Models for Complex Extreme Events

The last few years have seen very rapid advances in modelling complex extreme events, such as extreme spatial rainfall, wind- storms and the like. Much of this advance has been based on the use of max-stable processes for modelling maxima, but more recent work has concerned peaks over thresholds modelling, which is known to be more e cient in simpler settings. It turns out that it is both more e cient and somewhat easier in complex settings also. This talk will survey recent advances in this area, with special reference to modelling extreme rainfall.