Extreme Value Statistics for Analysing Simulated Environmental Extremes

We present the methods employed by team `Uniofbathtopia' as part of the Data Challenge organised for the 13th International Conference on Extreme Value Analysis (EVA2023), including our winning entry for the third sub-challenge. Our approaches unite ideas from extreme value theory, which provides a statistical framework for the estimation of probabilities/return levels associated with rare events, with techniques from unsupervised statistical learning, such as clustering and support identification. The methods are demonstrated on the data provided for the Data Challenge -- environmental data sampled from the fantasy country of `Utopia' -- but the underlying assumptions and frameworks should apply in more general settings and applications.