Simultaneous prediction for independent Poisson processes with different durations

Simultaneous predictive densities for independent Poisson observables are investigated. The observed data and the target variables to be predicted are independently distributed according to different Poisson distributions parametrized by the same parameter. The performance of predictive densities is evaluated by the Kullback-Leibler divergence. A class of prior distributions depending on the objective of prediction is introduced. A Bayesian predictive density based on a prior in this class dominates the Bayesian predictive density based on the Jeffreys prior.