Abstract Describing the complex dependence structure of extreme phenomena is particularly challenging. To tackle this issue, we develop a novel statistical method that describes extremal dependence taking advantage of the inherent tree-based dependence structure of the max-stable nested logistic distribution, and which identifies possible clusters of extreme variables using reversible jump Markov chain Monte Carlo techniques. Parsimonious representations are achieved when clusters of extreme variables are found to be completely independent. Moreover, we significantly decrease the computational complexity of full likelihood inference by deriving a recursive formula for the likelihood function of the nested logistic model. The method’s performance is verified through extensive simulation experiments which also compare different likelihood procedures. The new methodology is used to investigate the dependence relationships between extreme concentrations of multiple pollutants in California and how these concentrations are related to extreme weather conditions. Overall, we show that our approach allows for the representation of complex extremal dependence structures and has valid applications in multivariate data analysis, such as air pollution monitoring, where it can guide policymaking. Supplementary materials for this article are available online.

中文翻译：

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贝叶斯模型对多元极端的基于树的依赖结构进行平均

摘要 描述极端现象的复杂依赖结构尤其具有挑战性。为了解决这个问题，我们开发了一种新的统计方法，该方法利用最大稳定嵌套逻辑分布的固有的基于树的依赖结构来描述极值依赖，并使用可逆跳跃马尔可夫链蒙特卡罗技术识别可能的极端变量集群. 当发现极端变量的集群完全独立时，就实现了简约表示。此外，我们通过推导出嵌套逻辑模型的似然函数的递归公式，显着降低了全似然推理的计算复杂度。该方法的性能通过广泛的模拟实验得到验证，这些模拟实验还比较了不同的似然程序。新方法用于研究加利福尼亚多种污染物的极端浓度之间的依赖关系以及这些浓度与极端天气条件之间的关系。总的来说，我们表明我们的方法允许表示复杂的极值依赖结构，并且在多变量数据分析中具有有效的应用，例如空气污染监测，它可以指导决策。本文的补充材料可在线获取。我们表明，我们的方法允许表示复杂的极值依赖结构，并且在多变量数据分析中具有有效的应用，例如空气污染监测，它可以指导决策。本文的补充材料可在线获取。我们表明，我们的方法允许表示复杂的极值依赖结构，并且在多变量数据分析中具有有效的应用，例如空气污染监测，它可以指导决策。本文的补充材料可在线获取。