16 May 2024: Kirstin Strokorb (Cardiff University)

Title: Conditional Independence and Graphical Models for Extremes
Abstract: Statistical modelling of complex dependencies in extreme events requires meaningful sparsity structures in multivariate extremes. In this context two perspectives on conditional independence and graphical models have recently emerged: One that focuses on threshold exceedances and multivariate pareto distributions, and another that focuses on max-linear models and directed acyclic graphs. What connects these notions is the exponent measure that lies at the heart of each approach. In this work we develop a notion of conditional independence defined directly on the exponent measure (and even more generally on measures that explode at the origin) that builds a bridge between these approaches. We characterize this conditional independence in various ways through kernels and factorization of a modified density, including a Hammersley-Clifford type theorem for undirected graphical models. As opposed to the classical conditional independence, our notion is intimately connected to the support of the measure. Structural max-linear models turn out to form a Bayesian network with respect to our new form of conditional independence. Our general theory unifies and extends recent approaches to graphical modeling in the fields of extreme value analysis and Lévy processes. Our results for the corresponding undirected and directed graphical models lay the foundation for new statistical methodology in these areas.
This work arose as a follow-up from the RSS discussion meeting Graphical Models for Extremes by Engelke & Hitz ( • Graphical models for e... ). A preprint is available on arxiv.org/abs/....
Joint work with: Sebastian Engelke and Jevgenijs Ivanovs