A Bayesian latent process spatiotemporal regression model for areal count data

Model-based approaches for the analysis of areal count data are commonplace in spatiotemporal analysis. In Bayesian hierarchical models, a latent process is incorporated in the mean function to account for dependence in space and time. Typically, the latent process is modelled using a conditional autoregressive (CAR) prior. The aim of this paper is to offer an alternative approach to CAR-based priors for modelling the latent process. The proposed approach is based on a spatiotemporal generalization of a latent process Poisson regression model developed in a time series setting. Spatiotemporal dependence in the autoregressive model for the latent process is modelled through its transition matrix, with a structured covariance matrix specified for its error term. The proposed model and its parameterizations are fitted in a Bayesian framework implemented via MCMC techniques. Our findings based on real-life examples show that the proposed approach is at least as effective as CAR-based models.