a nonparametric estimation procedure for bivariate extreme value copulas summary a bivariate extreme value distribution with fixed marginals is generated by a onedimensional map called a dependence function this paper proposes a new nonparametric estimator of this function its asymptotic properties are examined and its small sample behaviour is compared to that of other rank based and likelihood based procedures the new estimator is shown to be uniformly strongly convergent and asymptotically unbiased through simulations it is also seen to perform reasonably well against the maximum likelihood estimator based on the correct model and to have smaller l1 l2 and l errors than any existing nonparametric alternative the n consistency of the proposed estimator leads to nonparametric estimation of tawn s 1988 dependence measure that may be used to test independence in small samples

spatio temporal patterns in population dynamics abstract the transient dynamics of interacting biological species extracted from two ecosystems is investigated we model the environment interaction by a multiplicative noise and the temperature oscillations by a periodic forcing we find noise induced effects such as enhanced temporal oscillations spatial patterns and noise delayed extinction for the model of two competing species we extend our analysis to an ecosystem of three interacting species namely one predator and two preys we find spatial patterns induced by the noise

modelling dependence within joint tail regions standard approaches for modelling dependence within joint tail regions are based on extreme value methods which assume max stability a particular form of joint tail dependence we develop joint tail models based on a broader class of dependence structure which provides a natural link between max stable models and weaker forms of dependence including independence and negative association this approach overcomes many of the problems that are encountered with standard methods and is the basis for a poisson process representation that generalizes existing bivariate results we apply the new techniques to simulated and environmental data and demonstrate the marked advantage that the new approach offers for joint tail extrapolation

modelling extreme multivariate events summary the classical treatment of multivariate extreme values is through componentwise ordering though in practice most interest is in actual extreme events here the point process of observations which are extreme in at least one component is considered parametric models for the dependence between components must satisfy certain constraints two new techniques for generating such models are presented aspects of the statistical estimation of the resulting models are discussed and are illustrated with an application to oceanographic data

localization of analytic regularity criteria on the vorticity and balance between the vorticity magnitude and coherence of the vorticity direction in the 3d nse the first part of the paper provides spatio temporal localization of a family of analytic regularity classes for the 3d nse obtained by beirao da veiga space time integrability of the gradient of the velocity on mathbb r 3 times 0 t which is out of the range of the sobolev embedding theorem reduction to the classical foias ladyzhenskaya prodi serrin space time integrability conditions on the velocity as well as the localization of the beale kato majda regularity criterion time integrability of the l norm of the vorticity the second part introduces a family of local scaling invariant hybrid geometric analytic classes in which coherence of the vorticity direction serves as a weight in the local spatio temporal integrability of the vorticity magnitude

bayesian computation via the gibbs sampler and related markov chain monte carlo methods the use of the gibbs sampler for bayesian computation is reviewed and illustrated in the context of some canonical examples other markov chain monte carlo simulation methods are also briefly described and comments are made on the advantages of sample based approaches for bayesian inference summaries

rank based inference for bivariate extreme value copulas consider a continuous random pair x y whose dependence is characterized by an extreme value copula with pickands dependence function a when the marginal distributions of x and y are known several consistent estimators of a are available most of them are variants of the estimators due to pickands bull inst internat statist 49 1981 859 878 and cap era a foug eres and genest biometrika 84 1997 567 577 in this paper rank based versions of these estimators are proposed for the more common case where the margins of x and y are unknown results on the limit behavior of a class of weighted bivariate empirical processes are used to show the consistency and asymptotic normality of these rank based estimators their finite and large sample performance is then compared to that of their known margin analogues as well as with endpoint corrected versions thereof explicit formulas and consistent estimates for their asymptotic variances are also suggested

l measure of non exchangeability for bivariate extreme value and archimax copulas in the class of bivariate extreme value copulas an upper bound is calculated for the measure of non exchangeability based on the l norm distance between a copula c and its transpose ct x y c y x copulas that are maximally non exchangeable with respect to are also determined moreover similar upper bounds are given respectively for the class of all ev copulas having a fixed upper tail dependence coefficient and for the larger class of archimax copulas

