Tree-structured multi-resolution spatial models (MRSMs) yield optimal and computationally feasible spatial smoothers of massive spatial data with nonstationary behavior. Instead of directly specifying the spatial variance-covariance (var-cov) structure for the process of interest (e.g., as in kriging), the MRSM specifies the joint var-cov structure indirectly through a stochastic, coarse-to-fine-resolution process model. The challenge is then to specify the var-cov components associated with the process model to reflect one's prior belief about the joint var-cov structure. We take an empirical-Bayes approach and present likelihood-based methods for the estimation and modeling of var-cov parameters associated each resolution of the process model. All the methods presented are resolution-specific; var-cov parameters associated with each spatial resolution are modeled and estimated separately. An application of the MRSMs is given to total column ozone (TCO) data obtained from a polar-orbiting satellite.
Meet the speaker in Room 212 Cockins Hall at 4:30 p.m. Refreshments will be served.