The standard version of the game Rock-Paper-Scissors is interesting in terms of game theory, but less so in terms of Statistics. However, we show that with a small rule change it can be made into an interactive exercise for degree-level students of Statistics that leads to a Bayesian change-point model, for which the Gibbs sampler provides an intuitive method of inference. First, students play the game to generate the data. Second, they are encouraged to formulate a model that reflects their experience from having played the game. And third, they participate in the development of a suitable MCMC algorithm to fit the model.

Aims: Swimmers commonly complain of nasal symptoms probably due to mucosal irritation caused by chlorinated water. The aim of the present prospective study was to investigate changes in nasal function and cytology in a cohort of 15 volunteer competitive swimmers, as compared with a control group of 15 competitive athletes practicing other sports. Methods: Olfactory threshold for n-butanol was measured in a population of competitive swimmers. Changes in nasal function and cytology were compared between the two groups of volunteer competitive athletes. Results: There were no significant differences between the two groups in terms of mean 20-Item Sino-Nasal Outcome Test scores, peak nasal inspiratory flow, pulmonary peak expiratory flow, or total nasal resistance on anterior active rhinomanometry. Nasal mucociliary transport time (MCTt) was significantly shorter for the non-swimmers than for the swimmers. The mean olfactory threshold for n-butanol in the swimmers was significantly lower than in the other group of athletes. Conclusions: Data seem to confirm the utility of MCTt in studying nasal mucosa damage caused by chlorinated water. The present results also support the hypothesis of a role for the olfactory threshold in evaluating damage to the olfactory mucosa exposed to chlorinated water.

A global database of large explosive volcanic eruptions has been compiled for the Holocene and analyzed using extreme value theory to estimate magnitude‐frequency relationships. The database consists of explosive eruptions with magnitude (M) greater than or equal to 4. Two models are applied to the data, one assuming no underreporting of eruptions and the other taking underreporting into consideration. Results from the latter indicate that the level of underreporting is high and fairly constant from the start of the Holocene until about 1 A.D. and then decreases dramatically toward the present. Results indicate there is only a ∼20% probability that an explosive eruption of M = 6 occurring prior to 1 A.D. is recorded. Analysis of the data set in the time periods 1750 A.D. and 1900 A.D. to present (assuming no underreporting) suggests that that these periods are likely to be too short to give reliable estimates of return periods for explosive eruptions with M > 6. Analysis of the Holocene data set with corrections for underreporting bias provide robust magnitude‐frequency relationships up to M = 7. Extrapolation of the model to greater magnitudes (M > 8) gives results inconsistent with geological data, predicting eruption size upper limits much smaller than known eruptions such as the Fish Canyon Tuff. We interpret this result as the consequence of different mechanisms operating for explosive eruptions with M > 7.

AIMS Measurement of Peak Nasal Inspiratory Flow (PNIF) seems to be a cheap and easily performed method to assess nasal patency. As demonstrated in a previous work, PNIF is influenced by SEX, AGE and HEIGHT. However there is a large degree of between-patient variability in PNIF levels. The purpose of this analysis is to determine whether the measurement of the pulmonary ventilatory capacity, by mean of Peak Expiratory Flow (PEF), enables more precise determination of PNIF. METHODS AND RESULTS Repeated measurements of PNIF and PEF were performed in 112 volunteers. 100 of these fulfilled the study criteria (55 females and 45 males) and all of them were non-smokers, non-asthmatic, without nose and paranasal sinuses problems, with ages ranging from 15 to 71 years. Statistical analysis was undertaken to determine whether a relationship existed between PNIF and age, sex and height, but which also considered PEF. The data from both experiments were analysed together. In both groups there is a clear tendency for PNIF to increase with PEF. As clearly demonstrated in this work the value of PEF is informative in predicting PNIF and that the larger the value of PEF, the larger the value of PNIF. CONCLUSIONS PNIF is a useful method to study nasal patency in both primary and secondary care to aid diagnosis of nasal disease, but low values of PNIF have to be confirmed by a study of the PEF as PNIF low values may be an expression of low ventilatory activity rather than an expression of nasal obstruction.

