Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Statistics of extreme ocean environments: Non-stationary inference for directionality and other covariate effects
AU - Jones, M.
AU - Randell, D.
AU - Ewans, K.
AU - Jonathan, P.
PY - 2016/6/1
Y1 - 2016/6/1
N2 - Numerous approaches are proposed in the literature for non-stationarity marginal extreme value inference, including different model parameterisations with respect to covariate, and different inference schemes. The objective of this paper is to compare some of these procedures critically. We generate sample realisations from generalised Pareto distributions, the parameters of which are smooth functions of a single smooth periodic covariate, specified to reflect the characteristics of actual samples from the tail of the distribution of significant wave height with direction, considered in the literature in the recent past. We estimate extreme values models (a) using Constant, Fourier, B-spline and Gaussian Process parameterisations for the functional forms of generalised Pareto shape and (adjusted) scale with respect to covariate and (b) maximum likelihood and Bayesian inference procedures. We evaluate the relative quality of inferences by estimating return value distributions for the response corresponding to a time period of 10× the (assumed) period of the original sample, and compare estimated return values distributions with the truth using Kullback-Leibler, Cramer-von Mises and Kolmogorov-Smirnov statistics. We find that Spline and Gaussian Process parameterisations, estimated by Markov chain Monte Carlo inference using the mMALA algorithm, perform equally well in terms of quality of inference and computational efficiency, and generally perform better than alternatives in those respects. © 2016 Elsevier Ltd. All rights reserved.
AB - Numerous approaches are proposed in the literature for non-stationarity marginal extreme value inference, including different model parameterisations with respect to covariate, and different inference schemes. The objective of this paper is to compare some of these procedures critically. We generate sample realisations from generalised Pareto distributions, the parameters of which are smooth functions of a single smooth periodic covariate, specified to reflect the characteristics of actual samples from the tail of the distribution of significant wave height with direction, considered in the literature in the recent past. We estimate extreme values models (a) using Constant, Fourier, B-spline and Gaussian Process parameterisations for the functional forms of generalised Pareto shape and (adjusted) scale with respect to covariate and (b) maximum likelihood and Bayesian inference procedures. We evaluate the relative quality of inferences by estimating return value distributions for the response corresponding to a time period of 10× the (assumed) period of the original sample, and compare estimated return values distributions with the truth using Kullback-Leibler, Cramer-von Mises and Kolmogorov-Smirnov statistics. We find that Spline and Gaussian Process parameterisations, estimated by Markov chain Monte Carlo inference using the mMALA algorithm, perform equally well in terms of quality of inference and computational efficiency, and generally perform better than alternatives in those respects. © 2016 Elsevier Ltd. All rights reserved.
KW - Covariate
KW - Extreme
KW - Gaussian process
KW - Kullback-Leibler
KW - mMALA
KW - Non-parametric
KW - Non-stationary
KW - Smoothing
KW - Spline
KW - Bayesian networks
KW - Computational efficiency
KW - Gaussian distribution
KW - Gaussian noise (electronic)
KW - Markov processes
KW - Maximum likelihood
KW - Pareto principle
KW - Splines
KW - Covariates
KW - Gaussian Processes
KW - Nonstationary
KW - Inference engines
KW - algorithm
KW - covariance analysis
KW - Gaussian method
KW - geostatistics
KW - Markov chain
KW - Monte Carlo analysis
KW - ocean wave
KW - parameterization
KW - smoothing
KW - wave height
U2 - 10.1016/j.oceaneng.2016.04.010
DO - 10.1016/j.oceaneng.2016.04.010
M3 - Journal article
VL - 119
SP - 30
EP - 46
JO - Ocean Engineering
JF - Ocean Engineering
SN - 0029-8018
ER -