Fast and flexible inference for spatial extremes

Statistical modelling of spatial extreme events has gained increasing attention over the last few decades with max-stable processes, and more recently r-Pareto processes, becoming the reference tools for the statistical analysis of asymptotically dependent data. Although inference for r-Pareto processes is easier than for max-stable processes, there remains major hurdles for their application to very high dimensional datasets within a reasonable timeframe. In addition, both approaches have almost exclusively considered the Brown-Resnick model for its Gaussian-based foundations and the continuity of its exponent measure. In this talk, we derive a class of models for which this continuity property holds and present the skewed Brown-Resnick model, an extension of the Brown-Resnick that allows for non-stationarity in the dependence structure, and the truncated extremal-t, a refinement of the well-known extremal-t model. We use an inference methodology based on the intensity function of the process which is derived from the exponent measure, and demonstrate the statistical and computational efficiency of this approach. Applications to two real-world problems illustrate valuable gains in flexibility from the proposed models as well as appealing computational gains over reference methodologies.

Jun 24, 2025