title: Using exact Poisson likelihood functions in Bayesian interpretation of counting measurements.
abstract: A technique for computing the exact marginalized (integrated) Poisson likelihood function for counting measurement processes involving a background subtraction is described. An empirical Bayesian method for determining the prior probability distribution of background count rates from population data is recommended and would seem to have important practical advantages. The exact marginalized Poisson likelihood function may be used instead of the commonly used Gaussian approximation. Differences occur in some cases of small numbers of measured counts, which are discussed. Optional use of exact likelihood functions in our Bayesian internal dosimetry codes has been implemented using an interpolation-table approach, which means that there is no computation time penalty except for the initial setup of the interpolation tables.
authors.affiliation: Los Alamos National Laboratory, NM 87545, USA. guthrie@lanl.gov
authors.forename: Guthrie
authors.initials: G
authors.lastname: Miller
authors.forename: Harry F
authors.initials: HF
authors.lastname: Martz
authors.forename: Tom T
authors.initials: TT
authors.lastname: Little
authors.forename: Ray
authors.initials: R
authors.lastname: Guilmette
mesh_terms: D001499:Bayes Theorem; D002138:Calibration; D016013:Likelihood Functions; D016012:Poisson Distribution; D011874:Radiometry / Q000379:methods*; D013223:Statistics as Topic