geometric regularity criteria for incompressible navier stokes equations with navier boundary conditions abstract we study the regularity criteria for weak solutions to the 3d incompressible navier stokes equations in terms of the direction of vorticity taking into account the boundary conditions a boundary regularity theorem is proved on regular curvilinear domains with a family of oblique derivative boundary conditions provided that the directions of vorticity are coherently aligned up to the boundary as an application we establish the boundary regularity for weak solutions to navier stokes equations in round balls half spaces and right circular cylindrical ducts subject to the classical navier and kinematic boundary conditions

on the geometric convergence of the gibbs sampler summary the rate of convergence of the gibbs sampler is discussed the gibbs sampler is a monte carlo simulation method with extensive application to computational issues in the bayesian paradigm conditions for the geometric rate of convergence of the algorithm for discrete and continuous parameter spaces are derived and an illustrative exponential family example is given this paper investigates conditions under which the gibbs sampler gelfand and smith 1990 tanner and wong 1987 geman and geman 1984 converges at a geometric rate the main results appear in sections 2 and 3 where geometric convergence results are established with respect to total variation and supremum norms under fairly natural conditions on the underlying distribution for ease of exposition we shall concentrate on the two most commonly encountered situations where the state space is finite or continuous all our results will establish uniform convergence a strong form of geometric convergence under appropriate regularity conditions uniform convergence is a useful property in its own right but also happens to be a sufficient condition for certain ergodic central limit theorems such results are important for estimation in markov chain simulation but will not be considered in detail here our approach is to apply the theory of markov chains to the specific gibbs sampler case in the finite state space case uniform ergodicity is automatic however the situation is more complicated for continuous state spaces where even well behaved underlying distributions can give rise to markov chains which converge slowly or have unbounded kernels we give two results in this context corollary 2 and corollary 3 which establish uniform convergence under different sets of conditions on the underlying density finally we apply these results to an example of a bayesian hierarchical model where regularity conditions for geometric convergence are naturally satisfied here the hierarchical structure of the model is crucial in permitting application of corollary 3

comment on bivariate extreme value distributions an application of the gibbs sampler to the analysis of floods by p t adamson a v metcalfe and b parmentier

an m estimator for tail dependence in arbitrary dimensions consider a random sample in the max domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model a new estimator for the unknown parameter is defined as the value that minimizes the distance between a vector of weighted integrals of the tail dependence function and their empirical counterparts the minimization problem has with probability tending to one a unique global solution the estimator is consistent and asymptotically normal the spectral measures of the tail dependence models to which the method applies can be discrete or continuous examples demonstrate the applicability and the performance of the method

markov chain models for threshold exceedances in recent research on extreme value statistics there has been an extensive development of threshold methods first in the univariate case and subsequently in the multivariate case as well in this paper an alternative methodology for extreme values of univariate time series is developed by assuming that the time series is markovian and using bivariate extreme value theory to suggest appropriate models for the transition distributions a new likelihood representation for threshold methods is presented which we apply to a markovian time series an important motivation for developing this kind of theory is the possibility of calculating probability distributions for functionals of extreme events we address this issue by 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 the methods are illustrated by application to temperature data

an extension and simpler proof of berselli cordoba s geometric regularity condition for the navier stokes system abstract in this short note we provide an simpler proof of berselli cordoba s geometric regularity condition for the navier stokes system moreover some interesting extensions are obtained

reply to comment on bivariate extreme value distributions an application of the gibbs sampler to the analysis of floods by p t adamson a v metcalfe and b parmentier

a mixture model for multivariate extremes this thesis is a contribution to multivariate extreme value statistics the tail of a multivariate distribution function is characterized by its spectral distribution for which we propose a new semi parametric model based on mixtures of dirichlet distributions to estimate the components of this model reversible jump monte carlo markov chain and em algorithms are developed their performances are illustrated on real and simulated data obtained using new representations of the extremal logistic and dirichlet models in parallel with the estimation of the spectral distribution extreme value statistic machinery requires the selection of a threshold in order to classify data as extreme or not this selection is achieved by a new method based on heuristic arguments it allows a selection independent of the dimension of the data its performance is illustrated on real and simulated data primal scientific interests behind a multivariate extreme value analysis reside in the estimation of quantiles of rare events and in the exploration of the dependence structure for which the estimation of the spectral measure is a means rather than an end these two issues are addressed for the first a monte carlo method is developed based on simulation of extremes it is compared with classical and new methods of the literature for the second one an original conditional dependence analysis is proposed which enlightens various aspects of the dependence structure of the data examples using real data sets are given in the last part the semi parametric model and the presented methods are extended to spatial extremes it is made possible by considering the spectral distribution as the distribution of a random probability an original viewpoint adopted throughout this thesis classical multivariate extremes are extended to extremes of random measures the application is illustrated on rainfall data in china

