TY - JOUR

T1 - Bayesian Spatial Clustering of Extremal Behavior for Hydrological Variables

AU - Rohrbeck, C.

AU - Tawn, J.A.

N1 - This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Computational and Graphical Statistics on 09/07/2020, available online: https://www.tandfonline.com/doi/abs/10.1080/10618600.2020.1777139

PY - 2020/7/9

Y1 - 2020/7/9

N2 - 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. © 2020, © 2020 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

AB - 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. © 2020, © 2020 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

KW - Bayesian clustering

KW - Composite likelihood

KW - Extreme value analysis

KW - Reversible jump Markov chain Monte Carlo

KW - Spatio-temporal modeling

U2 - 10.1080/10618600.2020.1777139

DO - 10.1080/10618600.2020.1777139

M3 - Journal article

JO - Journal of Computational and Graphical Statistics

JF - Journal of Computational and Graphical Statistics

SN - 1061-8600

ER -