Non-separable Dynamic Nearest-Neighbor Gaussian Process Models for Large spatio-temporal Data With an Application to Particulate Matter Analysis

TL;DR

This paper introduces a scalable, non-separable dynamic nearest neighbor Gaussian process model for large spatio-temporal datasets, enabling high-resolution environmental mapping and uncertainty quantification, demonstrated through particulate matter analysis across Europe.

Contribution

The authors develop a novel DNNGP model that offers scalable, sparse approximations for complex spatio-temporal Gaussian processes with non-separable covariance structures.

Findings

DNNGP provides superior approximation compared to low rank methods.

Model achieves linear storage and memory scalability.

Application improves PM level predictions across Europe.

Abstract

Particulate matter (PM) is a class of malicious environmental pollutants known to be detrimental to human health. Regulatory efforts aimed at curbing PM levels in different countries often require high resolution space-time maps that can identify red-flag regions exceeding statutory concentration limits. Continuous spatio-temporal Gaussian Process (GP) models can deliver maps depicting predicted PM levels and quantify predictive uncertainty. However, GP based approaches are usually thwarted by computational challenges posed by large datasets. We construct a novel class of scalable Dynamic Nearest Neighbor Gaussian Process (DNNGP) models that can provide a sparse approximation to any spatio-temporal GP (e.g., with non-separable covariance structures). The DNNGP we develop here can be used as a sparsity-inducing prior for spatio-temporal random effects in any Bayesian hierarchical model to deliver full posterior inference. Storage and memory requirements for a DNNGP model are linear in the size of the dataset thereby delivering massive scalability without sacrificing inferential richness. Extensive numerical studies reveal that the DNNGP provides substantially superior approximations to the underlying process than low rank approximations. Finally, we use the DNNGP to analyze a massive air quality dataset to substantially improve predictions of PM levels across Europe in conjunction with the LOTOS-EUROS chemistry transport models (CTMs).