Bayesian Hierarchical Spatial-temporal Modeling

Abstract

Spatial time series are commonly observed in environmental sciences and epidemiological research where, under most circumstances, the time series are non-stationary. For better estimation and prediction, the temporal-variability must be captured in traditional spatial models. We propose a Bayesian hierarchical spatial-temporal model to describe the dependence of time series data on spatial locations while accounting for time series properties. The first layer of the hierarchical model specifies a measurement process for the observed spatial data. The second layer characterizes a latent mean process and a latent variance process. The hierarchical formulation concludes with a third layer of priors on parameters. A key idea is to model spatial and temporal dependence simultaneously. Statistical inference is performed by Markov chain Monte Carlo methods which involve spatial dependence parameters. The methodology is applied to simulated data and real environmental data for illustration.