizeByTheory to "True". For external normalisation, a data-driven background measurement is fixed to the lumi of the dataset. In this case, set the tag attribute NormalizeByTheory to "False". For the normalisation factor, (e.g., "SigXsecOverSM"), the tag attribute "Name" should match the POI specified in the top level XML configuration file.

Systematic uncertainties

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For an overall relative rate systematic, the "OverallSys" tag is used with its appropriate tag attributes. For a shape systematic (a systematic that affects the shape of a histogram), the "HistoSys" tag is used with its appropriate tag attributes. Specifically, for the HistoSys tag attributes "HistoNameHigh" and "HistoNameLow", the respective histograms for the upper and lower shape systematic uncertainties are specified in a manner such as the following:

<HistoSys Name="myShapeSystematic_1" HistoNameHigh="myShapeSystematic_1_high" HistoNameLow="myShapeSystematic_1_low" />


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Example file: $ROOTSYS/tutorials/histfactory/example_channel.xml > > Example file:$ROOTSYS/tutorials/histfactory/example_channel.xml


<!DOCTYPE Channel  SYSTEM 'HistFactorySchema.dtd'>



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Datasets

General description

In RooFit, data can be stored in an unbinned or binned manner. Unbinned data is stored using the RooDataSet class while binned data is stored using the RooDataHist class. The user can define how many bins there are in a variable. For the purposes of plotting using the RooPlot class, a RooDataSet is binned into a histogram.

In general, working in RooFit with binned and unbinned data is very similar, as both class RooDataSet (for unbinned data) and class RooDataHist (for binned data) inherit from a common base class, RooAbsData, which defines the interface for a generic abstract data sample. With few exceptions, all RooFit methods take abstract datasets as input arguments, allowing for the interchangeable use of binned and unbinned data.

RooDataSet (unbinned data)

Example code: generating toy Monte Carlo, storing it as unbinned data and then plotting it

}
// Create a RooDataSet and fill it with generated toy Monte Carlo data:
RooDataSet* myData = gauss.generate(x, 100);
// Plot the dataset.
RooPlot* myFrame = x.frame();
myData.plotOn()(myFrame);
myFrame.Draw();
}



Plotting unbinned data is similar to plotting binned data with the exception that one can show it in some preferred binning.

Example code: plotting unbinned data (a RooDataSet) using a specified binning

RooPlot* myFrame = x.frame() ;
myData.plotOn(myFrame, Binning(25)) ;
myFrame->Draw()



Importing data from ROOT trees (how to populate RooDataSets from TTrees)

* Put stuff here, Will. *

RooDataHist (binned data)

Importing data from ROOT TH histogram objects (take a histogram and map it to a binned data set) (how to populate RooDataHists from histograms)

In RooFit, binned data is represented by the RooDataHist class. The contents of a ROOT histogram can be imported into a RooDataHist object. In importing a ROOT histogram, the binning of the original histogram is imported as well. A RooDataHist associates the histogram with a RooFit variable object of type RooRealVar. In this way it is always known what kind of data is stored in the histogram.

In displaying the data, RooFit, by default, shows the 68% confidence interval for Poisson statistics.

Example code: import a ROOT histogram into a RooDataHist (a RooFit binned dataset)

{
// Access the file.
TFile* myFile = new TFile("myFile.root");
TH1* myHistogram = (TH1*) myFile->Get("myHistogram");
myHistogram.Draw();

// Declare an observable x.
RooRealVar x("x", "x", -1, 2);

// Create a binned dataset that imports the contents of TH1 and associates its contents to observable 'x'.
RooDataHist myData("myData", "myData", RooArgList(x), myHistogram);

// Plot the imported dataset.
RooPlot* myFrame = x.frame();
myData.plotOn(myFrame)
myFrame.Draw()
}



Fitting

Fitting a model to data

Fitting a model to data can be done in many ways. The most common methods are the χ2 fit and the -log(L) fit. The default fitting method in ROOT is the χ2 method, while the default method in RooFit is the -log(L) method. The -log(L) method is often preferred because it is more robust for low statistics fits and because it can also be performed on unbinned data.

Fitting a PDF to unbinned data

Example code: fit a Gaussian PDF to data

// Fit gauss to unbinned data
gauss.fitTo(*myData);



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RooStats

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General description
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General description

RooStats provides tools for high-level statistics questions in ROOT. It builds on RooFit, which provides basic building blocks for statistical questions.

