Bayesian Modeling of Air Pollution Extremes Using Nested Multivariate Max-Stable Processes

TL;DR

This paper introduces a hierarchical Bayesian model for multivariate max-stable processes to effectively capture complex dependence among extreme air pollution and temperature data across spatial regions.

Contribution

A novel nested multivariate max-stable process model with a hierarchical structure for Bayesian inference in spatial extremes.

Findings

Successfully modeled complex tail dependence in Los Angeles air pollution data.

Captured multivariate spatial dependence among pollutants and temperatures.

Demonstrated the model's effectiveness in representing extreme value dependence.

Abstract

Capturing the potentially strong dependence among the peak concentrations of multiple air pollutants across a spatial region is crucial for assessing the related public health risks. In order to investigate the multivariate spatial dependence properties of air pollution extremes, we introduce a new class of multivariate max-stable processes. Our proposed model admits a hierarchical tree-based formulation, in which the data are conditionally independent given some latent nested $\alpha$-stable random factors. The hierarchical structure facilitates Bayesian inference and offers a convenient and interpretable characterization. We fit this nested multivariate max-stable model to the maxima of air pollution concentrations and temperatures recorded at a number of sites in the Los Angeles area, showing that the proposed model succeeds in capturing their complex tail dependence structure.