Computational methods for complex problems in extreme value theory.

Rare events are part of the real world but inevitably environmental extreme events may have a massive impact on everyday life. We are familiar, for example, with the consequences and damage caused by hurricanes and floods etc. Consequently, there is considerable attention in studying, understanding and predicting the nature of such phenomena and the problems caused by them, not least because of the possible link between extreme climate events and global warming or climate change. Thus the study of extreme events has become ever more important, both in terms of probabilistic and statistical research. This thesis aims to provide statistical modelling and methods for making inferences about extreme events for two types of process. First, non-stationary univariate processes; second, spatial stationary processes. In each case the statistical aspects focus on model fitting and parameter estimation with applications to the modelling of environmental processes including, in particular, nonstationary extreme temperature series and spatially recorded rainfall measures.