  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.
