extremal behaviour of aggregated data with an application to downscaling summary the distribution of spatially aggregated data from a stochastic process x may exhibit tail behaviour different from that of its marginal distributions for a large class of aggregating functionals ell we introduce the ell extremal coefficient which quantifies this difference as a function of the extremal spatial dependence in x we also obtain the joint extremal dependence for multiple aggregation functionals applied to the same process formulae for the ell extremal coefficients and multivariate dependence structures are derived in important special cases the results provide a theoretical link between the extremal distribution of the aggregated data and the corresponding underlying process which we exploit to develop a method for statistical downscaling we apply our framework to downscale daily temperature maxima in the south of france from a gridded dataset and use our model to generate high resolution maps of the warmest day during the 2003 heatwave

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

application of unsplit convolutional perfectly matched layer for scalar arbitrarily wide angle wave equation abstracta classical split perfectly matched layer pml method has recently been applied to the scalar arbitrarily wide angle wave equation awwe in terms of displacement however the classical split pml obviously increases computational cost and cannot efficiently absorb waves propagating into the absorbing layer at grazing incidence our goal was to improve the computational efficiency of awwe and to enhance the suppression of edge reflections by applying a convolutional pml cpml we reformulated the original awwe as a first order formulation and incorporated the cpml with a general complex frequency shifted stretching operator into the renewed formulation a staggered grid finite difference fd method was adopted to discretize the first order equation system for wavefield depth continuation the first order awwe with the cpml saved memory compared with the original second order awwe with the conventional split pml with the help of numerical examples we verified the correctness of the staggered

max infinitely divisible and max stable sample continuous processes conditions for a process on a compact metric spaces to be simultaneously max infinitely divisible and sample continuous are obtained although they fall short of a complete characterization of such processes these conditions yield complete descriptions of the sample continuous non degenerate max stable processes ons and of the infinitely divisible non void random compact subsets of a banach space under the operation of convex hull of unions

conditional simulation of max stable processes summary since many environmental processes such as heat waves or precipitation are spatial in extent it is likely that a single extreme event affects several loca tions and the areal modelling of extremes is therefore essential if the spatial dependence of e xtremes has to be appropriately taken into account this paper proposes a framework for conditional simulations of max stable processes and give closed forms for brown resnick and schlather processes we test the method on simulated data and give an application to extreme rainfall around zurich and extreme temperature in switzerland results show that the proposed framework provides accurate conditional simulations and can handle real sized problems

exact simulation of max stable processes max stable processes play an important role as models for spatial extreme events their complex structure as the pointwise maximum over an infinite number of random functions makes their simulation difficult algorithms based on finite approximations are often inexact and computationally inefficient we present a new algorithm for exact simulation of a max stable process at a finite number of locations it relies on the idea of simulating only the extremal functions that is those functions in the construction of a max stable process that effectively contribute to the pointwise maximum we further generalize the algorithm by dieker mikosch 2015 for brown resnick processes and use it for exact simulation via the spectral measure we study the complexity of both algorithms prove that our new approach via extremal functions is always more efficient and provide closed form expressions for their implementation that cover most popular models for max stable processes and multivariate extreme value distributions for simulation on dense grids an adaptive design of the extremal function algorithm is proposed

parabolic approximations to the time independent elastic wave equation a splitting matrix method is used to derive two parabolic approximation partial differential equations to the three dimensional linear elastic wave equation in isotropic inhomogeneous media the derivation is valid for media whose lame parameters vary slowly on the length scale of the wavelength of the elastic waves next an integral form of the full wave equation is derived based on the splitting matrix and the parabolic approximation solution iteration of this equation gives a three dimensional vector valued series which generalizes the one dimensional bremmer series which was used in the study of second order ordinary differential equations these results are expected to have applications to geophysical modeling and nondestructive evaluation

inference for clustered data using the independence loglikelihood we use the properties of independence estimating equations to adjust the independence loglikelihood function in the presence of clustering the proposed adjustment relies on the robust sandwich estimator of the parameter covariance matrix which is easily calculated the methodology competes favourably with established techniques based on independence estimating equations we provide some insight as to why this is so the adjustment is applied to examples relating to the modelling of wind speed in europe and annual maximum temperatures in the u k

