TY - JOUR

T1 - Cross-validatory extreme value threshold selection and uncertainty with application to ocean storm severity

AU - Northrop, P.J.

AU - Attalides, N.

AU - Jonathan, P.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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. © 2016 Royal Statistical Society

AB - 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. © 2016 Royal Statistical Society

KW - Cross-validation

KW - Extreme value theory

KW - Generalized Pareto distribution

KW - Predictive inference

KW - Threshold

U2 - 10.1111/rssc.12159

DO - 10.1111/rssc.12159

M3 - Journal article

VL - 66

SP - 93

EP - 120

JO - Journal of the Royal Statistical Society: Series C (Applied Statistics)

JF - Journal of the Royal Statistical Society: Series C (Applied Statistics)

SN - 0035-9254

IS - 1

ER -