B1457
Title: Multivariate extremes: Bayesian inference for radially-stable distributions
Authors: Ioannis Papastathopoulos - University of Edinburgh (United Kingdom)
Lambert De Monte - University of Edinburgh (United Kingdom) [presenting]
Ryan Campbell - Lancaster University (United Kingdom)
Haavard Rue - KAUST (Saudi Arabia)
Abstract: Multivariate extreme value theory (MEVT) is a branch of probability and statistics concerned with characterising the extremes of finite-dimensional random vectors and estimating the probability of joint, rare events. Particular interest lies in extrapolating beyond the range of observed data; common environmental applications include modelling extreme hydrological events linked with flooding, damaging wind gusts, heatwaves, and their impacts on livelihood. A classical approach to MEVT consists of studying the distribution of exceedances of high thresholds, but current methods mostly rely on the constraining notion of multivariate regular variation. A new framework is introduced for multivariate threshold exceedances involving radially stable distributions based on the geometric approach to MEVT, a recent branch of extreme value theory arising through the study of suitably scaled independent observations from random vectors and their convergence in probability onto compact limit sets. Using a radial-angular decomposition of the random vector of interest, a Bayesian inference approach is adopted based on a limiting Poisson point process likelihood using information from the distribution of the radial exceedances and the distribution of the angles along which the exceedances occur. The method is showcased on case studies of river flow and sea level extremes.
