TMVA::MethodLikelihood

    private:

      void GetSQRMats()
      void InitLik()

    public:

                              MethodLikelihood(TString jobName, vector<TString>* theVariables, TTree* theTree = 0, TString theOption = , TDirectory* theTargetDir = 0)
                              MethodLikelihood(vector<TString>* theVariables, TString theWeightFile, TDirectory* theTargetDir = NULL)
                              MethodLikelihood(const TMVA::MethodLikelihood&)
                      virtual ~MethodLikelihood()
               static TClass* Class()
                       Bool_t DecorrVarSpace()
             virtual Double_t GetMvaValue(TMVA::Event* e)
              virtual TClass* IsA() const
      TMVA::MethodLikelihood& operator=(const TMVA::MethodLikelihood&)
                 virtual void ReadWeightsFromFile()
                 virtual void ShowMembers(TMemberInspector& insp, char* parent)
                 virtual void Streamer(TBuffer& b)
                         void StreamerNVirtual(TBuffer& b)
                 virtual void Train()
                 virtual void WriteHistosToFile()
                 virtual void WriteWeightsToFile()

    private:

                       TFile* fFin               
      TMVA::PDF::SmoothMethod fSmoothMethod      
                        Int_t fNevt              total number of events in sample
                        Int_t fNsig              number of signal events in sample
                        Int_t fNbgd              number of background events in sample
                        Int_t fNsmooth           naumber of smooth passes
                     Double_t fEpsilon           minimum number of likelihood (to avoid zero)
                    TMatrixD* fSqS               square-root matrix for signal
                    TMatrixD* fSqB               square-root matrix for background
                vector<TH1*>* fHistSig           signal PDFs (histograms)
                vector<TH1*>* fHistBgd           background PDFs (histograms)
                vector<TH1*>* fHistSig_smooth    signal PDFs (smoothed histograms)
                vector<TH1*>* fHistBgd_smooth    background PDFs (smoothed histograms)
                       TList* fSigPDFHist        list of PDF histograms (signal)
                       TList* fBgdPDFHist        list of PDF histograms (background)
                vector<PDF*>* fPDFSig            list of PDFs (signal)    
                vector<PDF*>* fPDFBgd            list of PDFs (background)
                        Int_t fNbins             number of bins in reference histograms
                        Int_t fAverageEvtPerBin  average events per bin; used to calculate fNbins
                       Bool_t fDecorrVarSpace    flag for decorrelation method

Class Description

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Likelihood analysis ("non-parametric approach")

Also implemented is a "diagonalized likelihood approach", which improves over the uncorrelated likelihood ansatz by transforming linearly the input variables into a diagonal space, using the square-root of the covariance matrix

The method of maximum likelihood is the most straightforward, and certainly among the most elegant multivariate analyser approaches. We define the likelihood ratio, R_L, for event i, by:

Here the signal and background likelihoods, L_S, L_B, are products of the corresponding probability densities, p_S, p_B, of the N_var discriminating variables used in the MVA:
and accordingly for L_B. In practise, TMVA uses polynomial splines to estimate the probability density functions (PDF) obtained from the distributions of the training variables.

Note that in TMVA the output of the likelihood ratio is transformed by

to avoid the occurrence of heavy peaks at R_L=0,1. Decorrelated (or "diagonalized") Likelihood

The biggest drawback of the Likelihood approach is that it assumes that the discriminant variables are uncorrelated. If it were the case, it can be proven that the discrimination obtained by the above likelihood ratio is optimal, ie, no other method can beat it. However, in most practical applications of MVAs correlations are present.

Linear correlations, measured from the training sample, can be taken into account in a straightforward manner through the square-root of the covariance matrix. The square-root of a matrix C is the matrix C′ that multiplied with itself yields C: C=C′C′. We compute the square-root matrix (SQM) by means of diagonalising (D) the covariance matrix:

and the linear transformation of the linearly correlated into the uncorrelated variables space is then given by multiplying the measured variable tuple by the inverse of the SQM. Note that these transformations are performed for both signal and background separately, since the correlation pattern is not the same in the two samples.

The above diagonalisation is complete for linearly correlated, Gaussian distributed variables only. In real-world examples this is not often the case, so that only little additional information may be recovered by the diagonalisation procedure. In these cases, non-linear methods must be applied.

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 standard constructor

 MethodLikelihood options:
 format and syntax of option string: "Spline2:0:25:D"

 where:
  Splinei [i=1,2,3,5] - which spline is used for smoothing the pdfs
                   0  - how often the input histos are smoothed
                   25 - average num of events per PDF bin to trigger warning
                   D  - use square-root-matrix to decorrelate variable space

 construct likelihood references from file

 default initialisation called by all constructors

 destructor

 create reference distributions (PDFs) from signal and background events:
 fill histograms and smooth them; if decorrelation is required, compute
 corresponding square-root matrices

 returns the likelihood estimator for signal

 compute square-root matrices for signal and background

 write reference PDFs to file

 read reference PDFs from file

 write histograms and PDFs to file for monitoring purposes

 additional accessor