The main goal is to standardise the interface for major statistical procedures so that they can work on an arbitrary RooFit model and dataset and handle any parameters of interest and nuisance parameters. Another goal is to implement most accepted techniques from frequentist, Bayesian and likelihood based approaches. A further goal is to provide utilities to perform combined measurements.

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Datasets

In RooFit, data can be stored in an unbinned or binned manner. Unbinned data is stored using the RooDataSet class while binned data is stored using the RooDataHist class. The user can define how many bins there are in a variable. For the purposes of plotting using the RooPlot class, a RooDataSet is binned into a histogram.

Example code: generating toy Monte Carlo, storing it as unbinned data and then plotting it


}
// Create a RooDataSet and fill it with generated toy Monte Carlo data:
RooDataSet* myData = gauss.generate(x, 100);
// Plot the dataset.
RooPlot* myFrame = x.frame();
myData.plotOn()(myFrame);
myFrame.Draw();
}



Importing data (how to populate datasets from histograms and TTrees)

Importing data from ROOT trees

* Put stuff here, Will. *

Importing data from ROOT TH histogram objects (take a histogram and map it to a binned data set)

Example code: import a ROOT histogram into a RooDataHist (a RooFit binned dataset)

{
// Access the file.
TFile* myFile = new TFile("myFile.root");
TH1* myHistogram = myFile.Get("myHistogram");
myHistogram.Draw();

// Declare an observable x.
RooRealVar x("x", "x", -1, 2);

// Create a binned dataset that imports the contents of TH1 and associates its contents to observable 'x'.
RooDataHist myData("myData", "myData", RooArgList(x), myHistogram);

// Plot the imported dataset.
RooPlot* myFrame = x.frame();
myData.plotOn(myFrame)
myFrame.Draw()
}



Fitting

Fitting a PDF to unbinned data

Example code: fit a Gaussian PDF to data

// Fit gauss to unbinned data
gauss.fitTo(*myData);



Example code: create a simple model using the RooFit Workspace Factory. Specify parts of the model using ModelConfig. Create a simple dataset. Complete a confidence interval test using the ProfileLikelihoodCalculator of RooStats





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HistFactory

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General description

The HistFactory can be used to run an analysis without being a RooFit/RooStats expert. In a nutshell, ROOT files containing input histograms are set up and XML files are set up for those input ROOT files. The XML files specify details on the histograms and specify how RooFit should interpret the information in the files. An little executable contained in ROOT called hist2workspace is used to import the histograms into a RooFit workspace appropriately.