statistical physics model of an evolving population abstract there are many possible approaches by a theoretical physicist to problems of biological evolution some focus on physically interesting features like the self organized criticality p bak k sneppen phys rev lett 71 1993 n vadewalle m ausloos physica d 90 1996 262 others put on more effort taking into account factors considered by biologists to be important in determining one or another aspect of biological evolution d derrida p g higgs j phys a 24 1991 l985 i mroz a p kalski k sznajd weron phys rev lett 76 1996 3025 a p kalski physica a 265 1999 255 the intrinsic complexity of the problem enforces nevertheless drastic simplifications certain consolation may come from the fact that the mathematical models used by biologists themselves are quite often even more coarse grained

populations in a periodically changing habitat comparison of two extended models abstract we investigate the dynamics of a population in periodically changing external conditions and we determine the survival chance as a function of the selection pressure and changeability we compare two extended models in one an individual is characterized by its genetic structure from which a phenotype follows while in the second model an individual is described by a real number directly representing the phenotype we show that although the models exhibit in general similar behavior the simpler model could in some special conditions give incorrect results

estimating the probability of a rare event let x 1 y 1 x 2 y 2 x n y n be a random sample from a bivariate distribution function f which is in the domain of attraction of a bivariate extreme value distribution function g a subset c of r 2 is given which contains none of the observations we shall give an asymptotic confidence interval for pr x i y i c under certain conditions

on vorticity directions near singularities for the navier stokes flows with infinite energy we give a geometric nonblow up criterion on the direction of the vorticity for the three dimensional navier stokes flow whose initial data is just bounded and may have infinite energy we prove that under a restriction on behavior in time type i condition the solution does not blow up if the vorticity direction is uniformly continuous at the place where the vorticity magnitude is large this improves the regularity condition for the vorticity direction first introduced by p constantin and c fefferman 1993 for finite energy weak solution our method is based on a simple blow up argument which says that the situation looks like two dimensional under continuity of the vorticity direction we also discuss boundary value problems

space time localization of a class of geometric criteria for preventing blow up in the 3d nse a class of local in the space time conditions on the vorticity directions implying local regularity of weak solutions to the 3d navier stokes equations is established in all the preceding results the relevant geometric conditions although being local in nature have been assumed uniformly throughout the spatial regions of high vorticity magnitude and uniformly in time in addition similar results are obtained assuming a less restrictive integral condition on the vorticity directions

bivariate extreme value theory models and estimation summary bivariate extreme value distributions arise as the limiting distributions of renormalized componentwise maxima no natural parametric family exists for the dependence between the marginal distributions but there are considerable restrictions on the dependence structure we consider modelling the dependence function with parametric models for which two new models are presented tests for independence and discriminating between models are also given the estimation procedure and the flexibility of the new models are illustrated with an application to sea level data extreme value theory has recently been an area of much theoretical and practical work univariate theory is a well documented area whereas bivariate multivariate extreme value theory has until recently received surprisingly little attention in the multivariate case no natural parametric family exists for the dependence structure so this must be modelled in some way in the analysis of environmental extreme value data there is a need for models of dependence between extremes from different sources for example at various sea ports or at various points of a river in this paper we consider bivariate extreme value distributions we assume without loss of generality that we have exponential marginal distributions with unit means the class of bivariate exponential distributions in which we are interested satisfy a strong stability relation exponential variables x y satisfy the stability relation if and only if w min ax by is also exponentially distributed for all a b 0 pickands 1981 therefore the models we will consider have particular application in reliability and survival analysis one approach to modelling the dependence structure is via parametric models this requires a flexible family of models which satisfy certain constraints models are of two kinds either differentiable or nondifferentiable all nondifferentiable models give distri butions which are singular with nonzero probability concentrated on a certain subspace the differentiable models have densities but the existing models are symmetric which leads to the variables being exchangeable here we present two new asymmetric differenti able models which have increased flexibility properties of the differentiable models are examined estimation of the parametric models has previously been by ad hoc methods because there is a nonregular estimation problem when the margins are independent for the

