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

TL;DR

This paper introduces a Bayesian cross-validation approach for selecting thresholds in extreme value analysis of oceanographic data, improving the robustness of storm severity estimates by accounting for threshold uncertainty.

Contribution

It proposes a Bayesian model-averaging method combined with cross-validation to better handle threshold selection and uncertainty in extreme value analysis of ocean data.

Findings

Improved threshold selection via Bayesian cross-validation.

Reduced sensitivity to threshold choice through model-averaging.

Application to real oceanographic datasets demonstrates effectiveness.

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.