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 modern 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 data competition organised for the 13th International Conference on Extreme Value Analysis (EVA2023). 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：捕捉数据的极端行为通常需要基于严格渐近理论构建专门化的边缘与依赖模型，从而为数据生成分布的上尾区域提供可靠的外推能力。我们基于现代极值理论，提出了一套包含四种方法论框架的现代工具箱，可用于在单变量或多变量场景下精确估计极端超越概率及其对应水平。该工具箱助力Yalla团队在第十三届国际极值分析会议（EVA2023）组织的数据竞赛中取得优胜。该竞赛共有七支队伍参与四个独立子挑战赛，每个挑战需要基于已知但高度复杂的统计分布对模拟数据进行建模，并在样本范围外进行远距离外推以预测极端事件概率。这些数据模拟自虚构国度"乌托邦"的真实环境数据特征。