The ROOT release ships with a script called prepareHistFactory and a binary file called hist2workspace in the $ROOTSYS/bin directories. prepareHistFactory prepares a working area. It creates results/, data/ and config/ directories. It copies the HistFactorySchema.dtd and example XML files into the config/ directory. Also, it copies a ROOT file into the data/ directory for use with the examples. HistFactorySchema.dtd Changed: < < HistFactorySchema.dtd: This file is located in$ROOTSYS/etc/ specifies the XML schema. It is typically placed in the config/ direc-tory of a working area together with the top-level XML file and the individual channel XML files. The user should not modify this file. The HistFactorySchema.dtd is commented to specify exactly the meaning of the various options.
>
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HistFactorySchema.dtd: This file is located in $ROOTSYS/etc/ specifies the XML schema. It is typically placed in the config/ directory of a working area together with the top-level XML file and the individual channel XML files. The user should not modify this file. The HistFactorySchema.dtd is commented to specify exactly the meaning of the various options. hist2workspace Revision 212011-08-15 - WilliamBreadenMadden Line: 1 to 1  META TOPICPARENT name="WebHome" -- WilliamBreadenMadden - 2011-08-15 Line: 226 to 226 RooAbsPdf* myPDF = myWorkspace.pdf("g"); // Import the data saved as d. RooAbsData* myData = myWorkspace.data("d"); Added: > > // Import the ModelConfig saved as m. ModelConfig* myModelConfig = (ModelConfig*) myWorkspace.obj("m"); Revision 202011-08-15 - WilliamBreadenMadden Line: 1 to 1  META TOPICPARENT name="WebHome" Changed: < < -- WilliamBreadenMadden - 2011-08-11 > > -- WilliamBreadenMadden - 2011-08-15 Line: 122 to 122  list of space points RooAbsData integral RooRealIntegral Changed: < < Composite functions correspond to composite objects. > > Composite functions correspond to composite objects. The ArgSet class is dependent on argument order while the ArgList class is not. Example code: defining a RooFit variable Revision 192011-08-15 - WilliamBreadenMadden Line: 1 to 1  META TOPICPARENT name="WebHome" -- WilliamBreadenMadden - 2011-08-11 Line: 255 to 255 // RooGaussian::G[ x=x mean=mu sigma=sigma ] = 1 // sigma.Print() // RooRealVar::sigma = 5 L(0 - 20) Added: > > // Print the PDF contents in a detailed manner. myGaussianPDF.Print("verbose"); // Print the PDF contents to stdout. myGaussianPDF.Print("t"); // Example output: Revision 182011-08-11 - WilliamBreadenMadden Line: 1 to 1  META TOPICPARENT name="WebHome" -- WilliamBreadenMadden - 2011-08-11 Line: 496 to 496 Specific instructions Changed: < < Specify which bins to use inclusively using the Measurement tag attributes BinLow and BinHigh. > > There are several parts in the top-level XML file. Initially, the XML schema is specified. The output is specified next. Specifically, the prefix for any output files (ROOT files containing workspaces) is given. Now, the channel XML files are given for each measurement (e.g., signal, background, systematics information) using the Input tag. Next, the details for each channel are defined using the Measurement tag. Which bins to use are specified inclusively using the Measurement tag attributes BinLow and BinHigh. Within the Measurement tag, the POI tag is used to specify the point of interest for the channel, i.e. the test statistic. Example file:$ROOTSYS/tutorials/histfactory/example.xml

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• a name (which can be shared with the OverallSyst if correlated).
• +/- 1 sigma variational histograms.
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* text *

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General description

This file specifies a top level 'Combination' that is composed of:
• several 'Channels', which are described in separate XML files.
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• whether the tool should export the model only and skip the default fit.
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Specific instructions

Specify which bins to use inclusively using the Measurement tag attributes BinLow and BinHigh.

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General description

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This file specifies for each channel
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These files specify for each channel

• observed data (if absent, the tool will use the expectation, which is useful for expected sensitivity)
• several 'Samples' (e.g., signal, bkg1, bkg2 etc.), each of which specifies
• a name.
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• a name (which can be shared with the OverallSyst if correlated).
• +/- 1 sigma variational histograms.
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HistFactorySchema.dtd: This file is located in $ROOTSYS/etc/ specifies the XML schema. It is typically placed in the config/ direc-tory of a working area together with the top-level XML file and the individual channel XML files. The user should not modify this file. The HistFactorySchema.dtd is commented to specify exactly the meaning of the various options. hist2workspace The hist2workspace executable is used in the following manner: hist2workspace input.xml Top-Level XML file Example:$ROOTSYS/tutorials/histfactory/example.xml

This file specifies a top level 'Combination' that is composed of:

• several 'Channels', which are described in separate XML files.
• several 'Measurements' (corresponding to a full fit of the model), each of which specifies
• a name for this measurement to be used in tables and files.
• the luminosity associated with the measurement in picobarns.
• which bins of the histogram should be used.
• what the relative uncertainty on the luminosity is.
• what is(/are) the parameter(/s) of interest that will be measured.
• which parameter(/s) should be fixed/floating (e.g., nuisance parameters)
• which type of constriants are desired:
• default: Gaussian
• supported: Gamma, LogNormal, Uniform
• whether the tool should export the model only and skip the default fit.

Channel XML files

Example: \$ROOTSYS/tutorials/histfactory/example_channel.xml

This file specifies for each channel

• observed data (if absent, the tool will use the expectation, which is useful for expected sensitivity)
• several 'Samples' (e.g., signal, bkg1, bkg2 etc.), each of which specifies
• a name.
• whether the sample is normalized by theory (e.g., N = L * sigma) or whether the sample is data driven.
• a nominal expectation histogram.
• a named 'Normalization Factor' (which can be fixed or allowed to float in a fit).
• several 'Overall Systematics' in normalization with
• a name.
• +/- 1 sigma variations (e.g., 1.05 and 0.95 for a 5% uncertainty).
• several 'Histogram Systematics' in shape with
• a name (which can be shared with the OverallSyst if correlated).
• +/- 1 sigma variational histograms.