bayesian modeling of air pollution extremes using nested multivariate max stable processes capturing the potentially strong dependence among the peak concentrations of multiple air pollutants across a spatial region is crucial for assessing the related public health risks in order to investigate the multivariate spatial dependence properties of air pollution extremes we introduce a new class of multivariate max stable processes our proposed model admits a hierarchical tree based formulation in which the data are conditionally independent given some latent nested positive stable random factors the hierarchical structure facilitates bayesian inference and offers a convenient and interpretable characterization we fit this nested multivariate max stable model to the maxima of air pollution concentrations and temperatures recorded at a number of sites in the los angeles area showing that the proposed model succeeds in capturing their complex tail dependence structure

consistencies and rates of convergence of jump penalized least squares estimators we study the asymptotics for jump penalized least squares regression aiming at approximating a regression function by piecewise constant functions besides conventional consistency and convergence rates of the estimates in l 2 0 1 our results cover other metrics like skorokhod metric on the space of cadlag functions and uniform metrics on c 0 1 we will show that these estimators are in an adaptive sense rate optimal over certain classes of approximation spaces special cases are the class of functions of bounded variation piecewise holder continuous functions of order 0 1 and the class of step functions with a finite but arbitrary number of jumps in the latter setting we will also deduce the rates known from change point analysis for detecting the jumps finally the issue of fully automatic selection of the smoothing parameter is addressed

rational square root approximations for parabolic equation algorithms in this article stable pade approximations to the function 1 z are derived by choosing a branch cut in the negative half plane the pade coefficients are complex and may be derived analytically to arbitrary order from the corresponding real coefficients associated with the principal branch defined by z 1 i z 0 i z denotes the imaginary part of z the characteristics of the corresponding square root approximation are illustrated for various segments of the complex plane in particular for waveguide problems it is shown that an increasingly accurate representation may be obtained of both the evanescent part of the mode spectrum for the acoustic case and the complex mode spectrum for the elastic case an elastic parabolic equation algorithm is used to illustrate the application of the new pade approximations to a realistic ocean environment including elasticity in the ocean bottom

fourier finite difference migration many existing migration schemes cannot simultaneously handle the two most important problems of migration imaging of steep dips and imaging in media with arbitrary velocity variations in all directions for example phase shift k migration is accurate for nearly all dips but it is limited to very simple velocity functions on the other hand finite difference schemes based on one way wave equations consider arbitrary velocity functions but they attenuate steeply dipping events we propose a new hybrid migration method named fourier finite difference migration wherein the downward continuation operator is split into two downward continuation operators one operator is a phase shift operator for a chosen constant background velocity and the other operator is an optimized finite difference operator for the varying component of the velocity function if there is no variation of velocity then only a phase shift operator will be applied automatically on the other hand if there is a strong variatio

padded continued fraction absorbing boundary conditions for dispersive waves continued fraction absorbing boundary conditions cfabcs are new arbitrarily high order local absorbing boundary conditions that are highly effective in simulating wave propagation in unbounded domains the current versions of cfabcs are developed for the non dispersive acoustic wave equation with convex polygonal computational domains in this paper the cfabcs are modified through augmentation of special padding elements and are effective for absorbing evanescent waves occurring in dispersive wave problems while retaining their absorption properties for propagating waves the padded cfabcs for dispersive wave equations result in fourth order evolution equations which are solved using an efficient combination of crank nicholson method newmark time stepping scheme and operator splitting ideas the effectiveness of the padded cfabcs and their implementation is illustrated through numerical examples with varying levels of dispersion

on convergence toward an extreme value distribution in c 0 1 the structure of extreme value distributions in infinite dimensional space is well known we characterize the domain of attraction of such extreme value distributions in the framework of gine hahn and vatan we intend to use the result for statistical applications

applications and time domain solution of higher order parabolic equations in underwater acoustics a higher order parabolic equation and the corresponding higher order time domain parabolic equation are derived from a pade series and solved numerically these models provide accurate solutions for problems involving very wide angle propagation e g propagation in the nearfield or over a hard ocean bottom propagation in domains in which sound speed variations are large e g propagation in deep water deep within the ocean bottom in high speed ocean bottoms and possibly of different wave types and propagation out to very long ranges the possibility of modeling elastic wave propagation with a similar approach is considered

