Bayesian copula-based spatial random effects models for inference with complex spatial data

Abstract: In this article, we develop fully Bayesian, copula-based, spatial-statistical models for large, noisy, incomplete, and non-Gaussian spatial data. Our approach includes novel constructions of copulas that accommodate a spatial-random-effects structure, enabling low-rank representations and computationally efficient Bayesian inference. The spatial copula is used in a latent process model of the Bayesian hierarchical spatial-statistical model, and, conditional on the latent copula-based spatial process, the data model handles measurement errors and missing data. Our simulation studies show that a fully Bayesian approach delivers accurate and fast inference for both parameter estimation and spatial-process prediction, outperforming several benchmark methods, including fixed rank kriging (FRK). The new class of copula-based models is used to map atmospheric methane in the Bowen Basin, Queensland, Australia, from Sentinel 5P satellite data.