Further information

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Example code: What's in the workspace?




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Visual representations of the model/PDF contents

Graphviz

Graphviz consists of a graph description language called the DOT language and a set of tools that can generate and/or process DOT files.

Example code: examining PDFs and creating graphical representations of them


// Create variables and a PDF using those variables.
RooRealVar mu("mu", "mu", 150);
RooRealVar sigma("sigma", "sigma", 5, 0, 20);
RooGaussian myGaussianPDF("myGaussianPDF", "Gaussian PDF", x, mu, sigma);
// Create a Graphviz DOT file with a representation of the object tree.
myGaussianPDF.graphVizTree("myGaussianPDFTree.dot");
// This produced DOT file can be converted to some graphical representation:
// Convert the DOT file to a 'top-to-bottom graph' using UNIX commands:
// dot -Tgif -o myGaussianPDF_top-to-bottom_graph.gif myGaussianPDFTree.dot
// Convert the DOT file to a 'spring-model graph' using UNIX commands:
// fdp -Tgif -o myGaussianPDF_spring-model_graph.gif myGaussianPDFTree.dot
// Print the PDF contents.
myGaussianPDF.Print();
// Example output:
// RooGaussian::G[ x=x mean=mu sigma=sigma ] = 1
// sigma.Print()
// RooRealVar::sigma = 5  L(0 - 20)
// Print the PDF contents to stdout.
myGaussianPDF.Print("t");
// Example output:
// 0x166eab0 RooGaussian::G = 1 [Auto]
// 0x15f7fe0/V- RooRealVar::x = 150
// 0x1487090/V- RooRealVar::mu = 150
// 0x1487bc0/V- RooRealVar::sigma = 5
// Print the PDF contents to a file.
myGaussianPDF.printCompactTree("", "myGaussianPDFTree.txt")
// Example output file contents:
// 0x166eab0 RooGaussian::G = 1 [Auto]
// 0x15f7fe0/V- RooRealVar::x = 150
// 0x1487090/V- RooRealVar::mu = 150
// 0x1487bc0/V- RooRealVar::sigma = 5



Example code: accessing the workspace


// Open the appropriate ROOT file.
root -l BR5_MSSM_signal90_combined_datastat_model.root


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// Alternatively, you could open the file in a manner such as the following: myFileName = "BR5_MSSM_signal90_combined_datastat_model.root" TFile *myFile = TFile::Open(myFileName);
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myWorkspace = (RooWorkspace*) _file0->Get("combined");
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RooWorkspace* myWorkspace = (RooWorkspace*) _file0->Get("combined");
// Print the workspace contents. myWorkspace->Print(); // Import the PDF.
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Example code: Using both data and PDF from file


// Note that the following code is independent of actual PDF in the file. So, for example, a full Higgs combination could work with identical code.

// Open a file and import the workspace.
TFile myFile("myResults.root") ;
RooWorkspace* myWorkspace = f.Get("myWorkspace") ;
// Plot the data and PDF
RooPlot* xframe = w->var("x")->frame() ;
w->data("d")->plotOn(xframe) ;
w->pdf("g")->plotOn(xframe) ;
// Construct a likelihood and profile likelihood
RooNLLVar nll("nll","nll",*myWorkspace->pdf("g"),*w->data("d")) ;
RooProfileLL pll("pll","pll", nll,*myWorkspace->var("m")) ;
RooPlot* myFrame = w->var("m")->frame(-1,1) ;
pll.plotOn(myFrame) ;
myFrame->Draw()



RooStats

RooStats provides tools for high-level statistics questions in ROOT. It builds on RooFit, which provides basic building blocks for statistical questions.

