Practical strategies for fitting Extreme-Value statistical models with a view towards environmental and ecological applications

Over the last years, Extreme-Value Statistics (EVS) has gained considerable attention in environmental science, as extreme observations have increased in size and frequency. Mathematically, EVS has a well-developed asymptotic framework that allows us to study extreme events of single or multiple processes observed in one or many locations over space and time. Moreover, it enables us to make statements regarding future events that can be even more extremes than those observed. The mathematical elegance of these methods faces a couple of challenges in the applied arena. For instance, most asymptotically justified EVS models are computationally expensive, and their application to spatial data is limited to few locations. Moreover, some of these models cannot account for well-known features in environmental data, such as decaying dependence strength as events become more extreme. Other problems are related to constraints imposed by the limiting models that do not naturally exist in the observed processes.

In this talk, I will present three different approaches to tackle the previous issues. The first approach is a computationally appealing method to model multiple extreme events over spatially rich regions that successfully captures weakening extremal dependence. The second and third approaches leverage the integrated nested Laplace approximation (INLA) framework, which allows fast and accurate inference in complex models applied to data with different levels of spatial coverage. We will see how to apply these methodologies using precipitation, wind speed, fishery and pollution data. I will conclude with some reflections on how EVS can be incorporated into widely used classical statistical models.