Stuart Coles - Academia.edu (original) (raw)

Papers by Stuart Coles

Valori estremi e complessita ̀ computazionale: una applicazione agli

Nello studio di sistemi ambientali complessi, giocano un ruolo rilevante sia la statistica comput... more Nello studio di sistemi ambientali complessi, giocano un ruolo rilevante sia la statistica computazionale che la teoria dei valori estremi. In questo articolo verrà illustrata l'applicazione di un nuovo algoritmo MCMC likelihood-free ad un problema stereologico di valori estremi. Fare inferenza sulla dimensione di oggetti campionati in modo stereologicoè un problema classico. In alcune applicazioni industriali e biologiche, l'obiettivo primarioè la comprensione del comportamento estremo di tali oggetti. Ciò collega la stereologia classica alla teoria dei valori estremi. In questa presentazione verranno discussi due casi: il primo in cui gli oggetti possono essere assunti di forma sferica, il secondo in cui tale assunzione non può essere formulata. Nel primo caso, l'approccio stereologico standard combinato con la teoria dei valori estremi può portare alla formulazione di un modello gerarchico facilmente trattabile attraverso l'inferenza basata su MCMC. Nel secondo caso, dove non sono disponibili risultati stereologici standard, l'inferenza viene condotta mediante un nuovo algoritmo likelihood-free. Entrambe le versioni del problema sono illustrate utilizzando un'applicazione relativa alla produzione di acciaio, la cui purezzaè compromessa dalla presenza di microscopiche impurità .

The Annals of Applied Probability, 1997

It is known that maxima of independent Poisson variables cannot be normalized to converge to a no... more It is known that maxima of independent Poisson variables cannot be normalized to converge to a nondegenerate limit distribution. On the other hand, the Normal distribution approximates the Poisson distribution for large values of the Poisson mean, and maxima of random samples of Normal variables may be linearly scaled to converge to a classical extreme value distribution. We here explore the boundary between these two kinds of behavior. Motivation comes from the wish to construct models for the statistical analysis of extremes of background gamma radiation over the United Kingdom. The methods extend to row-wise maxima of certain triangular arrays, for which limiting distributions are also derived.

Stochastic Environmental Research and Risk Assessment, 2005

There is an urgent need for the development and implementation of modern statistical methodology ... more 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 inconsistenices 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.

Statistical Methods and Applications, 2007

Il programma di monitoraggio della costa di Holderness, iniziato nel 1951, fornisce un'inestimabi... more Il programma di monitoraggio della costa di Holderness, iniziato nel 1951, fornisce un'inestimabile sorgente di informazioni spazio-temporali del fenomeno dell'erosione costiera. Capire e prevedere l'entità dell'attività erosivaè importante per un'adeguata pianificazione dell'uso del territorio. Fino a poco tempo fa i metodi previsivi utilizzati nell'ambito dell'erosione costiera sono stati di tipo deterministico; solo negli ultimi anni siè cominciato ad utilizzare semplici modelli probabilistici per catturare la forte variabilità del processo erosivo. Il nostro scopo, presentando un modello gerarchico a effetti casuali,è quello di migliorare tali modelli cercando di utilizzare al meglio le conoscenze sulle dinamiche dell'erosione costiera. Si presenta anche una soluzione al problema dei dati mancanti, attraverso tecniche di Reversible Jump MCMC.

Journal of the American Statistical Association, 2002

Journal of the American Statistical Association, 2007

In the production of clean steels the occurrence of imperfections-so-called inclusions-is unavoid... more In the production of clean steels the occurrence of imperfections-so-called inclusions-is unavoidable. Furthermore, the strength of a clean steel block is largely dependent on the size of the largest imperfection 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 previously been tackled 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: to assess the robustness of such inferences with respect to the assumption of spherical inclusions, and to develop an inference procedure that is valid for non-spherical inclusions. We investigate both of these aspects by extending the spherical family for inclusion shapes to a family of ellipsoids. The issue of robustness is then addressed 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, since 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.

