A class of covariate-dependent spatiotemporal covariance functions for the analysis of daily ozone concentration

TL;DR

This paper introduces a flexible class of covariate-dependent spatiotemporal covariance functions that adapt to local characteristics, improving modeling of nonstationary phenomena like daily ozone levels.

Contribution

It proposes a novel, computationally feasible approach for modeling nonstationary spatial correlations based on local covariates, enhancing geostatistical analysis.

Findings

Effective modeling of ozone concentration variability.

Covariance functions depend on local covariates.

Improved fit over stationary models.

Abstract

In geostatistics, it is common to model spatially distributed phenomena through an underlying stationary and isotropic spatial process. However, these assumptions are often untenable in practice because of the influence of local effects in the correlation structure. Therefore, it has been of prolonged interest in the literature to provide flexible and effective ways to model nonstationarity in the spatial effects. Arguably, due to the local nature of the problem, we might envision that the correlation structure would be highly dependent on local characteristics of the domain of study, namely, the latitude, longitude and altitude of the observation sites, as well as other locally defined covariate information. In this work, we provide a flexible and computationally feasible way for allowing the correlation structure of the underlying processes to depend on local covariate information. We discuss the properties of the induced covariance functions and methods to assess its dependence on local covariate information. The proposed method is used to analyze daily ozone in the southeast United States.