Hierarchical bayes simultaneous estimation of poisson means

Equal-size samples are observed from k Poisson populations having means Assuming an exchangeable two-stage prior, conjugate at the first stage and noninformative at the second stage, formulas for the posterior means, variances and covariances of the A.λ's are expressed as the ratio of one-dimensional integrals. Approximations to the hierarchical Bayes posterior means and variances are developed, which do not require numerical integration. The performance of the Bayes estimator compared with other estimators is studied through computer simulation, using the frequentist criterion of percentage risk reduction and the Bayes risk criterion of relative savings loss.