1. Alberto Ribon CERN Geant4Workshop Vancouver, September 2003 Tutorial of the Statistical Toolkit http://www.ge.infn.it/geant4/analysis/TandA

2. Alberto Ribon Test & Analysis Test & Analysis is a project to develop a statistical analysis system for usage in Geant4 testing Main application areas Main application areas Provide tools to compare Geant4 simulation results with reference data – equivalent reference distributions (for instance, regression testing) – experimental measurements – data libraries from reference distribution sources – functions deriving from theoretical calculations or from fits physics validation regression testing system testing What is the Test & Analysis project?

3. Alberto Ribon Team of Geant4 Test The performed tests were established with the help of: Vladimir Ivanchenko (CERN) Michel Maire (IN2P3/LAPP) Coordinators: Maria Grazia Pia (INFN, Genova) Andreas Pfeiffer (CERN) Realisation of tests: Pablo Cirrone (INFN Catania) Susanna Guatelli (Genova, CERN) Alfonso Mantero (Genova, ESA) Luciano Pandola (INFN, Gran Sasso) Automatisation/production of tests: Sandra Parlati (INFN, Gran Sasso) Statistical analysis: Stefania Donadio (INFN, Genova) Barbara Mascialino (INFN, Genova) Maria Grazia Pia (INFN, Genova) Andreas Pfeiffer (CERN) Alberto Ribon (CERN) Paolo Viarengo (IST, Genova)

4. Alberto Ribon Electromagnetic physics: Hadronic physics G4LowE G4Standard G4Penelope Particle CSDA range Particle Stopping Power Transmission coefficient Backscattering coefficient Gamma Attenuation coefficient Gamma processes cross section Particle range Bremmstrahlung energy spectrum Multiple scattering test Energy deposition in absorber material etc. Proton Bragg Peak Study of possible tests to perform Flexibility Plug-in test50

5. Alberto Ribon X-ray Attenuation Coefficient - Ge G4 Standard G4 LowE NIST-XCOM 2 N-L =26.3 – =23 - p=0.29 2 N-S =27.9 – =23 - p=0.22

6. Alberto Ribon CSDA Range – Al –G4LowE Geant4-05-02 NIST-ESTAR Geant4-05-00 Regression testing

7. Alberto Ribon Backscattering low energies - Au

8. Alberto Ribon Download/setup the Statistical Toolkit http://www.ge.infn.it/geant4/analysis/HEPstatistics Download : StatisticsTesting-V1-00-00.tgz tarball You also need to install the following libraries: 1) GSL (GNU Scientific Library) 2) AIDA 3.0 3) Anaphe 5.0.5 Edit the script buildAll.py to set the proper GSL path GSL_DIR=/afs/cern.ch/sw/lhcxx/specific/redhat73/gcc3.2/ PublicDomainPackages/2.0.0/ Run the script: $./buildAll.py

9. Alberto Ribon Statistiscal Tests available Currently the available statistical tests are: 1) Chi2 test (for binned distributions); 2) Kolmogorov-Smirnov test (for unbinned distributions). For the next future: 3) Cramer-von Mises test (for both binned and unbinned distributions); 4) Anderson-Darling test (for both binned and unbinned distributions); …

10. Alberto Ribon The AIDA classes you need to know AIDA::IHistogram1D : for 1-dimensional binned distribution AIDA::ICloud1D : for 1-dimensional unbinned distribution AIDA::IDataPointSet : vector of IDataPoint; IDataPoint : is a vector of IMeasurement; IMeasurement : (value, errorPlus, errorMinus).

11. Alberto Ribon The StatisticsTesting classes you need to know namespace StatisticsTesting { template // For instance: Chi2ComparisonAlgorithm, // KolmogorovSmirnovComparisonAlgorithm. class StatisticsComparator { public: ComparisonResult compare (const AIDA::IDataPointSet & dps1, const AIDA::IDataPointSet & dps2); ComparisonResult compare (const AIDA::IHistogram1D & histo1, const AIDA::IHistogram1D & histo2); ComparisonResult compare (const AIDA::ICloud1D & cloud1, const AIDA::ICloud1D & cloud2);... } class ComparisonResult { public: double distance( ); double quality ( ); double ndf ( );... }

