Understanding multivariate extreme events play a crucial role in managing the risks of complex systems since extremes are governed by their own mechanisms. Conditional on a given variable exceeding a high threshold (e.g.\ traffic intensity), knowing which high-impact quantities (e.g\ air pollutant levels) are the most likely to be extreme in the future is key. This article investigates the contribution of marginal extreme events on future extreme events of related quantities. We propose an Extreme Event Propagation framework to maximise counterfactual causation probabilities between a known cause and future high-impact quantities. Extreme value theory provides a tool for modelling upper tails whilst vine copulas are a flexible device for capturing a large variety of joint extremal behaviours. We optimise for the probabilities of causation and apply our framework to a London road traffic and air pollutants dataset. We replicate documented atmospheric mechanisms beyond linear relationships. This provides a new tool for quantifying the propagation of extremes in a large variety of applications.

翻译：多重理解性极端事件在管理复杂系统的风险方面发挥着关键作用,因为极端事件受其自身机制的制约。对于超过高阈值(例如交通强度)的某一变量,有条件地设定一个条件,了解哪些高影响数量(例如空气污染物水平)最有可能在未来是极端的。本条款调查边缘极端事件对未来极端事件相关数量的贡献。我们提议了一个极端事件宣传框架,以尽量扩大已知原因与未来高影响数量之间的反实际因果关系概率。极端价值理论为模拟高尾部提供了一种工具,而葡萄干料则是捕捉大量联合极端行为的灵活手段。我们优化因果关系的概率,并将我们的框架应用于伦敦公路交通和空气污染物数据集。我们复制记录下来的大气机制,超越线性关系。这为在大量应用中量化极端的传播提供了一个新工具。