https://orcid.org/0000-0002-1228-2071
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Raphaël Huser, Seconder of the vote of thanks to Healy et al. and contribution to the Discussion of ‘Inference for extreme spatial temperature events in a changing climate with application to Ireland’, Journal of the Royal Statistical Society Series C: Applied Statistics, Volume 74, Issue 2, March 2025, Pages 302–305, https://doi.org/10.1093/jrsssc/qlae078
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I am grateful for the invitation to study this paper and reflect upon its novel contributions, limitations, and extensions. The authors propose an elegant framework for modelling the frequency, magnitude, and spatial extent of temperature extremes in Ireland. The proposed approach relies on a sliced bulk–tail semiparametric regression model with carefully chosen spatial and temporal covariates (for margins), and an r-Pareto process of Brown–Resnick type (for the extremal dependence structure), which, after some experimentation, was assumed to be stationary over both space and time. The use of high-resolution climate-model data to incorporate physical information into the statistical extreme-value model is interesting. My comments are mostly about the model assumptions and potential extensions.
While r-Pareto processes are asymptotically motivated, they are notorious for being threshold-stable and asymptotically dependent, which can strongly affect tail extrapolation and risk assessment if these assumptions are violated. Figure 4 in the paper aims at checking whether these properties hold by examining whether the bivariate χ-measure is stable across different thresholds. However, if an r-Pareto process is a valid model for the joint tail structure, then the multivariate χ-measure, , should also be constant in p for suitably large thresholds. Upon examination of this property for (subsets of) three Irish temperature data products (namely, the observational data and the climate-model data used in this paper, as well as the E-OBS dataset1 used in Huser & Wadsworth, 2022 and Huser et al., 2024), there is evidence against threshold-stability, both over the whole Ireland and over smaller subregions, see Figures 1, 2, and 3. Can the authors comment on this lack of stability, which contradicts their conclusions, and its practical implications when fitting a Pareto process in their application? To assess risk in a climate change context, capturing the time trend accurately is often more important than specifying the correct joint tail structure; is that the case here?