space time modelling of extreme events max stable processes are the natural analogues of the generalized extreme value distribution when modelling extreme events in space and time under suitable conditions these processes are asymptotically justified models for maxima of independent replications of random fields and they are also suitable for the modelling of extreme measurements over high thresholds this paper shows how a pairwise censored likelihood can be used for consistent estimation of the extremes of space time data under mild mixing conditions and illustrates this by fitting an extension of a model of schlather 2002 to hourly rainfall data a block bootstrap procedure is used for uncertainty assessment estimator efficiency is considered and the choice of pairs to be included in the pairwise likelihood is discussed the proposed model fits the data better than some natural competitors

local likelihood estimation of complex tail dependence structures applied to u s precipitation extremes to disentangle the complex nonstationary dependence structure of precipitation extremes over the entire contiguous united states u s we propose a flexible local approach based on factor copula

consistent transmitting boundary with continued fraction absorbing boundary conditions for analysis of soil structure interaction in a layered half space abstract a continued fraction absorbing boundary condition cfabc is combined with a consistent transmitting boundary and applied to an analysis of soil structure interaction in a layered half space in order to be a perfect absorber for in plane waves with an arbitrary horizontal wavenumber in a layered half space it is proposed that the cfabc be used in the form of a 2 layer a method for determination of parameters of the 2 layers was proposed for evanescent waves as well as propagating waves combined with consistent transmitting boundaries the 2 layers of cfabc are applied to problems of dynamics of rigid strip and circular foundations on a layered half space the results demonstrate that the proposed 2 layers of the cfabc can represent a layered half space accurately in the entire frequency range and absorb both evanescent and propagating p and s waves effectively

peaks over thresholds modeling with multivariate generalized pareto distributions when assessing the impact of extreme events it is often not just a single component but the combined behavior of several components which is important statistical modeling using multivariate gen

absorbing boundary conditions for time harmonic wave propagation in discretized domains while many successful absorbing boundary conditions abcs are developed to simulate wave propagation into unbounded domains most of them ignore the effect of interior discretization and result in spurious reflections at the artificial boundary we tackle this problem by developing abcs directly for the discretized wave equation specifically we show that the discrete system mesh can be stretched in a non trivial way to preserve the discrete impedance at the interface similar to the perfectly matched layers pml for continuous wave equation the stretch is designed to introduce dissipation in the exterior resulting in a pml type abc for discrete media the paper includes detailed formulation of the new discrete abc along with the illustration of its effectiveness over continuous abcs with the help of error analysis and numerical experiments for time harmonic problems the improvement over continuous abcs is achieved without any computational overhead leading to the conclusion that the discrete abcs should be used in lieu of continuous abcs

higher order pade approximations for accurate and stable elastic parabolic equations with application to interface wave propagation higher order pade approximations are applied to derive accurate and stable parabolic equations for sound propagation in oceans bounded below by an elastic bottom or bounded above by ice cover accuracy is achieved by placing constraints on the derivatives of the pade approximations at the point corresponding to the reference wave number stability is achieved by requiring that the pade approximations map part of the lower left quadrant of the complex plane into the upper half of the complex plane elastic parabolic equations based on these pade series can handle problems involving compressional shear and interface waves very wide propagation angles and large depth variations and weak range variations in the seismoacoustic parameters a finite difference spectral solution is developed for generating reference solutions and starting fields the rotated elastic parabolic equation is used to investigate the accuracy of the elastic parabolic equation for range dependent problems

migration with arbitrarily wide angle wave equations we develop a new scalar migration technique that is highly accurate for imaging steep dips in heterogeneous media this method is based on arbitrarily wide angle wave equations awwes that are highly accurate space domain one way wave equations and have a form similar to the 15 equation the accuracy of the proposed method is increased by introducing auxiliary variables as well as adjusting the parameters of the approximation poststack migration is carried out by downward continuation using the awwe for which we have developed a stable explicit double marching scheme up to 80 accuracy is achieved by second order awwe migration with only 2 3 times the computational effort of the 15 equation and requiring almost the same storage we illustrate the performance of awwe migration using impulse response graphs a single dipping reflector and a slice of the seg eage salt model

