Detecting causal covariates for extreme dependence structures

TL;DR

This paper introduces a methodology to identify causal covariates influencing tail dependence in extreme events, with applications to environmental data like NO2 pollution levels, enhancing understanding of extreme dependence structures.

Contribution

The paper proposes a novel approach to discover causal covariates affecting tail dependence, based on comparisons across different environments, specifically applied to environmental pollution data.

Findings

Identified causal predictors for extreme NO2 dependence.

Demonstrated the methodology's effectiveness on real environmental data.

Enhanced understanding of factors influencing extreme dependence in multivariate extremes.

Abstract

Determining the causes of extreme events is a fundamental question in many scientific fields. An important aspect when modelling multivariate extremes is the tail dependence. In application, the extreme dependence structure may significantly depend on covariates. As for the general case of modelling including covariates, only some of the covariates are causal. In this paper, we propose a methodology to discover the causal covariates explaining the tail dependence structure between two variables. The proposed methodology for discovering causal variables is based on comparing observations from different environments or perturbations. It is a desired methodology for predicting extremal behaviour in a new, unobserved environment. The methodology is applied to a dataset of $\text{NO}_2$ concentration in the UK. Extreme $\text{NO}_2$ levels can cause severe health problems, and understanding the behaviour of concurrent severe levels is an important question. We focus on revealing causal predictors for the dependence between extreme $\text{NO}_2$ observations at different sites.