class TRolke: public TObject

  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.

  The method is very similar to the one used in MINUIT (MINOS).

  Two options are offered to deal with cases where the maximum likelihood
  estimate (MLE) is not in the physical region. Version "bounded likelihood"
  is the one used by MINOS if bounds for the physical region are chosen. Versi//  on "unbounded likelihood (the default) allows the MLE to be in the 
  unphysical region. It has however better coverage.
  For more details consult the reference (see below).


   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 and Fred James
  "Limits and Confidence Intervals in presence of nuisance parameters"
   http://lanl.arxiv.org/abs/physics/0403059
   Nucl.Instrum.Meth.A551:493-503,2005

  Should I use TRolke, TFeldmanCousins, TLimit?

  1. I guess TRolke makes TFeldmanCousins obsolete?

  Certainly not. TFeldmanCousins is the fully frequentist construction and
  should be used in case of no (or negligible uncertainties). It is however
  not capable of treating uncertainties in nuisance parameters.
  TRolke is desined for this case and it is shown in the reference above
  that it has good coverage properties for most cases, ie it might be
  used where FeldmannCousins can't.

  2. What are the advantages of TRolke over TLimit?

  TRolke is fully frequentist. TLimit treats nuisance parameters Bayesian.
  For a coverage study of a Bayesian method refer to
  physics/0408039 (Tegenfeldt & J.C). However, this note studies
  the coverage of Feldman&Cousins with Bayesian treatment of nuisance
  parameters. To make a long story short: using the Bayesian method you
  might introduce a small amount of over-coverage (though I haven't shown it
  for TLimit). On the other hand, coverage of course is a not so interesting
  when you consider yourself a Bayesian.

 Author: Jan Conrad (CERN)

 see example in tutorial Rolke.C

 Copyright CERN 2004                Jan.Conrad@cern.ch