Northrop, PJ; Attalides, N; Jonathan, P; (2017) Cross-validatory extreme value threshold selection and uncertainty with application to ocean storm severity. Journal of the Royal Statistical Society Series C: Applied Statistics , 66 (1) pp. 93-120. 10.1111/rssc.12159.

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Abstract

Designs conditions for marine structures are typically informed by threshold-based extreme value analyses of oceanographic variables, in which excesses of a high threshold are modelled by a generalized Pareto (GP) distribution. Too low a threshold leads to bias from model mis-specification; raising the threshold increases the variance of estimators: a bias-variance trade-off. Many existing threshold selection methods do not address this trade-off directly, but rather aim to select the lowest threshold above which the GP model is judged to hold approximately. In this paper Bayesian cross-validation is used to address the trade-off by comparing thresholds based on predictive ability at extreme levels. Extremal inferences can be sensitive to the choice of a single threshold. We use Bayesian model-averaging to combine inferences from many thresholds, thereby reducing sensitivity to the choice of a single threshold. The methodology is applied to significant wave height datasets from the northern North Sea and the Gulf of Mexico.

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