Multivariate spatial meta kriging

Abstract

This work extends earlier work on spatial meta kriging for the analysis of large multivariate spatial datasets as commonly encountered in environmental and climate sciences. Spatial meta-kriging partitions the data into subsets, analyzes each subset using a Bayesian spatial process model and then obtains 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, spatial meta kriging offers posterior predictive inference at arbitrary locations for the outcome as well as the residual spatial surface after accounting for spatially oriented predictors. Our current work explores spatial meta kriging idea to enhance scalability of multivariate spatial Gaussian process model that uses linear model co-regionalization (LMC) to account for the correlation between multiple components. The approach is simple, intuitive and scales multivariate spatial process models to big data effortlessly. A simulation study reveals inferential and predictive accuracy offered by spatial meta kriging on multivariate observations.