Bayesian Clustering and Dimension Reduction in Multivariate Extremes

Abstract

Describing the complex dependence structure of multivariate extremes is particularly challenging and requires very versatile, yet interpretable, models. To tackle this issue we explore two related approaches: clustering and dimension reduction. In particular, we develop a novel statistical algorithm that takes advantage of the inherent hierarchical dependence structure of the maxstable nested logistic distribution and that uses reversible jump Markov chain Monte Carlo techniques to identify homogeneous clusters of variables. Dimension reduction is achieved when clusters are found to be completely independent. We signifficantly 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 consider different likelihood procedures. The new methodology is used to investigate the dependence relationships between extreme concentration of multiple pollutants across a number of sites in California and how these pollutants are related to extreme weather conditions. Overall, we show that our approach allows for the identification of homogeneous clusters of extremes and has valid applications in multivariate data analysis, such as air pollution monitoring, where it can guide policymaking