In a recent presentation at the Generative AI for Extreme Events conference, Christian Y. Robert delivered a comprehensive overview of Extreme Value Theory (EVT) and its critical role in modeling rare events. The talk underscored why standard statistical methods fall short when dealing with extremes in fields like finance, insurance, climate risk, and engineering.
Robert began by highlighting the unique challenges of extreme events: they are rare, poorly observed, and often exhibit strong dependencies across time, space, or variables. He then introduced the core univariate tools of EVT, including maxima, record values, upper order statistics, and threshold exceedances, with an emphasis on the Generalized Extreme Value (GEV) and Generalized Pareto (GPD) distributions.
The discussion expanded into multivariate extremes, covering componentwise maxima, tail dependence, asymptotic dependence and independence, max-stable distributions, and spectral measures. Further extending the framework to infinite-dimensional settings, Robert explored max-stable processes, spectral representations, and generalized Pareto processes for spatial-temporal fields.
A key takeaway was the point process viewpoint, which unifies exceedances, Poisson limits, clustering, and the extremal index. Robert stressed that generative models for rare events must do more than reproduce typical observations—they must accurately reflect tail behavior and extremal dependence structures.
The conference series continues with Parts II through V, promising deeper dives into the intersection of generative AI and extreme event modeling.