Simultaneous prediction of independent Poisson observables

Abstract

Simultaneous predictive distributions for independent Poisson observables are investigated. A class of improper prior distributions for Poisson means is introduced. The Bayesian predictive distributions based on priors from the introduced class are shown to be admissible under the Kullback–Leibler loss. A Bayesian predictive distribution based on a prior in this class dominates the Bayesian predictive distribution based on the Jeffreys prior.