Most of my research focuses on the statistics of extreme events, and its applications in meteorology: see Publications.
I am particularly interested in models based on a tail large deviation principle (see below), in optimal transport, and in spatial/temporal signatures of extreme events.
The probability of an extreme event can be estimated from data if the tail of the probability distribution exhibits a certain regularity. In classical extreme value theory, the regularity takes the form of a limit relation involving ratios of probabilities. I explore also a different type of regularity which is not yet common in extreme value theory but particularly suitable for rare extreme events: a large deviation principle (LDP). This tail LDP takes the form of a limit relation involving ratios of logarithms of probabilities. The tail LDP is a less restrictive assumption than the assumptions usually invoked to extend classical extreme value theory to handle such rare events. This model connects and extends seemingly separate nonstandard approaches in extreme value theory such as the Weibull tail limit, hidden regular variation, and convergence of sample clouds to a set. Furthermore, it rationalises earlier informal approaches to extreme value analysis such as the use of Weibull tails in oceanography, meteorology and engineering.
My applied research addresses the performance of LDP-based models and classical models for estimation of the tails of weather variables, the potential of large synthetic datasets generated by weather prediction models for extreme value analysis (with Henk van den Brink), modelling of the spatial signature of extreme sub-daily precipitation using weather radar data, and checking for spatial and temporal homogeneity of the statistics of meteorological extremes.
Modest attempts to do something useful in optimal transport address (with Johan Segers) regularities satisfied by optimal transport maps, assuming a certain form of tail regularity of the probability measures concerned, and (with Judith Bosboom and others) the application of a non-standard optimal coupling (a Moser coupling) to define a new metric of the deviation between two maps of the seabed.