Bayesian spatial clustering of extremal behaviour for hydrological variables

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