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The RooFit workspace

The RooFit "workspace" provides the ability to store the full likelihood model, any desired priors and the minimal data necessary to reproduce the likelihood function in a ROOT file. Thus, the workspace is needed for combinations and has potential for digitally publishing results (PhyStats agreed to publish likelihood functions). The RooFit workspace can be used for this.
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myWorkspace = (RooWorkspace*) _file0->Get("myWorkspace"); // Print the workspace contents. myWorkspace.Print();
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// Example printout:

variables --------- (x,m,s)

p.d.f.s ------- RooGaussian::g[ x=x mean=m sigma=s ] = 0

datasets -------- RooDataSet::d(x)

// Import the variable saved as x. RooRealVar* myVariable = myWorkspace.var("x"); // Import the PDF saved as g. RooAbsPdf* myPDF = myWorkspace.pdf("g"); // Import the data saved as d. RooAbsData* myData = myWorkspace.data("d");

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myWorkspace->Print(); // Import the PDF. RooAbsPdf* myPDF = myWorkspace->pdf("model_BR5_MSSM_signal90");
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// Import the variable for the observable.
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// Import the variable representing the observable.
RooRealVar* myObservable = myWorkspace->var("obs"); // Create a RooPlot frame using the imported variable.. RooPlot* myFrame = myObservable.frame();
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myPDF.plotOn(myFrame); // Draw the RooPlot. myFrame->Draw();
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RooStats

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// Create a Gaussian PDF using the Workspace Factory (this is essentially the shorthand for creating a Gaussian). RooWorkspace* myWorkspace = new RooWorkspace("myWorkspace"); myWorkspace->factory("Gaussian::g(x[-5, 5], mu[0], sigma[1]");
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Example code: What's in the workspace?


// Open the appropriate ROOT file.
root -l myFile.root
// Import the workspace.
myWorkspace = (RooWorkspace*) _file0->Get("myWorkspace");
// Print the workspace contents.
myWorkspace.Print();


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Example code: accessing the workspace


// Open the appropriate ROOT file.
root -l BR5_MSSM_signal90_combined_datastat_model.root
// Import the workspace.
myWorkspace = (RooWorkspace*) _file0->Get("combined");
// Print the workspace contents.
myWorkspace->Print();
// Import the PDF.
RooAbsPdf* myPDF = myWorkspace->pdf("model_BR5_MSSM_signal90");
// Import the variable for the observable.
RooRealVar* myObservable = myWorkspace->var("obs");
// Create a RooPlot frame using the imported variable..
RooPlot* myFrame = myObservable.frame();
// Plot the PDF on the created RooPlot frame.
myPDF.plotOn(myFrame);
// Draw the RooPlot.
myFrame->Draw();



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RooStats provides tools for high-level statistics questions in ROOT. It builds on RooFit, which provides basic building blocks for statistical questions.

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Wiki
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RooStats User's Guide (draft)
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RooStats User's Guide
Tutorials
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HistFactory manual

E-group for support with ATLAS-sensitive information: <atlas-phys-stat-root@cern.ch>

E-mail support for software issues, bugs etc.: <roostats-development@cern.ch>

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PDFs

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One of the things that makes the RooFit PDFs nice and flexible (but perhaps counterintuitive) is that they have no idea what is considered the observable. For example, a Gaussian has x, the mean and sigma while the PDF is always normalised to unity. What is one doing performing the integration on in order to get 1? For the Gaussian, it is x, by convention; the mean and sigma are parameters of teh model. RooFit doesn't know that x is not special; x, the mean and sigma are all on equal footing.
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One of the things that makes the RooFit PDFs nice and flexible (but perhaps counterintuitive) is that they have no idea what is considered the observable. For example, a Gaussian has x, the mean and sigma while the PDF is always normalised to unity. What is one doing performing the integration on in order to get 1? For the Gaussian, it is x, by convention; the mean and sigma are parameters of teh model. RooFit doesn't know that x is not special; x, the mean and sigma are all on equal footing. You can tell it that x is the variable to normalise over.

So, RooGaussian has no intrinsic notion of distinction between observables and parameters. The choice of observables (for unit normalisation) is always passed to gauss.getVal().

What is the value of this? In a nutshell, it allows one to do Bayesian stuff very easily.

Bayes' theorem holds that the probability of b given a is related to the probability of a given b. Normally, one might say that the mean of a Gaussian is 1 and that then gives a distribution for x. However, if one had a dataset for x, one might want to know the posterior for the mean. The RooFit ability to switch who it is a probability density function of is very useful for Bayesian stuff. Because RooFit allows this composition, the thing that acts as x in the Gaussian could actually be a function of, say, x^2. You picked up a Jacobian factor in going from x to x^2, so the normalisation no longer makes sense. Sometimes RooFit can figure out what the Jacobian factor should be and sometimes it resorts to numerical integration.

