Extreme value statistics for analysing simulated environmental extremes

We present the methods employed by team ‘Uniofbathtopia’ as part of a competition 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 EVA (2023) Conference 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.