fisher information for a multivariate extreme value distribution summary explicit algebraic formulae for the fisher information matrix of the multivariate extreme value distribution with generalised extreme value margins and logistic dependence structure are given

statistics for near independence in multivariate extreme values we propose a multivariate extreme value threshold model for joint tail estimation which overcomes the problems encountered with existing techniques when the variables are near independence we examine inference under the model and develop tests for independence of extremes of the marginal variables both when the thresholds are fixed and when they increase with the sample size motivated by results obtained from this model we give a new and widely applicable characterisation of dependence in the joint tail which includes existing models as special cases a new parameter which governs the form of dependence is of fundamental importance to this characterisation by estimating this parameter we develop a diagnostic test which assesses the applicability of bivariate extreme value joint tail models the methods are demonstrated through simulation and by analysing two previously published data sets

navier stokes equations green s matrices vorticity direction and regularity up to the boundary abstract we consider the initial boundary value problem for the 3d navier stokes equations the physical domain is a bounded open set with a smooth boundary on which we assume a condition of free boundary type we show that if a suitable hypothesis on the vorticity direction is assumed then weak solutions are regular the main tool we use in the proof is an explicit representation of the velocity in terms of the vorticity by means of green s matrices

regional modelling of extreme storms via max stable processes asymptotic models for extremes of random processes often form the basis for estimating the extremal behaviour of environmental phenomena most such phenomena have a spatial dimension and the aim of this paper is to develop a procedure for modelling in continuous space the spatial dependence within extreme events a principal objective in the analysis as with other current research on extremes is to base inference on as much of the available data as possible the modelling procedures are justified on simulated data and subsequently applied to a series of rainfall data

population dynamics in heterogeneous conditions abstract using a monte carlo approach we study a simple lattice model of populations living in a habitat where the external conditions are changing in space and in time we show that above a certain value of the climatic gradient the population gathers at a restricted part of the lattice the average trait of the individuals follows the optimum we also have shown that there exists a range of gradient values within which a population has over 10 chance of survival while outside it most likely to become extinct we have found that this phenomenon depends on the selection pressure and we have constructed a phase diagram in the selection gradient plane in the case of the time dependent optimum the populations go extinct after a long time depending on the speed of the changes

geometric statistics in turbulence the author presents results regarding certain average properties of incompressible fluids derived from the equations of motion the author estimates the average dissipation rate the average dimension of level sets the role played by the field of direction of vorticity in the three dimensional euler and navier stokes equations is discussed and a class of two dimensional equations that are useful models of incompressible dynamics is described the author presents results concerning scaling exponents in turbulence

diversity and extinction in a lattice model of a population with fluctuating environment i study a lattice stochastic model of a mutating population sensitive to the influence of a fluctuating environment the dynamics of the population stressed by linear and periodic disturbances is investigated in agreement with previous studies of nonspatial models i find a critical rate of change in the environmental variable beyond which the population becomes extinct and i show explicitly that the presence of space in the model can affect the critical rate further i study the diversity defined as the total number of different cell types present in the lattice as a function of intensity and frequency of the environmental disturbance if the disturbance becomes fast and intense the population becomes extinct interestingly i find that for moderate stresses the diversity increases with the intensity and frequency of disturbance the transition between large diversity and extinction is sharp implying that the populations with high diversity are generally the ones closest to the extinction threshold when subjected to colored noise of increasing intensity the system grows in diversity but at the same time is more likely to become extinct

bivariate extreme value distributions an application of the gibbs sampler to the analysis of floods the quantitative definition of the magnitude of a flood episode exclusively in terms of its peak rate of discharge is often insufficient in common with most episodic hydrological phenomena floods are intrinsically multivariate random events characterized not only by their peak flow but also by their volume and the duration of discharge above critical thresholds a complete definition in terms of these three component random variables has not found its way into standard analytical practice this may be partly because the theory of multivariate extremes is not straightforward and partly because no intuitively attractive way of presenting the component variables in a probabilistic framework has been put forward we propose that the gibbs sampler a member of the new generation of computer intensive methods in computational statistics bypasses the theoretical difficulties we demonstrate the gibbs sampler and provide graphical presentations of the results for the annual flood hydrograph on the mekong river at vientiane laos we extend the results to evaluate the potential distribution of flood damage to the city

