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

Abstract

Discrete-time point-referenced spatio-temporal data are obtained by collecting observations at arbitrary but fxed spatial loca‑ tions s1,s2, ... ,sn 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 ftting and prediction with them. While Gauss‑ ian 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 ftted classically, dynamic spatio-temporal models with their complex depend‑ ence structure, are more naturally accommodated within the fully Bayes‑ ian 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-tem‑ poral models as well as some recently proposed Bayesian models for massive spatio-temporal data