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Spatiotemporal models for Poisson areal data with an application to the AIDS epidemic in Rio de Janeiro

We present a class of spatiotemporal models for Poisson areal data suitable for the analysis of emerging infectious diseases. These models assume Poisson observations related through a link equation to a latent random field process. This latent random field process evolves through time with proper Gaussian Markov random field convolutions. Our approach naturally accommodates flexible structures such as distinct but interacting temporal trends for each region and across-time contamination among neighboring regions. We develop a Bayesian analysis approach with a simulation-based procedure: specifically, we construct a Markov chain Monte Carlo algorithm based on the generalized extended Kalman filter to obtain samples from an approximate posterior distribution. Finally, for the comparison of Poisson spatiotemporal models, we develop a simulation-based conditional Bayes factor. We illustrate the utility and flexibility of our Poisson spatiotemporal framework with an application to the number of acquired immunodeficiency syndrome (AIDS) cases during the period 1982-2007 in Rio de Janeiro.