Multivariate Extremes: Structure and Dependence

This lecture explores multivariate extremes, focusing on the structure variable S = s(X₁,..., XD) and the dependence between variables. It discusses scenarios where at least one or both variables exceed a high threshold, as well as functions that measure extremal dependence. The lecture also covers componentwise maxima, models for multivariate extremes, and the concept of copulas to determine dependence structure. Examples of copulas, such as the Gaussian and Logistic copulas, are presented to illustrate different dependence scenarios.