Multilevel Boundary Conditioning for Large Spatial Data Sets

• Activity Number: 89
• Type: Invited
• Date/Time: Sunday, August 9, 2015 : 8:30 PM to 9:15 PM
• Sponsor: Korean International Statistical Society
• Author(s): Zhen Zhang* and Michael L. Stein and Mihai Anitescu
• Companies: The University of Chicago and The University of Chicago and Argonne National Laboratory
• Keywords: Partitioning models ; Gaussian processes ; Spatial statistics ; Massive data sets ; Data visualization ; Parallel computing

Abstract

Partitioning models have been recently adopted and developed for decomposing a spatial domain with a large number of observations into a collection of relatively smaller subregions, which are individually modeled with Gaussian processes. However, for extremely large, irregularly spaced spatial data sets, some subregions may still have a large data size that causes issues in both computation and storage. We propose a model-based partitioning method called multilevel boundary conditioning for obtaining both data-driven models and computational efficiency. The tractable data size of subregions can be achieved by specifying or exploring different levels of decomposition of the precision matrix that admits sparsity. Other desired features include explicit communications between subregions for learning the spatial parameters, smooth predictions near the boundaries, and high parallelizability of the sampling scheme. We demonstrate the features of the proposed method and evaluate the performance in computation through a series of numerical studies and real data examples. We further discuss the applications in large spatial data mapping and visualization.