UCSC-SOE-17-07: Meta-Kriging: Scalable Bayesian Modeling and Inference for Large Spatial Datasets

Rajarshi Guhaniyogi and Sudipto Banerjee
05/09/2017 01:03 PM
Applied Mathematics & Statistics
Spatial process models for analyzing geostatistical data entail computations that
become prohibitive as the number of spatial locations becomes large. There is a bur-
geoning 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 optimally combining
the individual posterior distributions from each subset. Importantly, as is 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 ori-
ented 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 pro-
cesses and tapered Gaussian processes. The approach is intuitive, easy to implement,
and is supported by theoretical results that we develop here. Empirical illustrations
are provided using different simulation experiments and a geostatistical analysis of the
Pacific ocean sea surface temperature data.