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. By combining the models for the marginal tails and the dependence structure, we obtain a composite likelihood for the joint spatial distribution. 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. Code and data for the simulation study and river flow example are available in the online supplementary materials.
|Original language||English (US)|
|Number of pages||15|
|Journal||Journal of Computational and Graphical Statistics|
|State||Published - Jul 9 2020|
Bibliographical noteKAUST Repository Item: Exported on 2022-06-14
Acknowledged KAUST grant number(s): OSR-2017-CRG6-3434.02
Acknowledgements: Christian Rohrbeck is beneficiary of an AXA Research Fund postdoctoral grant. We gratefully acknowledge funding from the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) project “Statistical Estimation and Detection of Extreme Hot Spots with Environmental and Ecological Applications” (Award No. OSR-2017-CRG6-3434.02). We thank Rob Lamb, Raphël Huser, Daniel Cooley, the associate editor and the reviewers for helpful comments and suggestions, and Ida Scheel and Ross Towe for providing access to the Norwegian rainfall data and UK river flow data, respectively.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Statistics and Probability
- Statistics, Probability and Uncertainty