12. Alberto Ribon Chi2 test between histograms #Include AIDA/AIDA.h #include StatisticsTesting/StatisticsComparator.h #include Chi2ComparisonAlgorithm.h #include ComparisonResult.h using namespace StatisticsTesting; std::auto_ptr af( AIDA_createAnalysisFactory() ); std::auto_ptr tf( af -> createTreeFactory() ); std::auto_ptr tree( tf -> create() ); std::auto_ptr hf( af->createHistogramFactory( *tree ) ); AIDA::IHistogram1D& hA = *( hf->createHistogram1D( "A", 100, 0.0, 50.0) ); AIDA::IHistogram1D& hB = *( hf->createHistogram1D( "B", 100, 0.0, 50.0) ); hA.fill( 15.7 );... hB.fill( 23.4 );... StatisticsComparator comparator; ComparisonResult result = comparator.compare( hA, hB ); std::cout << distance= << result.distance() << ndf= << result.ndf() << p-value= << result.quality();

13. Alberto Ribon Kolmorogov-Smirnov test between clouds #Include AIDA/AIDA.h #include StatisticsTesting/StatisticsComparator.h #include KolmogorovSmirnovComparisonAlgorithm.h" #include ComparisonResult.h using namespace StatisticsTesting; std::auto_ptr af( AIDA_createAnalysisFactory() ); std::auto_ptr tf( af -> createTreeFactory() ); std::auto_ptr tree( tf -> create() ); std::auto_ptr hf( af->createHistogramFactory( *tree ) ); AIDA::ICloud1D& cloudA = *( hf->createCloud1D( "A" ) ); AIDA::ICloud1D& cloudB = *( hf->createCloud1D( "B" ) ); cloudA.fill( 15.7 );... cloudB.fill( 23.4 );... StatisticsComparator comparator; ComparisonResult result = comparator.compare( cloudA, cloudB ); std::cout << K-S distance= << result.distance() << p-value= << result.quality();

14. Alberto Ribon Example of an XML data file http://aida.freehep.org/schemas/3.0/aida.dtd <dataPointSet dimension=2 name=attenuation coefficient path=/ title=attenuation coefficient in Ge> …

15. Alberto Ribon How to write a XML data file aFact = AIDA_createAnalysisFactory(); treeFact = aFact -> createTreeFactory(); … theTree = treeFact -> create(test50.xml, xml, false, true, uncompress ); dataPointFactory = aFact -> createDataPointSetFactory( *theTree ); particleTransmissionDataPoint = dataPointFactory -> create(Transmission test, 2); … particleTransmissionDataPoint -> addPoint(); AIDA::IDataPoint* point = particleTransmissionDataPoint -> point( PointNumber ); AIDA::IMeasurement* coordinateX = point -> coordinate( 0 ); coordinateX -> setValue( primaryParticleEnergy ); AIDA::IMeasurement* coordinateY = point -> coordinate( 1 ); coordinateY -> setValue( TransFraction ); coordinateY -> setErrorPlus( TransError ); coordinateY -> setErrorMinus( TransError ); … theTree -> commit(); theTree -> close();

16. Alberto Ribon How to compare XML dataPointSets #Include AIDA/AIDA.h #include StatisticsTesting/StatisticsComparator.h #include Chi2ComparisonAlgorithm.h #include ComparisonResult.h using namespace StatisticsTesting; std::auto_ptr af( AIDA_createAnalysisFactory() ); std::auto_ptr tf( af -> createTreeFactory() ); std::auto_ptr tree( tf -> create() ); std::auto_ptr dpsf( af -> createDataPointSetFactory( *tree ) ); std::auto_ptr treeXML1( tf -> create(gamma_lowE_Ge.xml, xml, true, false); std::auto_ptr treeXML2( tf -> create(NIST_attenuationGamma_Ge.xml, true, false); AIDA::IDataPointSet & dps1 = * ( dynamic_cast ( treeXML1 -> find(Gamma attenuation coefficient test ) ) ); AIDA::IDataPointSet & dps2 = * ( dynamic_cast ( treeXML2 -> find( Gamma attenuation coefficient test ) ) ); std::cout << title << dps1.title() << size= << dps1.size() << dimension= << dps1.dimension() StatisticsComparator comparator; ComparisonResult result = comparator.compare( dps1, dps2 ); std::cout << distance= << result.distance() << ndf= << result.ndf() << p-value= << result.quality();

17. Alberto Ribon ConclusionsConclusions The Statistical Toolkit provides already some important functionalities; It is already used in test50 for Geant4 physics tests and regression; it is simple to install and to use; we are working on the documentation; other statistical tests are under development; various long-term extensions are foreseen …