Conditional Decomposition Approach for Modeling Multivariate Extreme Events

Abstract

The class of max-stable models is commonly used for modeling multivariate and spatial extremes. Despite recent advancements in model construction and implementation, a fundamental limitation persists in incorporating timing information for extreme events due to the "component-wise maximum" data selection process. This limitation can lead to inaccurate assessments of multivariate and spatial extreme risk. In this talk, I will present a conditional approach to model multivariate extremes, aiming to capture extremes at the event level by conditioning on the timing and corresponding vector values when at least one variable is extreme. The proposed approach shares some similarities with the conditional extreme value models developed by Jonathan Tawn and his collaborators, but it treats the modeling of the conditional distribution of the concomitant variable(s) differently when the conditioning variable is extreme. Specifically, the conditional distribution function is modeled by a composition of distribution functions, where an extreme value base distribution is enriched by a conditional beta distribution. Simulated examples and an application to bivariate concurrent wind and precipitation extremes will illustrate the proposed approach.