Interval estimation in the presence of nuisance parameters. 1. Bayesian   approach
  We address the common problem of calculating intervals in the presence of systematic uncertainties. We aim to investigate several approaches, but here describe just a Bayesian technique for setting upper limits. The particular example we study is that of inferring the rate of a Poisson process when there are uncertainties on the acceptance and the background. Limit calculating software associated with this work is available in the form of C functions. 
Joel Heinrich, Craig Blocker, John Conway, Luc Demortier, Louis Lyons,   Giovanni Punzi and Pekka K. Sinervo