arbitrarily wide angle wave equations for complex media by combining various ideas related to one way wave equations owwes half space stiffness relation special finite element discretization and complex coordinate stretching a systematic procedure is developed for deriving a series of highly accurate space domain versions of owwes the resulting procedure is applicable to complex media where the governing equation full wave equation is a second order differential system making the procedure applicable for general heterogeneous anisotropic porous viscoelastic media owing to their high accuracy in representing waves propagating in an arbitrarily wide range of angles the resulting equations are named arbitrarily wide angle wave equations awwes in order to illustrate the proposed procedure awwes are derived for one way propagation in acoustic as well as elastic media while acoustic awwes can be considered as modified versions of well known space domain owwes based on rational approximations of the square root operator the elastic awwes are significantly different from the existing elastic owwes unlike the existing elastic owwes elastic awwes are displacement based and are applicable to general anisotropic media furthermore awwes are simple in their form and appear amenable to easy numerical implementation

continued fraction absorbing boundary conditions for convex polygonal domains continued fraction absorbing boundary conditions cfabcs are highly effective boundary conditions for modelling wave absorption into unbounded domains they are based on rational approximation of the exact dispersion relationship and were originally developed for straight computational boundaries in this paper cfabcs are extended to the more general case of polygonal computational domains the key to the current development is the surprising link found between the cfabcs and the complex co ordinate stretching of perfectly matched layers pmls this link facilitates the extension of cfabcs to oblique corners and thus to polygonal domains it is shown that the proposed cfabcs are easy to implement expected to perform better than pmls and are effective for general polygonal computational domains in addition to the derivation of cfabcs a novel explicit time stepping scheme is developed for efficient numerical implementation numerical examples presented in the paper illustrate that effective absorption is attained with a negligible increase in the computational cost for the interior domain although this paper focuses on wave propagation its theoretical development can be easily extended to the more general class of problems where the governing differential equation is second order in space with constant coefficients copyright 2005 john wiley sons ltd

modeling spatial processes with unknown extremal dependence class abstractmany environmental processes exhibit weakening spatial dependence as events become more extreme well known limiting models such as max stable or generalized pareto processes cannot capture this which can lead to a preference for models that exhibit a property known as asymptotic independence however weakening dependence does not automatically imply asymptotic independence and whether the process is truly asymptotically in dependent is usually far from clear the distinction is key as it can have a large impact upon extrapolation that is the estimated probabilities of events more extreme than those observed in this work we present a single spatial model that is able to capture both dependence classes in a parsimonious manner and with a smooth transition between the two cases the model covers a wide range of possibilities from asymptotic independence through to complete dependence and permits weakening dependence of extremes even under asymptotic dependence censored likelihood based

exploiting occurrence times in likelihood inference for componentwise maxima multivariate extreme value distributions arise as the limiting distributions of normalised componentwise maxima they are often used to model multivariate data that can be regarded as the componentwise maxima of some unobserved underlying multivariate process in many applications we have extra information we often know the locations of the maxima within the underlying process if the process is temporal this knowledge is frequently available through the dates on which the maxima are recorded we show how to incorporate this extra information into maximum likelihood procedures asymptotic and small sample efficiency results are presented for the dependence parameter in the logistic parametric sub class of bivariate extreme value distributions we conclude with an application to sea levels

highly accurate absorbing boundary conditions for wide angle wave equations we develop a new class of absorbing boundary conditions abcs to prevent unwanted artifacts and wraparounds associated with aperture truncation in migration modeling using high order one way wave equations the fundamental approach behind the proposed development is the efficient discretization of the half space beyond the boundary of interest using midpoint integrated imaginary finite elements an idea recently utilized in the development of effective one way wave equations the proposed absorbing boundary conditions essentially add absorbing layers at the aperture truncation points we derive the absorbing boundary conditions analyze their properties and develop a stable explicit finite difference scheme to solve the downward continuation problem modified by these boundary conditions with the help of numerical examples we conclude that with as few as three absorbing layers i e two additional gridpoints the waves can be absorbed completely thus preventing associated artifacts

