Title: An asymptotically justified framework for modelling extreme ocean states with Markov processes and tail graphs
Authors: Ioannis Papastathopoulos - University of Edinburgh (United Kingdom) [presenting]
Abstract: Recent developments on asymptotic characterizations of extremes of Markov processes are described. We flesh out flexible extreme value models that are used to infer spatio-temporal characteristics of extreme ocean states. The advantage of the proposed statistical models is that they facilitate spatio-temporal graphical modelling of variables such as significant wave height, wind speed and current speed, but also combinations of the different variables within one model, with quite general extremal dependence structure between nodes. This is particularly useful because the most important characteristics of environmental extremes are not contemporaneous. For example, the extremum of significant wave height within a storm may not coincide with extrema of wind speed or wave peak frequency and the proposed models offer a way of understanding this temporal incoherence. The methodology is also appropriate to describe the evolution of individual storm events including the evolution of inter dependent wave, wind and current fields in space and time. We outline a likelihood based procedure, model selection criteria and shrinkage methods for estimating graphical structures and illustrate the proposed methods with an application to extremes of North Sea waves.