ordered multivariate extremes multivariate extreme value models and associated statistical methods are developed for vector observations whose components are subject to an order restriction the approach extends the multivariate threshold methodology of coles and tawn joe and co workers and smith and co workers the results are illustrated by an analysis of extreme rainfalls of different durations and by a study of the problem of linking a long series of daily rainfall extremes with a partially overlapping shorter series of hourly extremes

localization and geometric depletion of vortex stretching in the 3d nse vortex stretching and consequently the evolution of the vorticity is localized on an arbitrarily small space time cylinder this yields a complete localization of the geometric condition s for the regularity involving coherence of the vorticity direction in particular it implies the regularity of any geometrically constrained leray solution independently of the type of the spatial domain or the boundary conditions

notes on the geometric regularity criterion of 3d navier stokes system in this note we show that if the volume of parallelepiped which is defined by three unit vectors direction of the velocity direction of the vorticity and the direction of the curl of the vorticity is small enough then the solution to the 3d navier stokes equations is classical

estimation of quantiles of the maximum of n observations summary given independent and identically distributed random variables from an unknown distribution f we want to estimate quantiles of fn using asymptotic extreme value theory two parametric approximations to fn are considered ahd approximate maximum likelihood estimates are obtained conditions for consistency and asymptotic normality of these estimates are given and properties of the estimates are obtained through a small simulation study

ozone concentrations a robust analysis of multivariate extremes data on ozone concentrations at four monitoring sites in central canada are examined univariate extreme value methods do not allow for the required inference and multivariate methods exploiting the joint dependence of the data are necessary families of multivariate extreme value copulas with a flexible dependence structure and closed form cumulative distribution functions have recently been derived this article shows that maximum likelihood estimates of these parametric models may be obtained numerically and that their use can lead to increased efficiency in the estimation of margins we do not however have any assurance that all data are well modeled by these distributions because the space of multivariate extreme value copulas is infinite dimensional and data on ozone levels are prone to outliers this article addresses the robust methods required for proper analysis

bivariate threshold methods for extremes summary an extension of the threshold method for extreme values is developed to consider the joint distribution of extremes of two variables the methodology is based on the point process representation of bivariate extremes both parametric and nonparametric models are considered the simplest case to handle is that in which both marginal distributions are known for the more realistic case in which the marginal distributions are unknown a mixed parametric nonparametric method is proposed the techniques are illustrated with data on sulphate and nitrate levels taken from a major study of acid rain

on depletion of the vortex stretching term in the 3d navier stokes equations certain new cancellation properties in the vortex stretching term are detected leading to new geometric criteria for preventing finite time blow up in the 3d navier stokes equations

a conditional approach for multivariate extreme values with discussion summary 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 ex tremal dependence between some pollutants being significantly greater than the dependence at non extreme levels

multivariate hydrological frequency analysis using copulas 1 this article presents the modeling of multivariate extreme values using copulas our approach allows us to model the dependence structure independently of the marginal distributions which is not possible with standard classical methods the methodology has been applied on two different problems in hydrology the first application is concerned with the combined risk in the framework of frequency analysis four copulas have been tested on peak flows from the watershed of peribonka in quebec canada the second application relates to the joint modeling of peak flows and volumes three copulas have been applied to the watershed of the rimouski river in quebec canada this approach using copulas is promising since it allows us to take into account a wide range of correlation which can happen in hydrology

dynamics of populations in a changing environment we present an individual based model of a population that lives in a changing environment the individuals forming the population are subject to mutations and selection pressure using monte carlo simulations we have shown that depending on the values of the mutation rate and selection the population may reach either an active phase it will survive or an absorbing phase it will become extinct we have determined that the transition between the two states phases is continuous we have shown that when the selection is weaker the population lives in all available space while if the selection is stronger it will move to the regions where the living conditions are better avoiding those with more difficult conditions the dependence of the mean time to extinction on the rate of mutations has been determined and discussed

global well posedness of 3 d anisotropic navier stokes system with large vertical viscous coefficient abstract in this paper we first prove the global well posedness of 3 d anisotropic navier stokes system provided that the vertical viscous coefficient of the system is sufficiently large compared to some critical norm of the initial data then we shall construct a family of initial data u 0 which vary fast enough in the vertical variable and which can be arbitrarily large in the space b m o 1 yet u 0 still generates a unique global solution to the classical 3 d navier stokes system provided that is sufficiently large

