A heavy-tailed model for multivariate spatial processes

 

Abstract

Environmental data commonly involves measuring multiple pollutants, such as NO2 and PM10 levels, at some fixed sites across a region. Data analysts aim to describe the processes accounting for covariance across space and among pollutants, usually assuming a multivariate spatial Gaussian model with a stationary covariance function. However, the observed data distribution often exhibits heterogeneous variability, resulting in heavier tails than the Gaussian distribution. To address these challenges by avoiding data transformation, we propose a flexible multivariate spatial model with spatially varying covariate-dependent variance that naturally accommodates heavy-tailed distributions. Specifically, we extend the linear model of coregionalization by modeling the variances of the processes, allowing them to vary across space and depending on covariates. We discuss the properties of the proposed model and outline a Bayesian inference procedure implemented using the software Stan. As the model involves several Gaussian process components, we further discuss Vecchia-based approximation methods for analyzing large spatial datasets. Artificial data analyses suggest that the model’s parameters are identifiable and can accurately detect outlying observations if they exist, underscoring the model’s reliability and robustness. The model quantifies uncertainty and captures local structures more effectively than the multivariate Gaussian model when applied to maximum concentrations of NO2 and PM10 on a day at 382 sites across Italy. Further, the described approximation methods show effectiveness in analyzing large spatial datasets.