Meta-Kriging: Scalable Bayesian Modeling and Inference for Massive Spatial Datasets

ABSTRACT

Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations becomes large. There is a burgeoning literature on approaches for analyzing large spatial datasets. In this article, we propose a divide-and-conquer strategy within the Bayesian paradigm. 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 posterior distributions from each subset. Importantly, as often desired in spatial analysis, we offer full posterior predictive inference at arbitrary locations for the outcome as well as the residual spatial surface after accounting for spatially oriented predictors. We call this approach “spatial meta-kriging” (SMK). We do not need to store the entire data in one processor, and this leads to superior scalability. We demonstrate SMK with various spatial regression models including Gaussian processes with Matern and compactly supported correlation functions. The approach is intuitive, easy to implement, and is supported by theoretical results presented in the supplementary material available online. Empirical illustrations are provided using different simulation experiments and a geostatistical analysis of Pacific Ocean sea surface temperature data. Supplementary materials for this article are available online.

KEYWORDS:

• Bayesian inference
• Gaussian process models
• Low-rank models
• M-posterior
• Posterior consistency
• Spatial process models
• Tapered Gaussian processes