  In this note we present studies of coverage and power for confidence
intervals for a Poisson process with known background calculated using the
Likelihood ratio (aka Feldman & Cousins) ordering with Bayesian treatment of
uncertainties in nuisance parameters. We consider both the variant where the
Bayesian integration is done in both the numerator and the denominator and the
modification where the integration is done only in the numerator whereas in the
denominator the likelihood is taken at the maximum likelihood estimate of the
parameters. Furthermore we discuss how measurements can be combined in this
framework and give an illustration with limits on the branching ratio of a rare
B-meson decay recently presented by CDF/D0. A set of C++ classes has been
developed which can be used to calculate confidence intervals for single or
combining multiple experiments using the above algorithms and considering a
variety of parameterizations to describe the uncertainties.
