Spatial extremes: a conditional approach

The past decade has seen a huge effort in modelling the extremes of spatial processes. Significant challenges include the development of models with an appropriate asymptotic justification for the tail; ensuring model assumptions are compatible with the data; and the fitting of these models to (at least reasonably) high-dimensional datasets. I will review basic ideas of modelling spatial extremes, and introduce an approach based on the (multivariate) conditional extreme value model of Heffernan and Tawn (2004) and Heffernan and Resnick (2007). Advantages of the conditional approach include its asymptotic motivation, flexibility, and comparatively simple inference, meaning that it can be fitted to reasonably large datasets. The modelling approach is applied to understand the spatial extent of high temperature extremes across Australia.