Dimension reduced modeling of space-time processes with application to statistical downscaling

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 extremely computationally expensive when the datasets are large. Dimension-reduced modeling approach has proved to be effective in such situations. In this talk we focus on the problem of modeling two spatio-temporal processes where the primary goal is to predict one process from the other and where the datasets for both processes are large. We outline a general dimension-reduced Bayesian hierarchical approach where the spatial structures of both processes are modeled in terms of a low number of basis vectors, hence reducing the spatial dimension of the problem. The temporal evolution of the spatio-temporal processes and their dependence is then modeled through the coefficients (also called amplitudes) of the basis vectors. We present a new method of obtaining data-dependent basis vectors that are geared to the goal of predicting one process from the other: (Orthogonal) Maximum Covariance Patterns. We apply these methods to a statistical downscaling example, where surface temperatures on a coarse grid over the Antarctic are downscaled onto a finer grid.