Capturing the extremal behaviour of data often requires bespoke marginal and dependence models which are grounded in rigorous asymptotic theory, and hence provide reliable extrapolation into the upper tails of the data-generating distribution. We present a toolbox of four methodological frameworks, motivated by modern extreme value theory, that can be used to accurately estimate extreme exceedance probabilities or the corresponding level in either a univariate or multivariate setting. Our frameworks were used to facilitate the winning contribution of Team Yalla to the EVA (2023) Conference Data Challenge, which was organised for the 13$^\text{th}$ International Conference on Extreme Value Analysis. This competition comprised seven teams competing across four separate sub-challenges, with each requiring the modelling of data simulated from known, yet highly complex, statistical distributions, and extrapolation far beyond the range of the available samples in order to predict probabilities of extreme events. Data were constructed to be representative of real environmental data, sampled from the fantasy country of "Utopia"

翻译：捕获数据的极值行为通常需要基于严格渐近理论的定制化边缘和依赖模型，从而为数据生成分布的上尾提供可靠的外推。我们提出了一个由现代极值理论驱动的四种方法论框架组成的工具箱，可用于在单变量或多变量设置中精确估计极端超越概率或相应的水平。这些框架支撑了Yalla团队在EVA（2023）会议数据挑战赛中的获胜贡献，该竞赛是为第13届国际极值分析会议组织的。本次比赛有七个团队参与四个独立子挑战，每个子挑战均需对从已知但高度复杂的统计分布中模拟的数据进行建模，并外推至远超可用样本范围以预测极端事件概率。数据被构建为具有真实环境数据的代表性特征，采样自虚构国家"乌托邦"。