an algebraic reduction of the scaling gap in the navier stokes regularity problem it is shown within a mathematical framework based on the suitably defined scale of sparseness of the super level sets of the positive and negative parts of the vorticity components and in the context of a blow up type argument that the ever resisting scaling gap that is the scaling distance between a regularity criterion and a corresponding a priori bound shortly a measure of the super criticality of the three dimensional navier stokes regularity problem can be reduced by an algebraic factor since independent fundamental works of ladyzhenskaya prodi and serrin as well as kato and fujita in 1960s all the reductions have been logarithmic in nature regardless of the functional set up utilized more precisely it is shown that it is possible to obtain an a priori bound that is algebraically better than the energy level bound while keeping the corresponding regularity criterion at the same level as all the classical regularity criteria the mathematics presented was inspired by morphology of the regions of intense vorticity velocity gradients observed in computational simulations of turbulent flows as well as by the physics of turbulent cascades and turbulent dissipation

nonparametric bayesian bioassay including ordered polytomous response abstract previous attempts at implementing fully bayesian nonparametric bioassay have enjoyed limited success due to computational difficulties we show here how this problem may be generally handled using a sampling based approach to develop desired marginal posterior distributions and their features a useful extension is presented which treats the case of ordered polytomous response illustrative examples are provided

maximum empirical likelihood estimation of the spectral measure of an extreme value distribution consider a random sample from a bivariate distribution function f in the max domain of attraction of all extreme value distribution function g this g is characterized by two extreme value indices and a spectral measure the latter determining the tail dependence structure of f a major issue in multivariate extreme value theory is the estimation of the spectral measure 1 p with respect to the l p norm for every p is an element of 1 infinity a nonparametric maximum empirical likelihood estimator is proposed for phi p the main novelty is that these estimators are guaranteed to satisfy the moment constraints by which spectral measures are characterized asymptotic normality of the estimators is proved under conditions that allow for tail independence moreover the conditions are easily verifiable as we demonstrate through a number of theoretical examples a simulation study shows a substantially improved performance of the new estimators two case studies illustrate how to implement the methods in practice

spatial statistics and bayesian computation on wednesday may 6th 1992 professor b w silverman in the chair summary markov chain monte carlo mcmc algorithms such as the gibbs sampler have provided a bayesian inference machine in image analysis and in other areas of spatial statistics for several years founded on the pioneering ideas of ulf grenander more recently the observation that hyperparameters can be included as part of the updating schedule and the fact that almost any multivariate distribution is equivalently a markov random field has opened the way to the use of mcmc in general bayesian computation in this paper we trace the early development of mcmc in bayesian inference review some recent computational progress in statistical physics based on the introduction of auxiliary variables and discuss its current and future relevance in bayesian applications we briefly describe a simple mcmc implementation for the bayesian analysis of agricultural field experiments with which we have some practical experience

non parametric bayesian inference on bivariate extremes the tail of a bivariate distribution function in the domain of attraction of a bivariate extreme value distribution may be approximated by the one of its extreme value attractor the extreme value attractor has margins that belong to a three parameter family and a dependence structure which is characterised by a probability measure on the unit interval with mean equal to one half called spectral measure inference is done in a bayesian framework using a censored likelihood approach a prior distribution is constructed on an in nite dimensional model for this measure the model being at the same time dense and computationally manageable a trans dimensional markov chain monte carlo algorithm is developed and convergence to the posterior distribution is established in simulations the bayes estimator for the spectral measure is shown to compare favorably with frequentist nonparametric estimators an application to a data set of danish re insurance claims is provided

models for the extremes of markov chains the modelling of extremes of a time series has progressed from the assumption of independent observations to more realistic forms of temporal dependence in this paper we focus on markov chains deriving a class of models for their joint tail which allows the degree of clustering of extremes to decrease at high levels overcoming a key limitation in current methodologies theoretical aspects of the model are examined and a simulation algorithm is developed through which the stochastic properties of summaries of the extremal txhaviour of the chain are evaluated the approach is illustrated through a simulation study of extremal events of gaussian autoregressive processes and an application to temperature data