Inspired by the One World Probability Project and supported by the Bernoulli Society, the One World Extremes Seminar is an initiative to keep researchers with an interest in Extreme Value Theory (EVT) virtually connected in novel ways. It features both theoretical advances and important applications of EVT.
log-in link: https://umich.zoom.us/j/93887313242
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 in particular 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.
Stochastic simulation of extreme events in a multivariate setting is of great interest as it captures not only the statistical behaviour of the extremes, but also the dependence between large values of complex processes. Based on a spectral representation of multivariate generalised Pareto distributed random vectors, we present two non-parametric algorithms for simulating multivariate extreme events. These algorithms can be used, in particular, to improve the estimation of various risk measures at extreme levels by increasing the number of extreme samples available. The performance of the algorithms is demonstrated using both simulated and real-world data.
This presentation is based on joint work with P. Ailliot, P. Naveau, and N. Raillard, and with N. Madhar and M. Thomas.
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Dan Cooley (Colorado State University)
Anna Kiriliouk (Université catholique de Louvain)
Jordan Richards (University of Edinburgh)
Tiandong Wang (Fudan University)
Kirstin Strokorb (Bath University) - past organiser, now technical advice
Gilles Stupfler (ENSAI) - newsletter editor
2023 - 2025
Thomas Opitz (INRAE, Avignon)
Kate Saunders (Monash University)
Emma Simpson (University College London)
Stilian Stoev (University of Michigan)
2020 - 2023
Raphaël Huser (KAUST)
Natalia Nolde (UBC Vancouver)
Marco Oesting (University of Stuttgart)
Kirstin Strokorb (Cardiff University)
Gilles Stupfler (ENSAI)
Yizao Wang (University of Cincinnati)