Minimum risk, fixed cost sampling designs for independent Poisson processes - ARCHIVED

Optimal and approximately optimal fixed-cost Bayesian sampling designs are considered for simultaneous estimation in independent homogeneous Poisson processes. General allocation formulae are developed for a basic Poisson-Gamma model and these are compared with more traditional allocation methods. Techniques for finding representative gamma priors under more general hierarchical models are also discussed. The techniques show that, in many practical situations, these gamma priors provide reasonable approximations to the hierarchical prior and Bayes risk. The methods developed are general enough to apply to a wide variety of models and are not limited to Poisson processes.