In the production of clean steels, the occurrence of imperfections-so-called "inclusions"-is unavoidable. The strength of a clean steel block is largely dependent on the size of the largest imperfection that it contains, so inference on extreme inclusion size forms an important part of quality control. Sampling is generally done by measuring imperfections on planar slices, leading to an extreme value version of a standard stereological problem: how to make inference on large inclusions using only the sliced observations. Under the assumption that inclusions are spherical, this problem has been tackled previously using a combination of extreme value models, stereological calculations, a Bayesian hierarchical model, and standard Markov chain Monte Carlo (MCMC) techniques. Our objectives in this article are twofold: (1) to assess the robustness of such inferences with respect to the assumption of spherical inclusions, and (2) to develop an inference procedure that is valid for nonspherical inclusions. We investigate both of these aspects by extending the spherical family for inclusion shapes to a family of ellipsoids. We then address the issue of robustness by assessing the performance of the spherical model when fitted to measurements obtained from a simulation of ellipsoidal inclusions. The issue of inference is more difficult, because likelihood calculation is not feasible for the ellipsoidal model. To handle this aspect, we propose a modification to a recently developed likelihood-free MCMC algorithm. After verifying the viability and accuracy of the proposed algorithm through a simulation study, we analyze a real inclusion dataset, comparing the inference obtained under the ellipsoidal inclusion model with that previously obtained assuming spherical inclusions.

There is an urgent need for the development and implementation of modern statistical methodology for long-term risk assessment of extreme hydrological hazards in the Caribbean. Notwithstanding the inevitable scarcity of data relating to extreme events, recent results and approaches call into question standard methods of estimation of the risks of environmental catastrophes that are currently adopted. Estimation of extreme hazards is often based on the Gumbel model and on crude methods for estimating predictive probabilities. In both cases the result is often a remarkable underestimation of the predicted probabilities for disasters of large magnitude. Simplifications do not stop here: assumptions of data homogeneity and temporal independence are usually made regardless of potential inconsistencies with genuine process behaviour and the fact that results may be sensitive to such mis-specifications. These issues are of particular relevance for the Caribbean, given its exposure to diverse meteorological climate conditions.In this article we present an examination of predictive methodologies for the assessment of long-term risks of hydrological hazards, with particular focus on applications to rainfall and flooding, motivated by three data sets from the Caribbean region. Consideration is given to classical and Bayesian methods of inference for annual maxima and daily peaks-over-threshold models. We also examine situations where data non-homogeneity is compromised by an unknown seasonal structure, and the situation in which the process under examination has a physical upper limit. We highlight the fact that standard Gumbel analyses routinely assign near-zero probability to subsequently observed disasters, and that for San Juan, Puerto Rico, standard 100-year predicted rainfall estimates may be routinely underestimated by a factor of two.

AIMS:Measurement of Peak Nasal Inspiratory Flow (PNIF) seems to be a cheap, simple, easily performed method to assess nasal patency. The purpose of this study is to establish normative PNIF data for a healthy adult population and provide charts relating PNIF normal values with age, height and sex in adults.METHODS AND RESULTS:Repeated measurements of PNIF were performed in 170 volunteers. In total, 137 of these fulfilled the study criteria (66 females and 50 males) and all of them were non-smokers, non-asthmatic, without nose and paranasal sinuses problems, with ages ranging from 16 to 84 years. Data were statistically analysed and tables were produced relating PNIF to age, sex and height. There was no interaction of sex with age or height. There was considerable residual variability of PNIF between individuals not explained by any of the variables studied.CONCLUSIONS:We conclude that PNIF could be a useful method to study nasal patency in both primary and secondary care to aid diagnosis of nasal disease. The study provides normative data for a Caucasian population. Further variables need to be explored to predict expected PNIF values more accurately.

