Event Details

Statistics seminar in the School of Mathematical Sciences.

Title: Geometry‑aware extrapolation for multivariate extremes

Abstract: In this talk, I will present several strands of work on statistical inference for multivariate extremes. To motivate the details, I will begin with the setup: the limit set as a geometric lens for tail behaviour under light‑tailed standardisation, then show in two and three dimensions how this geometry underpins current methods for extrapolation and rare-event risk estimation. I will next describe a new approach for stochastic processes that decomposes trajectories into magnitude and shape, learns quantile sets and exceedance laws, and delivers probabilities for function‑level events such as prolonged exceedance. To scale up inference in unstructured multivariate settings, I will then introduce geometric extremal graphical models that factorise tail geometry and provide simple propagation rules for interpretable, high‑dimensional inference. Finally, I will connect these strands via optimal transport—using multivariate ranks and center‑outward maps—to align the bulk with a reference and carry learned tail geometry back to data space for principled extrapolation and simulation.