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Statistics of extreme ocean environments: Non-stationary inference for directionality and other covariate effects

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Statistics of extreme ocean environments: Non-stationary inference for directionality and other covariate effects. / Jones, M.; Randell, D.; Ewans, K.; Jonathan, P.

In: Ocean Engineering, Vol. 119, 01.06.2016, p. 30-46.

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Jones, M. ; Randell, D. ; Ewans, K. ; Jonathan, P. / Statistics of extreme ocean environments: Non-stationary inference for directionality and other covariate effects. In: Ocean Engineering. 2016 ; Vol. 119. pp. 30-46.

Bibtex

@article{cb117f2efa644f9faa90d965b2074054,
title = "Statistics of extreme ocean environments: Non-stationary inference for directionality and other covariate effects",
abstract = "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. {\textcopyright} 2016 Elsevier Ltd. All rights reserved.",
keywords = "Covariate, Extreme, Gaussian process, Kullback-Leibler, mMALA, Non-parametric, Non-stationary, Smoothing, Spline, Bayesian networks, Computational efficiency, Gaussian distribution, Gaussian noise (electronic), Markov processes, Maximum likelihood, Pareto principle, Splines, Covariates, Gaussian Processes, Nonstationary, Inference engines, algorithm, covariance analysis, Gaussian method, geostatistics, Markov chain, Monte Carlo analysis, ocean wave, parameterization, smoothing, wave height",
author = "M. Jones and D. Randell and K. Ewans and P. Jonathan",
year = "2016",
month = jun,
day = "1",
doi = "10.1016/j.oceaneng.2016.04.010",
language = "English",
volume = "119",
pages = "30--46",
journal = "Ocean Engineering",
issn = "0029-8018",
publisher = "Elsevier Ltd",

}

RIS

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 -