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To capture the extremal behaviour of complex environmental phenomena inpractice, flexible techniques for modelling tail behaviour are required. Inthis paper, we introduce a variety of such methods, which were used by theLancopula Utopiversity team to tackle the data challenge of the 2023 ExtremeValue Analysis Conference. This data challenge was split into four sections,labelled C1-C4. Challenges C1 and C2 comprise univariate problems, where thegoal is to estimate extreme quantiles for a non-stationary time seriesexhibiting several complex features. We propose a flexible modelling technique,based on generalised additive models, with diagnostics indicating generallygood performance for the observed data. Challenges C3 and C4 concernmultivariate problems where the focus is on estimating joint extremalprobabilities. For challenge C3, we propose an extension of available models inthe multivariate literature and use this framework to estimate extremeprobabilities in the presence of non-stationary dependence. Finally, forchallenge C4, which concerns a 50 dimensional random vector, we employ aclustering technique to achieve dimension reduction and use a conditionalmodelling approach to estimate extremal probabilities across independent groupsof variables.

Extreme value methods for estimating rare events in Utopia