TRolke

class TRolke : public TObject

    protected:

      static Double_t Chi2Percentile(Double_t df, Double_t CL1)
             Double_t EvalLikeMod1(Double_t mu, Int_t x, Int_t y, Int_t z, Double_t e, Double_t tau, Double_t b, Int_t m, Int_t what)
             Double_t EvalLikeMod2(Double_t mu, Int_t x, Int_t y, Double_t em, Double_t e, Double_t sde, Double_t tau, Double_t b, Int_t what)
             Double_t EvalLikeMod3(Double_t mu, Int_t x, Double_t bm, Double_t em, Double_t e, Double_t sde, Double_t sdb, Double_t b, Int_t what)
             Double_t EvalLikeMod4(Double_t mu, Int_t x, Int_t y, Double_t tau, Double_t b, Int_t what)
             Double_t EvalLikeMod5(Double_t mu, Int_t x, Double_t bm, Double_t sdb, Double_t b, Int_t what)
             Double_t EvalLikeMod6(Double_t mu, Int_t x, Int_t z, Double_t e, Double_t b, Int_t m, Int_t what)
             Double_t EvalLikeMod7(Double_t mu, Int_t x, Double_t em, Double_t e, Double_t sde, Double_t b, Int_t what)
      static Double_t EvalMonomial(Double_t x, const Int_t* coef, Int_t N)
      static Double_t EvalPolynomial(Double_t x, const Int_t* coef, Int_t N)
      static Double_t InverseIncompleteGamma(Double_t df, Double_t CL1)
      static Double_t InverseNormal(Double_t CL1)
             Double_t LikeGradMod1(Double_t e, Double_t mu, Int_t x, Int_t y, Int_t z, Double_t tau, Int_t m)
             Double_t Likelihood(Double_t mu, Int_t x, Int_t y, Int_t z, Double_t bm, Double_t em, Double_t e, Int_t mid, Double_t sde, Double_t sdb, Double_t tau, Double_t b, Int_t m, Int_t what)
             Double_t LikeMod1(Double_t mu, Double_t b, Double_t e, Int_t x, Int_t y, Int_t z, Double_t tau, Int_t m)
             Double_t LikeMod2(Double_t mu, Double_t b, Double_t e, Int_t x, Int_t y, Double_t em, Double_t tau, Double_t v)
             Double_t LikeMod3(Double_t mu, Double_t b, Double_t e, Int_t x, Double_t bm, Double_t em, Double_t u, Double_t v)
             Double_t LikeMod4(Double_t mu, Double_t b, Int_t x, Int_t y, Double_t tau)
             Double_t LikeMod5(Double_t mu, Double_t b, Int_t x, Double_t bm, Double_t u)
             Double_t LikeMod6(Double_t mu, Double_t b, Double_t e, Int_t x, Int_t z, Int_t m)
             Double_t LikeMod7(Double_t mu, Double_t b, Double_t e, Int_t x, Double_t em, Double_t v)
                 void ProfLikeMod1(Double_t mu, Double_t& b, Double_t& e, Int_t x, Int_t y, Int_t z, Double_t tau, Int_t m)

    public:

                      TRolke(Double_t CL = 0.9, Option_t* option)
                      TRolke(const TRolke&)
              virtual ~TRolke()
             Double_t CalculateInterval(Int_t x, Int_t y, Int_t z, Double_t bm, Double_t em, Double_t e, Int_t mid, Double_t sde, Double_t sdb, Double_t tau, Double_t b, Int_t m)
       static TClass* Class()
             Double_t GetCL() const
             Double_t GetLowerLimit() const
             Double_t GetUpperLimit() const
      virtual TClass* IsA() const
              TRolke& operator=(const TRolke&)
                 void SetCL(Double_t CL)
         virtual void ShowMembers(TMemberInspector& insp, char* parent)
         virtual void Streamer(TBuffer& b)
                 void StreamerNVirtual(TBuffer& b)

Data Members

    protected:

      Double_t fCL          confidence level as a fraction [e.g. 90% = 0.9]
      Double_t fUpperLimit  the calculated upper limit
      Double_t fLowerLimit  the calculated lower limit

Class Description

  TRolke

  This class computes confidence intervals for the rate of a Poisson
  in the presence of background and efficiency with a fully frequentist
  treatment of the uncertainties in the efficiency and background estimate
  using the profile likelihood method.

   The signal is always assumed to be Poisson.

   It allows the following Models:

       1: Background - Poisson, Efficiency - Binomial  (cl,x,y,z,tau,m)
       2: Background - Poisson, Efficiency - Gaussian  (cl,xd,y,em,tau,sde)
       3: Background - Gaussian, Efficiency - Gaussian (cl,x,bm,em,sd)
       4: Background - Poisson, Efficiency - known     (cl,x,y,tau,e)
       5: Background - Gaussian, Efficiency - known    (cl,x,y,z,sdb,e)
       6: Background - known, Efficiency - Binomial    (cl,x,z,m,b)
       7: Background - known, Efficiency - Gaussian    (cl,x,em,sde,b)

  Parameter definition:

  cl  =  Confidence level

  x = number of observed events

  y = number of background events

  z = number of simulated signal events

  em = measurement of the efficiency.

  bm = background estimate

  tau = ratio between signal and background region (in case background is
  observed) ratio between observed and simulated livetime in case
  background is determined from MC.

  sd(x) = sigma of the Gaussian

  e = true efficiency (in case known)

  b = expected background (in case known)

  m = number of MC runs

  mid = ID number of the model ...

