Structure learning for multivariate extremes: A comparative study of regional UK rainfall

Characterizing extremal structural relationships between sets of variables is central to the development of parsimonious models in extreme value analysis, particularly as statistical modeling in high dimensions remains challenging. In this study, we considered recently proposed statistical methods for learning the dependence structure of multivariate variables, with a focus on their ability to capture relationships at extreme levels. We considered complementary approaches that differed in their underlying modeling assumptions. One approach was less model-based and relied on the notion of partial tail correlation to assess extremal dependence between pairs of variables given the others. The other methods were rooted in graphical modeling frameworks, which provided a flexible means of representing complex dependence patterns and facilitated the investigation of higher-order extremal dependencies. We applied the methods to extreme rainfall data from the Lancashire region of the United Kingdom. The resulting dependence structures revealed some spatial heterogeneity, with distinct clustering behavior observed between northern and southern subregions. In particular, evidence of stronger higher-order dependence was concentrated in the southeastern area. These findings suggested that the effectiveness of flood defense and mitigation strategies may vary across subregions, highlighting the importance of accounting for extremal dependence structure in regional risk assessment and infrastructure planning.