Bayesian inference for nonstationary marginal extremes

Randell, David; Turnbull, Kathryn; Ewans, Kevin; Jonathan, Philip

doi:10.1002/env.2403

Cited by 36 publications

(31 citation statements)

References 49 publications

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“…This would also mean that the different smoothness of the spline basis would have to adjust to different dimensions. A robust estimation of the spline parameters could possibly be attempted through the extension of the recently proposed Bayesian inference (Randell et al, 2015b), which appears to offer yet further computational advantages. The validation approach shown here for hindcast values with respect to measurements needs to be extended and an appropriate calibration strategy formulated.…”

Section: Resultsmentioning

confidence: 99%

Consistent Design Criteria for South China Sea With a Large-Scale Extreme Value Model

Raghupathi

Randell

Jonathan

et al. 2016

Day 4 Fri, March 25, 2016

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Existing metocean design criteria for offshore facilities in the South China Sea have been estimated using different data and procedures, some of which are at least partly ad hoc. As a result, it is probable that existing criteria are inconsistent, in the sense that assets designed to the same design codes have different realised levels of integrity. To address this concern in this paper, we apply a large-scale extreme value model adapted to parallel computing environment, applied to the recent high-resolution SEAFINE hindcast database. This not only ensures design criteria that are statistically and spatially consistent but is also faster by avoiding the need for repetitive site-specific analysis. We have to overcome several challenges before we can apply a large-scale extreme model on the SEAFINE database. These include identifying a spatially consistent set of storm peaks and validating the hindcast data with real measurements. We then estimate marginal return values for significant wave height for locations within a large spatial neighbourhood, accounting for spatial and storm directional variability of peaks over threshold. A quantile regression identifies the extreme value threshold, the rate of exceedance of which is described using a Poisson process. The size of threshold exceedances is described by a generalised Pareto model. The characteristics of the threshold, rate and size models are all non-stationary with respect to directional and spatial covariates, parameterised in terms of (multidimensional) penalised B-splines. Parameter estimation is computationally challenging, but a combination of efficient generalised linear array algorithms executed within a parallel computing environment enable maximum likelihood estimation of all models. Bootstrap resampling is used to estimate uncertainties of model parameters and return values. We thus estimate consistent marginal return values for significant wave height and their uncertainties, at all locations in the spatial neighbourhood. In addition, we quantify directional variability of return values across different return periods. We rigorously validate the proposed spatiodirectional model with that of a direction-only model by deriving model diagnostics for the same site and demonstrating equivalent goodness of fits. To our knowledge this is the first of a kind of application of large-scale estimation for the South China Sea. With this approach, design criteria for large spatial domains, non-stationary with respect to the appropriate environmental covariates, can be estimated efficiently, consistently and with quantified uncertainty.

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Section: Resultsmentioning

confidence: 99%

Consistent Design Criteria for South China Sea With a Large-Scale Extreme Value Model

Raghupathi

Randell

Jonathan

et al. 2016

Day 4 Fri, March 25, 2016

Self Cite

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“…Examples include the work of Frigessi et al (2002), Behrens et al (2004), MacDonald et al (2011) and Randell et al (2015). At the current time, however, given sample quality and the need for a simple "designer" distribution for straightforward application, we judge the proposed WGP model fit for purpose .…”

Section: Discussion and Suggestions For Further Investigationmentioning

confidence: 99%

On the distribution of wave height in shallow water

Randell

Christou

et al. 2016

Coastal Engineering

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The statistical distribution of the height of sea waves in deep water has been modelled using the Rayleigh (LonguetHiggins 1952) and Weibull distributions (Forristall 1978). Depth-induced wave breaking leading to restriction on the ratio of wave height to water depth require new parameterisations of these or other distributional forms for shallow water. Glukhovskiy (1966) proposed a Weibull parameterisation accommodating depth-limited breaking, modified by van Vledder (1991). Battjes and Groenendijk (2000) suggested a two-part Weibull-Weibull distribution. Here we propose a two-part Weibull-generalised Pareto model for wave height in shallow water, parameterised empirically in terms of sea state parameters (significant wave height, H S , local wave-number, k L , and water depth, d), using data from both laboratory and field measurements from 4 o↵shore locations. We are particularly concerned that the model can be applied usefully in a straightforward manner; given three pre-specified universal parameters, the model further requires values for sea state significant wave height and wave number, and water depth so that it can be applied. The model has continuous probability density, smooth cumulative distribution function, incorporates the Miche upper limit for wave heights (Miche 1944) and adopts H S as the transition wave height from Weibull body to generalised Pareto tail forms. Accordingly, the model is e↵ectively a new form for the breaking wave height distribution. The estimated model provides good predictive performance on laboratory and field data.

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“…It appears that specification of a piecewise model for the whole sample (e.g. Behrens et al 2004, Mac-Donald et al 2011, Randell et al 2015b) incorporating the appropriate tail form, rather than a model for threshold exceedances in isolation is a promising route, since then threshold and tail parameters can be estimated together. However, even the simplest form of a whole sample model requires estimation of additional parameters for the model below the threshold; these parameters are also typically non-stationary with respect to covariates.…”

Section: Discussionmentioning

confidence: 99%

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

et al. 2016

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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractNumerous 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 article 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.

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Bayesian inference for nonstationary marginal extremes

Cited by 36 publications

References 49 publications

Consistent Design Criteria for South China Sea With a Large-Scale Extreme Value Model

Consistent Design Criteria for South China Sea With a Large-Scale Extreme Value Model

On the distribution of wave height in shallow water

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

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