https://orcid.org/0000-0003-1207-3437
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S Rizzelli, Stefano Rizzelli’s contribution to the Discussion of ‘Inference for extreme spatial temperature events in a changing climate with application to Ireland’ by Healy et al., Journal of the Royal Statistical Society Series C: Applied Statistics, Volume 74, Issue 2, March 2025, Pages 318–319, https://doi.org/10.1093/jrsssc/qlae083
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This work has the merit of highlighting the many challenges posed by modelling of spatio-temporal extremes in the presence of time non-stationarity, such as properly assessing the goodness of fit for models on marginal distributions and joint dependence structure, dwelling with missing data and intractable likelihoods, including covariates information in a principled way and quantifying uncertainty, not to mention evaluating model misspecification effects on estimation, which always represent a delicate issue when adopting extreme value models for distributions tails. Foremost, the article draws attention to the issue of how to treat climate model data from a statistical point of view for the purpose of analysing weather extremes, a complex question that requires in-depth reflection.
Data fusion paradigms as that in Li and Luedtke (2023) seem unsuitable to inference about extremal features, as sufficient alignment conditions on observational and climate data distributions tails are likely to be violated, all the more so in the presence of short tails, with potentially different end-points. In fact, the complex nature of simulation mechanisms even raises doubts about the legitimacy of directly applying some of the statistical techniques in the extreme value toolbox (Beirlant et al., 2004; de Haan & Ferreira, 2006; Reiss & Thomas, 2007) to climate model data. The use of climate model data as covariates (e.g. Berrocal et al., 2010) thus seems the most sensible course of action, yet the far from simple question of how to appropriately do this in an extreme value context must be addressed (e.g. Poschlod & Koh, 2024).
