Conditional Extremes with Graphical Models

TL;DR

This paper introduces an extended conditional multivariate extreme value model that captures both asymptotic dependence and independence in spatial data, enabling better prediction and understanding of joint extreme events.

Contribution

It extends graphical extremes models to include asymptotically independent variables and proposes a scalable inference method for high-dimensional data.

Findings

Accurately models extremal dependence in river discharge data.

Flexible approach captures both dependence types.

Efficient inference procedure for high-dimensional settings.

Abstract

Multivariate extreme value analysis quantifies the probability and magnitude of joint extreme events. River discharges from the upper Danube River basin provide a challenging dataset for such analysis because the data, which is measured on a spatial network, exhibits both asymptotic dependence and asymptotic independence. To account for both features, we extend the conditional multivariate extreme value model (CMEVM) with a new approach for the residual distribution. This allows sparse (graphical) dependence structures and fully parametric prediction. Our approach fills a current gap in statistical methodology by extending graphical extremes models to asymptotically independent random variables. Further, the model can be used to learn the graphical dependence structure when it is unknown a priori. To support inference in high dimensions, we propose a stepwise inference procedure that is computationally efficient and loses no information or predictive power. We show our method is flexible and accurately captures the extremal dependence for the upper Danube River basin discharges.