Speaker: Professor Jonathan Tawn, Department of Mathematics and Statistics, Lancaster University, UK
Title: "Multivariate Extremes: different routes to extrapolation"
Abstract: When estimating the probability of extreme values of a vector variable it is necessary to consider not only the extreme values of the separate variables but also the dependence between them.
Extreme value theory provides a very flexible class of asymptotically justified probability distributions to describe the behaviour of the extreme values. In the univariate case the well-established class of distributions fully described by a 3 parameter class of models. This parsimony and flexibly provides a strong basis for modelling.
In multivariate extremes the dependence structure also has critical structure imposed on it by focusing on extreme events. The nature of the structure imposed though depends on the form of the asymptotic argument used and in no case is it fully parameterized. In this talk I will discuss the various different probabilistic routes to extrapolation, their underlying assumptions, their inter-connections, and their statistical inference.