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

Particulate matter (PM) is a class of malicious environmental pollutants known to cause detrimental effects on human health. Regulatory efforts aimed at curbing PM levels in different countries require high resolution space-time maps that can identify red-flag regions exceeding statutory concentration limits. Continuous space-time Gaussian Process (GP) models can potentially deliver uncertainty quantified map predictions for PM levels. However, traditional GP based approaches are 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 non-separable and possibly non-stationary spatio-temporal GP. The DNNGP 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).