Department of Biostatistics

Spatial process models for analyzing geostatistical data entail computations that become prohibitive asthe number of spatial locations becomes large. There is a burgeoning literature on approaches for analyzinglarge spatial datasets. In this article, we propose a divide-and-conquer strategy within the Bayesianparadigm. We partition the data into subsets, analyze each subset using a Bayesian spatial process model,and then obtain approximate posterior inference for the entire dataset by combining the individual posteriordistributions from each subset. Importantly, as often desired in spatial analysis, we offer full posteriorpredictive inference at arbitrary locations for the outcome as well as the residual spatial surface afteraccounting for spatially oriented predictors. We call this approach “spatial meta-kriging” (SMK). We do notneed to store the entire data in one processor, and this leads to superior scalability. We demonstrate SMKwith various spatial regression models including Gaussian processeswithMatern and compactly supportedcorrelation functions. The approach is intuitive, easy to implement, and is supported by theoretical resultspresented in the supplementary material available online. Empirical illustrations are provided using differentsimulation experiments and a geostatistical analysis of Pacific Ocean sea surface temperature data.Supplementary materials for this article are available online.