On identification in Bayesian disease mapping and ecological-spatial regression models.

We discuss identification of structural characteristics of the underlying relative risks ensemble for posterior relative risks inference within Bayesian generalized linear mixed model framework for small-area disease mapping and ecological-spatial regression. We revisit conditionally specified and locally characterized Gaussian Markov random field risks ensemble priors in univariate disease mapping and communicate insight into Gaussian Markov random field variance-covariance characteristics for representing disease risks variability and spatial risks interactions and for structural identification with respect to risks ensemble prior choices. Illustrative examples of identification in Bayesian disease mapping and ecological-spatial regression models are presented for Bayesian hierarchical generalized linear mixed Poisson models and zero-inflated Poisson models.