[STAT/AP] Frank Röttger: Graphical models in extremes from threshold exceedances
The recent introduction of conditional independence for multivariate extremes from threshold exceedances has inspired a new line of research in extremal dependence modeling. In this talk we summarize recent developments and try to highlight connections with related fields. In particular we discuss undirected and directed graphical models for multivariate extremes from threshold exceedances, as well as approaches for structure and parameter learning. Here, a central tool is the parametric family of Hüsler--Reiss distributions, which can be characterized via Laplacian-constrained Gaussian graphical models, i.e. degenerate Gaussians with graph Laplacian inverse covariance matrix. This characterization allows to describe extremal conditional independence parametrically and therefore leads to a parametric encoding of extremal graphical models. Finally, we introduce colored Hüsler--Reiss graphical models and discuss statistical methodology for those, which we demonstrate on a real data example.