Extreme value analysis of sea levels is an essential component of risk analysis and protection strategy for many coastal regions. Since the tidal component of the sea level is deterministic, it is the stochastic variation in extreme surges that is the most important to model. Historically, this modelling has been accomplished by fitting classical extreme value models to series of annual maxima data. Recent developments in extreme value modelling have led to alternative procedures that make better use of available data, and this has led to much refined estimates of extreme surge levels. However, one aspect that has been routinely ignored is seasonality. In an earlier study we identified strong seasonal effects at one of the number of locations along the eastern coastline of the United Kingdom. In this article, we discuss the construction and inference of extreme value models for processes that include components of seasonality in greater detail. We use a point process representation of extreme value behaviour, and set our inference in a Bayesian framework, using simulation-based techniques to resolve the computational issues. Though contemporary, these techniques are now widely used for extreme value modelling. However, the issue of seasonality requires delicate consideration of model specification and parameterization, especially for efficient implementation via Markov chain Monte Carlo algorithms, and this issue seems not to have been much discussed in the literature. In the present paper we make some suggestions for model construction and apply the resultant model to study the characteristics of the surge process, especially in terms of its seasonal variation, on the eastern UK coastline. Furthermore, we illustrate how an estimated model for seasonal surge can be combined with tide records to produce return level estimates for extreme sea levels that accounts for seasonal variation in both the surge and tidal processes.

Extreme value analysis of sea levels is an essential component of risk analysis and protection strategy for many coastal regions. Since the tidal component of the sea level is deterministic, it is the stochastic variation in extreme surges that is the most important to model. Historically, this modelling has been accomplished by fitting classical extreme value models to series of annual maxima data. Recent developments in extreme value modelling have led to alternative procedures that make better use of available data, and this has led to much refined estimates of extreme surge levels. However, one aspect that has been routinely ignored is seasonality. In an earlier study we identified strong seasonal effects at one of the number of locations along the eastern coastline of the United Kingdom. In this article, we discuss the construction and inference of extreme value models for processes that include components of seasonality in greater detail. We use a point process representation of extreme value behaviour, and set our inference in a Bayesian framework, using simulation-based techniques to resolve the computational issues. Though contemporary, these techniques are now widely used for extreme value modelling. However, the issue of seasonality requires delicate consideration of model specification and parameterization, especially for efficient implementation via Markov chain Monte Carlo algorithms, and this issue seems not to have been much discussed in the literature. In the present paper we make some suggestions for model construction and apply the resultant model to study the characteristics of the surge process, especially in terms of its seasonal variation, on the eastern UK coastline. Furthermore, we illustrate how an estimated model for seasonal surge can be combined with tide records to produce return level estimates for extreme sea levels that accounts for seasonal variation in both the surge and tidal processes.

The catastrophic surge event of 1953 on the eastern UK and northern European coastlines led to widespread agreement on the necessity of a coordinated response to understand the risk of future oceanographic flood events and, so far as possible, to afford protection against such events. One element of this response was better use of historical data and scientific knowledge in assessing flood risk. The timing of the event also coincided roughly with the birth of extreme value theory as a statistical discipline for measuring risks of extreme events, and over the last 50 years, as techniques have been developed and refined, various attempts have been made to improve the precision of flood risk assessment around the UK coastline. In part, this article provides a review of such developments. Our broader aim, however, is to show how modern statistical modelling techniques, allied with the tools of extreme value theory and knowledge of sea-dynamic physics, can lead to further improvements in flood risk assessment. Our long-term goal is a coherent spatial model that exploits spatial smoothness in the surge process characteristics and we outline the details of such a model. The analysis of the present article, however, is restricted to a site-by-site analysis of high-tide surges. Nonetheless, we argue that the Bayesian methodology adopted for such analysis enables a risk-based interpretation of results that is most natural in this setting, and preferable to inferences that are available from more conventional analyses.

Journal of the Royal Statistical Society: Series B (Statistical Methodology)Volume 66, Issue 3 p. 530-546 Discussion on the paper by Heffernan and Tawn First published: 28 June 2008 https://doi.org/10.1111/j.1467-9868.2004.2050b.xCitations: 1Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume66, Issue3August 2004Pages 530-546 RelatedInformation

Multivariate extreme value theory and methods concern the characterization, estimation and extrapolation of the joint tail of the distribution of a d-dimensional random variable. Existing approaches are based on limiting arguments in which all components of the variable become large at the same rate.This limit approach is inappropriate when the extreme values of all the variables are unlikely to occur together or when interest is in regions of the support of the joint distribution where only a subset of components is extreme. In practice this restricts existing methods to applications where d is typically 2 or 3. Under an assumption about the asymptotic form of the joint distribution of a d-dimensional random variable conditional on its having an extreme component, we develop an entirely new semiparametric approach which overcomes these existing restrictions and can be applied to problems of any dimension. We demonstrate the performance of our approach and its advantages over existing methods by using theoretical examples and simulation studies. The approach is used to analyse air pollution data and reveals complex extremal dependence behaviour that is consistent with scientific understanding of the process. We find that the dependence structure exhibits marked seasonality, with extremal dependence between some pollutants being significantly greater than the dependence at non-extreme levels.

