| Abstract: |
| We introduce geometric extremal graphical models, a new framework for describing dependence in multivariate extreme events. The approach is based on a geometric representation of the limiting behaviour of suitably scaled random vectors with light-tailed margins. For block graphs, we show how different measures of extremal dependence propagate through the graph. We focus on measures connected to conditional extreme value theory, which are useful when extreme events occur in some variables without requiring all variables to be extreme at the same time. We also discuss the case of joint extreme behaviour, where several variables become extreme together. Together with recent work linking geometric ideas in multivariate extremes to practical statistical models, these results open the way to modelling high-dimensional extremes with complex dependence structures.
Joint work with Jennifer L. Wadsworth |
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