Bayesian dynamic modeling for large space-time datasets using Gaussian predictive processes

In this paper, we extend the applicability of a previously proposed class of dynamic space-time models by enabling them to accommodate large datasets. We focus on the common setting where space is viewed as continuous but time is taken to be discrete. Scalability is achieved by using a low-rank predictive process to reduce the dimensionality of the data and ease the computational burden of estimating the spatio-temporal process of interest. The proposed models are illustrated using weather station data collected over the northeastern United States between 2000 and 2005. Here our interest is to use readily available predictors, association among measurements at a given station, as well as dependence across space and time to improve prediction for incomplete station records and locations where station data does not exist.