Bayesian Modeling of Discrete-Time Point-Referenced Spatio-Temporal Data

Discrete-time point-referenced spatio-temporal data are obtained by collecting observations at arbitrary but fixed spatial locations s(1),s(2),...,s(n) at regular intervals of time t := 1,2,...,T. They are encountered routinely in meteorological and environmental studies. Gaussian linear dynamic spatio-temporal models (LDSTMs) are the most widely used models for fitting and prediction with them. While Gaussian LDSTMs demonstrate good predictive performance at a wide range of scenarios, discrete-time point-referenced spatio-temporal data, often being the end product of complex interactions among environmental processes, are better modeled by nonlinear dynamic spatio-temporal models (NLDSTMs). Several such nonlinear models have been proposed in the context of precipitation, deposition, and sea-surface temperature modeling. Some of the above-mentioned models, although are fitted classically, dynamic spatio-temporal models with their complex dependence structure, are more naturally accommodated within the fully Bayesian framework. In this article, we review many such linear and nonlinear Bayesian models for discrete-time point-referenced spatio-temporal data. As we go along, we also review some nonparametric spatio-temporal models as well as some recently proposed Bayesian models for massive spatio-temporal data.