  For a description of the method and its properties:

  W.Rolke, A. Lopez, J. Conrad
  "A marvelous and completely perfect method without flaws"
  NiM xyz blabla

 Author: Jan Conrad (CERN)

 see example in tutorial Rolke.C

 Copyright CERN 2004                Jan.Conrad@cern.ch

 Calculates the Confidence Interval

 Chooses between the different profile likelihood functions to use for the
 different models.
 Returns evaluation of the profile likelihood functions.

 Calculates the Profile Likelihood for MODEL 1:
  Poisson background/ Binomial Efficiency
 what = 1: Maximum likelihood estimate is returned
 what = 2: Profile Likelihood of Maxmimum Likelihood estimate is returned.
 what = 3: Profile Likelihood of Test hypothesis is returned
 otherwise parameters as described in the beginning of the class)

 Profile Likelihood function for MODEL 1:
 Poisson background/ Binomial Efficiency

 Void needed to calculate estimates of efficiency and background for model 1

 Calculates the Profile Likelihood for MODEL 2:
  Poisson background/ Gauss Efficiency
 what = 1: Maximum likelihood estimate is returned
 what = 2: Profile Likelihood of Maxmimum Likelihood estimate is returned.
 what = 3: Profile Likelihood of Test hypothesis is returned
 otherwise parameters as described in the beginning of the class)

 Profile Likelihood function for MODEL 2:
 Poisson background/Gauss Efficiency

 Calculates the Profile Likelihood for MODEL 3:
 Gauss  background/ Gauss Efficiency
 what = 1: Maximum likelihood estimate is returned
 what = 2: Profile Likelihood of Maxmimum Likelihood estimate is returned.
 what = 3: Profile Likelihood of Test hypothesis is returned
 otherwise parameters as described in the beginning of the class)

 Profile Likelihood function for MODEL 3:
 Gauss background/Gauss Efficiency

 Calculates the Profile Likelihood for MODEL 4:
 Poiss  background/Efficiency known
 what = 1: Maximum likelihood estimate is returned
 what = 2: Profile Likelihood of Maxmimum Likelihood estimate is returned.
 what = 3: Profile Likelihood of Test hypothesis is returned
 otherwise parameters as described in the beginning of the class)

 Profile Likelihood function for MODEL 4:
 Poiss background/Efficiency known

 Calculates the Profile Likelihood for MODEL 5:
 Gauss  background/Efficiency known
 what = 1: Maximum likelihood estimate is returned
 what = 2: Profile Likelihood of Maxmimum Likelihood estimate is returned.
 what = 3: Profile Likelihood of Test hypothesis is returned
 otherwise parameters as described in the beginning of the class)

 Profile Likelihood function for MODEL 5:
 Gauss background/Efficiency known

 Calculates the Profile Likelihood for MODEL 6:
 Gauss  known/Efficiency binomial
 what = 1: Maximum likelihood estimate is returned
 what = 2: Profile Likelihood of Maxmimum Likelihood estimate is returned.
 what = 3: Profile Likelihood of Test hypothesis is returned
 otherwise parameters as described in the beginning of the class)

 Profile Likelihood function for MODEL 6:
 background known/ Efficiency binomial

 Calculates the Profile Likelihood for MODEL 7:
 background known/Efficiency Gauss
 what = 1: Maximum likelihood estimate is returned
 what = 2: Profile Likelihood of Maxmimum Likelihood estimate is returned.
 what = 3: Profile Likelihood of Test hypothesis is returned
 otherwise parameters as described in the beginning of the class)

 Profile Likelihood function for MODEL 6:
 background known/ Efficiency binomial

 Finds the Chi-square argument x such that the integral
 from x to infinity of the Chi-square density is equal
 to the given cumulative probability y.

 This is accomplished using the inverse gamma integral
 function and the relation
    x/2 = igami( df/2, y );

   Author Jan Conrad (CERN) Jan.Conrad@cern.ch
   Copyright by Stephen L. Moshier (Cephes Math Library)

 calculates the inverse of the incomplete (complemented)gamma integral
 for df degrees of freedom and fraction CL1
 * Given p, the function finds x such that
 Starting with the approximate value
          3
  x = df t

 where

  t = 1 - d - InverseNormal(p) sqrt(df)

 and

 d = 1/9df,

 the routine performs up to 10 Newton iterations to find the
 root of 1- TMath::Gamma(df,CL1) - p = 0.
 Author Jan Conrad (CERN) Jan.Conrad@cern.ch
 Copyright by Stephen L. Moshier (Cephes Math Library)

 evaluate polynomial

 evaluate mononomial

Inline Functions

           Double_t GetUpperLimit() const
           Double_t GetLowerLimit() const
           Double_t GetCL() const
               void SetCL(Double_t CL)
            TClass* Class()
            TClass* IsA() const
               void ShowMembers(TMemberInspector& insp, char* parent)
               void Streamer(TBuffer& b)
               void StreamerNVirtual(TBuffer& b)
             TRolke TRolke(const TRolke&)
            TRolke& operator=(const TRolke&)