Estimation in Bayesian Disease Mapping
Summary Recent work on Bayesian inference of disease mapping models discusses the advantages of the fully Bayesian (FB) approach over its empirical Bayes (EB) counterpart, suggesting that FB posterior standard deviations of small‐area relative risks are more reflective of the uncertainty associated with the relative risk estimation than counterparts based on EB inference, since the latter fail to account for the variability in the estimation of the hyperparameters. In this article, an EB bootstrap methodology for relative risk inference with accurate parametric EB confidence intervals is developed, illustrated, and contrasted with the hyperprior Bayes. We elucidate the close connection between the EB bootstrap methodology and hyperprior Bayes, present a comparison between FB inference via hybrid Markov chain Monte Carlo and EB inference via penalized quasi‐likelihood, and illustrate the ability of parametric bootstrap procedures to adjust for the undercoverage in the “naive” EB interval estimates. We discuss the important roles that FB and EB methods play in risk inference, map interpretation, and real‐life applications. The work is motivated by a recent analysis of small‐area infant mortality rates in the province of British Columbia in Canada.