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Title: A uniform shrinkage prior in spatio-temporal Poisson models for count data Authors:  Yisheng Li - The University of Texas MD Anderson Cancer Center (United States) [presenting]
Abstract: Default Bayesian inference is considered in a Poisson generalized linear mixed model for spatio-temporal data. Normal random effects are used to model the within-area correlation over time and spatial effects represented with a proper conditional autoregressive model are used to model the between-area correlations. We develop a uniform shrinkage prior for the variance components of the spatiotemporal random effects. We prove that the proposed USP is proper, and the resulting posterior is proper under the proposed USP, an independent flat prior for each fixed effect, and a uniform prior for a spatial parameter, under suitable conditions. Posterior simulation is implemented and inference is made using the OpenBUGS, R2OpenBUGS and RStan software packages. We illustrate the proposed method by applying it to a leptospirosis count dataset with observations from 17 northern provinces of Thailand across four quarters in 2011 to construct the disease maps. According to the deviance information criterion, the proposed USP for the variance components of the spatiotemporal effects yields better performance than the conventional inverse gamma priors. A simulation study suggests that the estimated fixed-effect parameters are accurate, based on a relative bias criterion.