1. Hands-on Session RooStats and TMVA Exercises

2. Getting Started A few advice words: Install version 5.25.02 locally
setting up
. root_Installaton_directory/bin/thisroot.sh (or .csh)
recommend to compile your macros and run with:
.x macro.C+; or .L macro.C+ then macro();,
include: using namespace RooFit; using namespace RooStats;,
avoid running a macro multiple times in the same ROOT session
If not working locally:
setting ROOT using the CERN AFS installation:
on SLC4:
/afs/cern.ch/sw/lcg/app/releases/ROOT/ /slc4_amd64_gcc34/root/bin/thisroot.csh or .sh

3. RooStats Exercises (1) Generate a Poisson Model (use RooFit factory)
Use RooStats calculators class to find limits, significances and produce plots
// Use a RooWorkspace to store the PDF models, prior
// informations, list of parameters, ...
myWS.factory("S[2,0,10]"); // default value 2 and range [0,10]
// Number of signal and background events
RooWorkspace myWS("myWS");
// Observable (dummy observable used)
myWS.factory("B[1]"); // value fixed to 1
// Signal and background distribution of the observable
myWS.var("x")->setBins(1);
myWS.factory("x[0,1]"); // arbitrary range [0,1]
myWS.factory("Uniform::bkgPdf(x)");
myWS.factory("Uniform::sigPdf(x)");
myWS.factory("ExtendPdf::modelBkg(bkgPdf,B)");
myWS.factory("SUM::model(S*sigPdf,B*bkgPdf");
// S+B and B-only models (both extended PDFs)
RooAbsData* data = myWS.pdf("model")->generateBinned(*myWS.var("x"),myWS.var("S")->getVal()+myWS.var("B")->getVal(),Name("data"));
// generate binned data with fixed number of events
//plot the data

4. ProfileLikelihood Exercise
ProfileLikelihoodCalculator
get interval:
get significance:
RooRealVar * S = myWS.var("S");RooArgSet POI(*S);RooAbsPdf * model = myWS.pdf("model");ProfileLikelihoodCalculator plc(*data,*model,POI);
//set thest sizeplc.SetTestSize(0.10);
model->fitTo(*data,SumW2Error(kFALSE));LikelihoodInterval * interval = plc.GetInterval();const double lowerLimit = interval->LowerLimit(*S);const double upperLimit = interval->UpperLimit(*S);LikelihoodIntervalPlot lplot(interval);lplot.Draw()
// Create a copy of the POI parameters to set the values to zeroRooArgSet nullparams;nullparams.addClone(*myWS.var("S"));((RooRealVar *) (nullparams.first()))->setVal(0);plc.SetNullParameters(nullparams);
HypoTestResult* plcResult = plc.GetHypoTest();const double significance = plcResult->Significance();
//get significance

5. Result
for S=2 you should get:
Significance =

6. Gaussian Model Generate Gaussian signal over flat background
systematics in sigma of mass and background
RooWorkspace myWS("myWS");
// ObservablemyWS.factory("mass[0,500]"); // range [0,500]// Signal and background distribution of the observable
myWS.factory("Gaussian::sigPdf(mass,200,sigSigma[0,100])") ;myWS.factory("Uniform::bkgPdf(mass)") ;myWS.factory("SUM::model(S[5,0,30]*sigPdf,B[10,0,100]*bkgPdf") ;// Background only pdfmyWS.factory("ExtendPdf::modelBkg(bkgPdf,B)") ;
// Prior for signalmyWS.factory("Uniform::priorPOI(S)") ;// Priors for nuisance parameters (signal + backg) myWS.factory("Gaussian::prior_sigSigma(sigSigma,50,5)") ;myWS.factory("Gaussian::prior_B(B,10,3)") ;myWS.factory("PROD::priorNuisance(prior_sigSigma,prior_B)") ;
RooAbsData * data = myWS.pdf("model")->generate(*myWS.set("observables"),Extended(),Name("data"));
myWS.defineSet("observables","mass");
// generate unbinned data

7. RooStats Exercise Compute:
68% CL 2-sided confidence interval and significance from the (profiled-) likelihood ratio
plot profile log-likelihood ratio
Frequentist p-value in the S+B and B-only hypotheses, signal significance, CL_S ratio (HybridCalculator)
Repeat including systematic uncertainty in the background and signal width
Use also Bayesian calculator , MCMCCalculator and Neyman construction for finding limits (with Poisson or Gaussian example)
More examples and code available in

8. HybridCalculator //Run and retrieve the results
HybridCalculator hc("hc","HybridCalculator",*data,*modelSB,*modelB);
hc.SetNumberOfToys(5000);
hs.SetTestStatistics(1);
//Run and retrieve the results
HybridResult* hcResult = hc.GetHypoTest();
double p_value_sb = hcResult->AlternatePValue();
double p_value_b = hcResult->NullPValue();
double cl_s = hcResult->CLs();
double significance = hcResult->Significance();
//Making a plot of the results
HybridPlot* hcPlot = hcResult->GetPlot("hcPlot","p-Values plot",100);
hcPlot->Draw();

9. Bayesian Calculator //Compute the credibility interval
BayesianCalculator bc(data,*model,RooArgSet(*POI),*priorPOI,&nuisanceParameters);
//Compute the credibility interval
//Set the confidence level of the credibility interval and compute it. Returns a SimpleInterval.
bc.SetTestSize(0.05);
SimpleInterval* interval = bc.GetInterval();
double lowerLimit = interval->LowerLimit();
double upperLimit = interval->UpperLimit();
// The code below produce a plot:
RooAbsPdf* fPosteriorPdf = bcalc.GetPosteriorPdf();
RooPlot* plot = POI->frame();
plot->SetTitle(TString("Posterior probability of parameter \"")+TString(POI->GetName())+TString("\""));
fPosteriorPdf->plotOn(plot,RooFit::Range(interval->LowerLimit(),interval->UpperLimit(),kFALSE),RooFit::VLines(),RooFit::DrawOption("F"),RooFit::MoveToBack(),RooFit::FillColor(kGray));
fPosteriorPdf->plotOn(plot);
plot->GetYaxis()->SetTitle("posterior probability");
plot->Draw();

10. RooStats Exercises (2) Generate a multi-dimensional model
have both S and mass as parameter of interest
Compare results of Profile likelihood, Neyman construction and MCMC calculator
examples are to be downloaded from:
run to generate data:
rs500e_PrepareWorkspace_GaussOverFlat_withSystematics_floatingMass.C
to run exercise:
rs501_ThreeTypesOfLimits.C

11. TMVA exercises Download macro code from
Try first generating different data-sets (use RooFit for doing it )
macro makesample.C
usage: makesample(int sampleID)
ID=0,1,2,3,4 depending on type of data to generate
Try and play with the various methods
macro driver.C
driver(Int_t sampleID = 0, TString obsList = "x,y,z", TString myMethodList = "Fisher,Likelihood,MLP,BDT")
Obtaine TMVA GUI from macro
produce plots of the signal and background distribution
look at the result, classifier outputs and performances (ROC curve )