Extremes Without Borders: Multivariate and Spatial Perspectives

Extreme events such as floods, heatwaves, or severe pollution episodes can have devastating consequences. Assessing the risk of events that are more severe than those observed in historical data is therefore a crucial challenge in many fields, from environmental science to finance. In practice, evaluating these risks is complex because extreme events rarely involve a single variable or occur at a single location. For instance, understanding extreme pollution levels in Sydney requires studying several pollutants simultaneously and how they interact during high-pollution episodes. Likewise, extreme events often affect entire regions rather than isolated locations. The catastrophic flooding that struck northern New South Wales in February–March 2022, particularly in Lismore, illustrates how extreme rainfall can occur across large spatial areas. From a statistical perspective, predicting events beyond the range of observed data is far from straightforward. Extreme Value Theory provides a framework for analysing and extrapolating rare events. In this lecture, we will introduce the key ideas behind modelling multivariate and spatial extremes, discuss the principles that underpin these models, and highlight recent developments that allow more realistic and computationally efficient approaches. We will conclude with a discussion of emerging challenges and future research directions.

Mar 24, 2026