Journal of Hydrology, 2003

It is an embarrassingly frequent experience that statistical practice fails to foresee historical... more 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.

Extremes, 1999

Meteorological data are often recorded at a number of spatial locations. This gives rise to the p... more Meteorological data are often recorded at a number of spatial locations. This gives rise to the possibility of pooling data through a spatial model to overcome some of the limitations imposed on an extreme value analysis by a lack of information. In this paper we develop a spatial model for extremes based on a standard representation for site-wise extremal behavior, combined with a spatial latent process for parameter variation over the region. A smooth, but possibly non-linear, spatial structure is an intrinsic feature of the model, and difficulties in computation are solved using Markov chain Monte Carlo inference. A simulation study is carried out to illustrate the potential gain in efficiency achieved by the spatial model. Finally, the model is applied to data generated from a climatological model in order to characterize the hurricane climate of the Gulf and Atlantic coasts of the United States.

Extremes, 2003

General theory on the extremes of stationary processes leads only to a limited representation for... more 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.

Biostatistics, 2001

Biomedical trials often give rise to data having the form of time series of a common process on s... more Biomedical trials often give rise to data having the form of time series of a common process on separate individuals. One model which has been proposed to explain variations in such series across individuals is a random effects model based on sample periodograms. The use of spectral coefficients enables models for individual series to be constructed on the basis of standard asymptotic theory, whilst variations between individuals are handled by permitting a random effect perturbation of model coefficients. This paper extends such methodology in two ways: first, by enabling a nonparametric specification of underlying spectral behaviour; second, by addressing some of the tricky computational issues which are encountered when working with this class of random effect models. This leads to a model in which a population spectrum is specified nonparametrically through a dynamic system, and the processes measured on individuals within the population are assumed to have a spectrum which has a random effect perturbation from the population norm. Simulation studies show that standard MCMC algorithms give effective inferences for this model, and applications to biomedical data suggest that the model itself is capable of revealing scientifically important structure in temporal characteristics both within and between individual processes.

Biometrika, 1997

In recent research on extreme value statistics, there has been an extensive development of thresh... more In recent research on extreme value statistics, there has been an extensive development of threshold methods, first in the univariate case but subsequently in the multivariate case as well. In this paper, we develop an alternative methodology for extreme values of univariate time series, by assuming that the time series is Markovian and using bivariate extreme value theory to suggest appropriate models for the transition distributions. We develop an alternative form of the likelihood representation for threshold methods, and then show how this can be applied to a Markovian time series. A major motivation for developing this kind of theory, in comparison with existing methods based on cluster maxima, is the possibility of calculating probability distributions for extremal functionals more complicated than the maxima or extreme quantiles of the series. In the latter part of the paper, we develop this theme, showing how a theory of compound Poisson limits for additive functionals can be combined with simulation to obtain numerical solutions for problems of practical interest.

Bernoulli, 2000

At extreme levels, it is known that for a particular choice of marginal distribution, transitions... more At extreme levels, it is known that for a particular choice of marginal distribution, transitions of a Markov chain behave like a random walk. For a broad class of Markov chains, we give a characterization for the step length density of the limiting random walk, which leads to an interesting suf®ciency property. This representation also leads us to propose a new technique for kernel density estimation for this class of models.

MSOR Connections, 2019

The standard version of the game Rock-Paper-Scissors is interesting in terms of game theory, but ... more 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.

Journal of the Royal Statistical Society: …, 1997

A parametric model is developed and fitted to English league and cup football data from 1992 to 1... more A parametric model is developed and fitted to English league and cup football data from 1992 to 1995. The model is motivated by an aim to exploit potential inefficiencies in the association football betting market, and this is examined using bookmakers' odds from 1995 to 1996. The technique is based on a Poisson regression model but is complicated by the data structure and the dynamic nature of teams' performances. Maximum likelihood estimates are shown to be computationally obtainable, and the model is shown to have a positive return when used as the basis of a betting strategy.