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.

The Generalized Pareto (GP) and Generalized extreme value (GEV) distributions play an important role in extreme value analyses, as models for threshold excesses and block maxima respectively.For each of these distributions we consider Bayesian inference using "reference" prior distributions (in the general sense of priors constructed using formal rules) for the model parameters, specifically a Jeffreys prior, the maximal data information (MDI) prior and independent uniform priors on separate model parameters.We investigate the important issue of whether these improper priors lead to proper posterior distributions.We show that, in the GP and GEV cases, the MDI prior, unless modified, never yields a proper posterior and that in the GEV case this also applies to the Jeffreys prior. We also show that a sample size of three (four) is sufficient for independent uniform priors to yield a proper posterior distribution in the GP (GEV) case.