SummaryWhen catastrophes strike it is easy to be wise after the event. It is also often argued that such catastrophic events are unforeseeable, or at least so implausible as to be negligible for planning purposes. We consider these issues in the context of daily rainfall measurements recorded in Venezuela. Before 1999 simple extreme value techniques were used to assess likely future levels of extreme rainfall, and these gave no particular cause for concern. In December 1999 a daily precipitation event of more than 410 mm, almost three times the magnitude of the previously recorded maximum, caused devastation and an estimated 30000 deaths. We look carefully at the previous history of the process and offer an extreme value analysis of the data—with some methodological novelty—that suggests that the 1999 event was much more plausible than the previous analyses had claimed. Deriving design parameters from the results of such an analysis may have had some mitigating effects on the consequences of the subsequent disaster. The themes of the new analysis are simple: the full exploitation of available data, proper accounting of uncertainty, careful interpretation of asymptotic limit laws and allowance for non-stationarity. The effect on the Venezuelan data analysis is dramatic. The broader implications are equally dramatic; that a naïve use of extreme value techniques is likely to lead to a false sense of security that might have devastating consequences in practice.

General theory on the extremes of stationary processes leads only to a limited representation for extreme-state behaviour, usually summarised by the extremal index. In practice this means that other quantities such as the duration of extreme episodes or aggregate of threshold exceedances within a cluster require stronger model assumptions. In this paper we propose a model based on a Markov assumption for the underlying process, with high-level transitions determined by an asymptotically motivated distribution. This idea is not new: Smith et al. (1997) first developed the statistical basis for such a procedure, which was subsequently extended by Bortot and Tawn (1998) to better handle the case of weak extremal temporal dependence for which the extremal index is unity. We adopt similar procedures to each of these earlier works, but suggest a different model for the Markov transitions. The model we use was developed by Coles and Pauli (2002) to enable a Bayesian inference of multivariate extremes that provides a posterior distribution on the status of asymptotic independence. By adopting this model in the Markov framework, we show here that the model has all the flexibility of the model developed by Bortot and Tawn (1998), but with the additional advantage of providing a posterior probability on the extremal index and inferences that take full account of the uncertainty in the extremal index. We demonstrate the methodology on both simulated data and a time series of daily rainfall that exhibit weak temporal dependence at extreme levels.

It is an embarrassingly frequent experience that statistical practice fails to foresee historical disasters. It is all too easy to blame global trends or some sort of external intervention, but in this article we argue that statistical methods that do not take comprehensive account of the uncertainties involved in both model and predictions, are bound to produce an over-optimistic appraisal of future extremes that is often contradicted by observed hydrological events. Based on the annual and daily rainfall data on the central coast of Venezuela, different modeling strategies and inference approaches show that the 1999 rainfall which caused the worst environmentally related tragedy in Venezuelan history was extreme, but not implausible given the historical evidence. We follow in turn a classical likelihood and Bayesian approach, arguing that the latter is the most natural approach for taking into account all uncertainties. In each case we emphasize the importance of making inference on predicted levels of the process rather than model parameters. Our most detailed model comprises of seasons with unknown starting points and durations for the extremes of daily rainfall whose behavior is described using a standard threshold model. Based on a Bayesian analysis of this model, so that both prediction uncertainty and process heterogeneity are properly modeled, we find that the 1999 event has a sizeable probability which implies that such an occurrence within a reasonably short time horizon could have been anticipated. Finally, since accumulation of extreme rainfall over several days is an additional difficulty—and indeed, the catastrophe of 1999 was exaggerated by heavy rainfall on successive days—we examine the effect of timescale on our broad conclusions, finding results to be broadly similar across different choices.