Title: Functional Peaks-over-threshold Analysis and its Applications
Abstract: Estimating the risk of single occurrences of natural hazards has become impor- tant in recent decades, but up until now it has been largely limited to re-using catalogues of historical events, which usually do not exceed 40 to 50 years in length, and to numerical models, which require heavy computation and are often unreliable for extrapolation. Extreme value theory provides statistical methods for estimating the frequency of past extreme events as well as for extrapolating beyond observed severities, but it has mostly been focused on studying univari- ate quantities. Consequently the majority of its applications to natural hazards have neglected their spatio-temporal characteristics. We present an extension of peaks-over-threshold analysis to functions which allows one to define complex extreme events as special types of exceedances, and then obtain their limit tail distribution, namely the generalized r-Pareto process. We focus on a specific model based on log-Gaussian random functions using classical covariance structures to characterize extremal dependence. Then, we describe a stochastic weather generator for extreme events, capable of quan- tifying the recurrence of past events as well as generating completely new ones. The methodology is applied to several natural hazards such as windstorms and rainfall.