Valérie Chavez-Demoulin, Anthony C Davison and Erwan Koch’s contribution to the Discussion of ‘The First Discussion Meeting on Statistical aspects of climate change’
这篇讨论文章探讨了极值理论在气候建模中的应用，提出了使用年上阶统计量替代阈值、保留广义极值分布参数等替代方法，并讨论了随机效应模型、先验分布选择和参数正交化等问题。
This interesting paper poses many questions on the use of extreme value theory for climate modelling. An alternative to defining separate annual thresholds for the peaks over thresholds model would be to use the upper r order statistics for each year. This extends the use of annual maxima but requires only a single value r to be chosen rather than many thresholds. Moreover, this approach has the advantage of retaining the parameters of the generalized extreme-value (GEV) distribution, which typically have a more stable interpretation than do those of the generalized Pareto distribution; when the threshold changes, so do the exceedance probability and the scale parameter. Since threshold stability is a key property of the generalized Pareto model, it seems unfortunate that the joint distribution of the random effects will change if the threshold is varied. While the prior distribution appears to be chosen purely for computational convenience and as an approach to penalisation, comparison of results for different thresholds would entail appropriate transformations of their respective priors. It would be interesting to see if the Markov chain Monte Carlo output was more readily interpretable when transformed to the GEV scale. As the authors point out, the random effects model can be seen as adjusting for variation not captured by observed explanatory variables, but if phenomena appear that have been rarely observed in the past, such as so-called ‘heat domes’, then the basis of the mixture model, exchangeability of the unobserved variation from year to year, becomes moot. On a more computational note, the scale and shape parameters of both models are negatively correlated, because higher observations could be explained by increasing either, so it may be preferable to impose the priors and perform the sampling after some form of parameter orthogonalisation. We assume that the Global Mean Surface Temperature is somehow localised. A broad-brush covariate such as this should presumably be adapted for application in a rather small region, perhaps using similar local covariates or some form of smoothing. The term ‘return level’ is well-anchored in the literature, but nevertheless it seems preferable to avoid it, because of its underlying assumption of stationarity. Moreover the appearance of so-called ‘100-year events’ every few years is poor publicity for statistics and it seems better to avoid the term.