To address the need for efficient inference for a range of hydrological extreme value problems, spatial pooling of information is the standard approach for marginal tail estimation. We propose the first extreme value spatial clustering methods which account for both the similarity of the marginal tails and the spatial dependence structure of the data to determine the appropriate level of pooling. Spatial dependence is incorporated in two ways: to determine the cluster selection and to account for dependence of the data over sites within a cluster when making the marginal inference. We introduce a statistical model for the pairwise extremal dependence which incorporates distance between sites, and accommodates our belief that sites within the same cluster tend to exhibit a higher degree of dependence than sites in different clusters. We use a Bayesian framework which learns about both the number of clusters and their spatial structure, and that enables the inference of site-specific marginal distributions of extremes to incorporate uncertainty in the clustering allocation. The approach is illustrated using simulations, the analysis of daily precipitation levels in Norway and daily river flow levels in the UK.

中文翻译：

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水文变量极值行为的贝叶斯空间聚类

为了满足对一系列水文极值问题进行有效推理的需要，信息的空间池化是边缘尾部估计的标准方法。我们提出了第一个极值空间聚类方法，它考虑了边缘尾部的相似性和数据的空间依赖性结构，以确定适当的池化水平。空间相关性以两种方式合并：确定集群选择，并在进行边际推断时考虑集群内数据的相关性。我们为成对极值依赖引入了一个统计模型，该模型包含站点之间的距离，并适应我们的信念，即同一集群中的站点往往比不同集群中的站点表现出更高程度的依赖。我们使用贝叶斯框架来了解集群的数量及其空间结构，并且能够推断特定地点的极端边缘分布，从而将不确定性纳入集群分配中。使用模拟、挪威每日降水量和英国每日河流流量分析来说明该方法。