SUMMARYIn this paper, we investigate the effects of declustering applied to sequences of extreme observations. Through a simulation study, we demonstrate that the common practice of analysing peaks over thresholds (POT) is liable to incur serious bias in the estimation of parameters, as well as the return levels used as design specifications when building to withstand extremes of wind or rain, or river or sea level. We demonstrate that a much simpler approach, the direct analysis of all exceedances of a high threshold, can reduce this bias to negligible levels. This approach has, until now, been unpopular, because the data being analysed are not independent. The effect of this is to cause the standard errors associated with parameter estimates to underestimate the uncertainty attached to these estimates. We employ existing but little-used methodology to inflate these standard errors, and we demonstrate that the adjusted values are very good representations of the true uncertainty associated with maximum likelihood estimates. The overall approach has thus achieved the effect of eliminating the bias in estimation, while accounting for any undesirable effects caused by dependent data.We apply our approach to a sequence of sea-surge data from southwest England, and illustrate the discrepancies between this and a POT approach, which are consistent with the POT approach underestimating long-period return levels. We also pay considerable attention to checking the robustness of our results, demonstrating that the problems of bias caused by the POT approach apply systematically over all of the declustering schemes we consider, as well as over the entire range of tail behaviours. When the primary interest is in return-level estimation, we recommend that our procedure will generally prove to be much more effective and reliable than the POT approach. Should there be a deeper interest in the serial dependence itself, then we recommend that this dependence is explicitly modelled, and we refer the reader to an earlier paper by the authors, published in this journal.

In this paper, we investigate the relationship between return levels of a process and the strength of serial correlation present in the extremes of that process. Estimates of long period return levels are often used as design requirements, and peaks over thresholds analyses have, in the past, been used to obtain such estimates. However, analyses based on such declustering schemes are extremely wasteful of data, often resulting in great estimation uncertainty represented by very wide confidence intervals. Using simulated data, we show that—provided the extremal index is estimated appropriately—using all threshold excesses can give more accurate and precise estimates of return levels, allowing us to avoid altogether the sometimes arbitrary process of cluster identification. We then apply our method to two data examples concerning sea‐surge and wind‐speed extremes. Copyright © 2012 John Wiley & Sons, Ltd.

SUMMARYUnderstanding and quantifying the behaviour of extreme wind speeds has important applications for design in civil engineering. As in the extremal analysis of any environmental process, estimates are often required of the probability of events that are rarer than those already recorded. Consequently, research has focused on the development of techniques that make optimal use of the available data. One such approach lies in threshold methods, which, unlike the more traditional annual maxima approach to the modelling of extremes, takes into consideration all extreme events, extreme in the sense that they exceed some high threshold. However, the implications of using all extremes in an analysis include problems of temporal dependence and non-stationarity. Several pragmatic ways of circumventing the problem of temporal dependence have been developed, though these often include the deletion of many extreme observations, for example, filter out a set of independent extremes. This paper looks at another approach to inference-one which explicitly models the temporal dependence of the process and so can use information on all extremes-and investigates the appropriateness of assumptions of short-term temporal dependence for wind speeds. We also examine the success of such methods at estimating some extreme events commonly studied for wind-speed data. Throughout this paper extreme wind speeds are analysed within a Bayesian framework, which can be argued to be particularly advantageous for extreme value analyses. For example, the objective of an extreme value analysis is usually an estimate of the probability of future events reaching extreme levels-something which is handled quite naturally in a Bayesian analysis through predictive distributions.

A typical extreme value analysis is often carried out on the basis of simplistic inferential procedures, though the data being analysed may be structurally complex. Here we develop a hierarchical model for hourly gust maximum wind speed data, which attempts to identify site and seasonal effects for the marginal densities of hourly maxima, as well as for the serial dependence at each location. A Gaussian model for the random effects exploits the meteorological structure in the data, enabling increased precision for inferences at individual sites and in individual seasons. The Bayesian framework that is adopted is also exploited to obtain predictive return level estimates at each site, which incorporate uncertainty due to model estimation, as well as the randomness that is inherent in the processes that are involved. Copyright 2006 Royal Statistical Society.

This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License Newcastle University ePrints-eprint.ncl.ac.uk Fawcett L, Walshaw D. Sea-surge and wind speed extremes: optimal estimation strategies for planners and engineers. Stochastic Environmental Research and Risk Assessment 2016, 30(2), 463-480.