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Example code: telling a RooFit PDF what to normalise over


Not normalised (i.e., this is not a PDF):
gauss.getVal();
Hey, RooFit! This is the thing to normalise over (i.e., guarantees Int[xmin, xmax] Gauss(x, m, s)dx == 1):
gauss.getVal(x);
What is the value if sigma is considered the observable? (i.e., guarantees Int[smin, smax] Gauss(x, m, s)ds == 1):


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Fitting a PDF to unbinned data

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A note on code and formatting

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Example code is generally indented and given highlighting. Explanatory code and text directly relating to it has yellow highlighting while example code that one might run directly in ROOT is given a green-text-on-black-background console style. Scripts are given grey highlighting.
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Example code is generally indented and given highlighting. Explanatory code and text directly relating to it has yellow highlighting while example code that one might run directly in ROOT is given a green-text-on-black-background console style. Scripts are given grey highlighting. So, in a nutshell, code segments are in yellow, while full scripts are in terminal. In code examples given, user-created objects are generally prefaced with "my", for example, "myData" for the purposes of clarity.

What is RooStats?

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A RooPlot is essentially an empty frame that is capable of holding anything plotted verses its variable.

PDFs

One of the things that makes the RooFit PDFs nice and flexible (but perhaps counterintuitive) is that they have no idea what is considered the observable. For example, a Gaussian has x, the mean and sigma while the PDF is always normalised to unity. What is one doing performing the integration on in order to get 1? For the Gaussian, it is x, by convention; the mean and sigma are parameters of teh model. RooFit doesn't know that x is not special; x, the mean and sigma are all on equal footing.

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Example code: create a Gaussian PDF using RooStats and plot it using the RooPlot class


{
// Build a Gaussian PDF.


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The RooFit "workspace" provides the ability to store the full likelihood model, any desired priors and the minimal data necessary to reproduce the likelihood function in a ROOT file. Thus, the workspace is needed for combinations and has potential for digitally publishing results (PhyStats agreed to publish likelihood functions). The RooFit workspace can be used for this.
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One might create a Gaussian PDF and then import it into a workspace. All of the dependencies of the Gaussian shall be drawn in and owned by the workspace. There are no nightmarish ownership problems. Alternatively, one might simply create the Gaussian inside the workspace using the Workspace Factory.

Example code: using the Workspace Factory to create a Gaussian PDF


// Create a Gaussian PDF using the Workspace Factory (this is essentially the shorthand for creating a Gaussian).
RooWorkspace* myWorkspace = new RooWorkspace("myWorkspace");
myWorkspace->factory("Gaussian::g(x[-5, 5], mu[0], sigma[1]");



RooStats

RooStats provides tools for high-level statistics questions in ROOT. It builds on RooFit, which provides basic building blocks for statistical questions.

The main goal is to standardise the interface for major statistical procedures so that they can work on an arbitrary RooFit model and dataset and handle any parameters of interest and nuisance parameters. Another goal is to implement most accepted techniques from frequentist, Bayesian and likelihood based approaches. A further goal is to provide utilities to perform combined measurements.

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Datasets

In RooFit, data can be stored in an unbinned or binned manner. Unbinned data is stored using the RooDataSet class while binned data is stored using the RooDataHist class. The user can defined how many bins there are in a variable. For the purposes of plotting using the RooPlot class, a RooDataSet is binned into a histogram.

Example code: generating toy Monte Carlo, storing it as unbinned data and then plotting it


}
// Create a RooDataSet and fill it with generated toy Monte Carlo data:
RooDataSet* myData = gauss.generate(x, 100);
// Plot the dataset.
RooPlot* myFrame = x.frame();
myData.plotOn()(myFrame);
myFrame.Draw();
}



Example code: generating toy Monte Carlo, storing it as unbinned data and then plotting it


// Fit gauss to unbinned data
gauss.fitTo(*myData);



Example code: create a simple model using the RooFit Workspace Factory. Specify parts of the model using ModelConfig. Create a simple dataset. Complete a confidence interval test using the ProfileLikelihoodCalculator of RooStats





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Higgs analysis at ATLAS using RooStats

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This page contains basic information on getting started with Higgs analysis at ATLAS using RooStats.
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