B0784
Title: Colored graphical models in multivariate extremes
Authors: Frank Roettger - TU Eindhoven (Netherlands) [presenting]
Jane Coons - Oxford University (United Kingdom)
Alexandros Grosdos - University of Augsburg (Germany)
Abstract: Coloured graphical models provide a parsimonious approach to modelling high-dimensional data by exploiting symmetries in the model parameters. The notion of colouring is introduced for extremal graphical models on multivariate Pareto distributions, a natural class of limiting distributions for threshold exceedances. Thanks to a stability property of multivariate Pareto distributions, coloured extremal tree models can be defined fully nonparametrically. For more general graphs, the parametric family of Huesler-Reiss distributions allows for two alternative approaches to coloured graphical models. Both model classes are studied and a statistical methodology is introduced for parameter estimation. It turns out that for Huesler-Reiss tree models, the different definitions of coloured graphical models coincide. In addition, a general parametric description of extremal conditional independence statements is shown for Huesler-Reiss distributions. Finally, it is demonstrated that the methodology outperforms existing approaches on a real data set.
