2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/86419We 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.CDF Statistics Committee http://www-cdf.fnal.gov/physics/statistics/ Report, LaTeX, 30 pages, 11 eps filesData Analysis, Statistics and Probabilitytext