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

TL;DR

This paper introduces a Bayesian copula-based spatial model that efficiently handles complex, noisy, and incomplete spatial data, providing accurate inference and prediction, demonstrated through simulation and satellite data application.

Contribution

It develops a novel copula-based spatial model with low-rank structures for Bayesian inference, improving computational efficiency and accuracy over existing methods.

Findings

Outperforms fixed rank kriging in simulations

Provides accurate parameter estimation and spatial prediction

Successfully maps atmospheric methane from satellite 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.