Cross‐validatory extreme value threshold selection and uncertainty with application to ocean storm severity

Summary

Design 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 distribution. Too low a threshold leads to bias from model misspecification, and 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 generalized Pareto model is judged to hold approximately. In the 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 data sets from the northern North Sea and the Gulf of Mexico.