Bayesian model averaging over tree-based dependence structures for multivariate extremes

TL;DR

This paper introduces a novel Bayesian algorithm for modeling complex extremal dependence structures in multivariate data, utilizing hierarchical models and reversible jump MCMC to improve inference and identify variable clusters.

Contribution

It develops a new Bayesian method with recursive likelihood computation for better modeling of extremal dependence, including cluster detection and reduced computational complexity.

Findings

Algorithm accurately models extremal dependence in simulations.

Identifies clusters of extreme variables effectively.

Applied to air pollution data to reveal dependence patterns.

Abstract

Describing the complex dependence structure of extreme phenomena is particularly challenging. To tackle this issue we develop a novel statistical algorithm that describes extremal dependence taking advantage of the inherent hierarchical dependence structure of the max-stable nested logistic distribution and that identifies possible clusters of extreme variables using reversible jump Markov chain Monte Carlo techniques. Parsimonious representations are achieved when clusters of extreme variables are found to be completely independent. Moreover, we significantly decrease the computational complexity of full likelihood inference by deriving a recursive formula for the nested logistic model likelihood. The algorithm performance is verified through extensive simulation experiments which also compare different likelihood procedures. The new methodology is used to investigate the dependence relationships between extreme concentration of multiple pollutants in California and how these pollutants are related to extreme weather conditions. Overall, we show that our approach allows for the representation of complex extremal dependence structures and has valid applications in multivariate data analysis, such as air pollution monitoring, where it can guide policymaking.