Dimension-Reduced Modeling of Spatio-Temporal Processes

The field of spatial and spatio-temporal statistics is increasingly faced with the challenge of very large datasets. The classical approach to spatial and spatio-temporal modeling is very computationally demanding when datasets are large, which has led to interest in methods that use dimension-reduction techniques. In this article, we focus on modeling of two spatio-temporal processes where the primary goal is to predict one process from the other and where datasets for both processes are large. We outline a general dimension-reduced Bayesian hierarchical modeling approach where spatial structures of both processes are modeled in terms of a low number of basis vectors, hence reducing the spatial dimension of the problem. Temporal evolution of the processes and their dependence is then modeled through the coefficients of the basis vectors. We present a new method of obtaining data-dependent basis vectors, which is geared toward the goal of predicting one process from the other. We apply these methods to a statistical downscaling example, where surface temperatures on a coarse grid over Antarctica are downscaled onto a finer grid. Supplementary materials for this article are available online.