composite likelihood estimation for the brown resnick process summary genton et al 2011 investigated the gain in efficiency when triplewise rather than pairwise likelihood is used to fit the popular smith max stable model for spatial extremes we generalize their results to the brown resnick model and show that the efficiency gain is substantial only for very smooth processes which are generally unrealistic in applications

parabolic wave equation approximations in heterogenous media the properties of different variants of parabolic approximations of scalar wave equations are analyzed these equations are of general form which includes those used in seismology underwater acoustics and other applications a new version of the parabolic approximation is derived for heterogeneous media it has optimal properties with respect to wave reflection at material interfaces the amplitudes of the reflected and transmitted waves depend continuously on the interface existence uniqueness and energy estimates are proved

exponential convergence through linear finite element discretization of stratified subdomains motivated by problems where the response is needed at select localized regions in a large computational domain we devise a novel finite element discretization that results in exponential convergence at pre selected points the key features of the discretization are a use of midpoint integration to evaluate the contribution matrices and b an unconventional mapping of the mesh into complex space named complex length finite element method cfem the technique is linked to pade approximants that provide exponential convergence of the dirichlet to neumann maps and thus the solution at specified points in the domain exponential convergence facilitates drastic reduction in the number of elements this combined with sparse computation associated with linear finite elements results in significant reduction in the computational cost the paper presents the basic ideas of the method as well as illustration of its effectiveness for a variety of problems involving laplace helmholtz and elastodynamics equations

likelihood based inference for max stable processes the last decade has seen max stable processes emerge as a common tool for the statistical modeling of spatial extremes however their application is complicated due to the unavailability of the multivariate density function and so likelihood based methods remain far from providing a complete and flexible framework for inference in this article we develop inferentially practical likelihood based methods for fitting max stable processes derived from a composite likelihood approach the procedure is sufficiently reliable and versatile to permit the simultaneous modeling of marginal and dependence parameters in the spatial context at a moderate computational cost the utility of this methodology is examined via simulation and illustrated by the analysis of united states precipitation extremes

dynamic analysis of a poroelastic layered half space using continued fraction absorbing boundary conditions abstract a methodology for dynamic analysis of a poroelastic layered half space is proposed a poroelastic layered half space is discretized with regular thin layers to a certain depth below the layers continued fraction absorbing boundary conditions cfabcs which are accurate and effective in modeling wave propagation in various unbounded domains are applied in order to represent the infinite extent of the half space with the representation a spectral decomposition which is an effective approach in the solution of wave propagation problems is utilized green functions of a poroelastic layered half space are obtained accurately with the proposed numerical model the green functions can be applied to various dynamic problems in the half space including foundation dynamics and soil structure interaction problems

on the occurrence times of componentwise maxima and bias in likelihood inference for multivariate max stable distributions full likelihood based inference for high dimensional multivariate extreme value distributions or max stable processes is feasible when incorporating occurrence times of the maxima without this information ddd dimensional likelihood inference is usually precluded due to the large number of terms in the likelihood however some studies have noted bias when performing high dimensional inference that incorporates such event information particularly when dependence is weak we elucidate this phenomenon showing that for unbiased inference in moderate dimensions dimension ddd should be of a magnitude smaller than the square root of the number of vectors over which one takes the componentwise maximum a bias reduction technique is suggested and illustrated on the extreme value logistic model

one way spatial integration of hyperbolic equations in this paper we develop and demonstrate a method for constructing well posed one way approximations of linear hyperbolic systems we use a semi discrete approach that allows the method to be applied to a wider class of problems than existing methods based on analytical factorization of idealized dispersion relations after establishing the existence of an exact one way equation for systems whose coefficients do not vary along the axis of integration efficient approximations of the one way operator are constructed by generalizing techniques previously used to create nonreflecting boundary conditions when physically justified the method can be applied to systems with slowly varying coefficients in the direction of integration to demonstrate the accuracy and computational efficiency of the approach the method is applied to model problems in acoustics and fluid dynamics via the linearized euler equations in particular we consider the scattering of sound waves from a vortex and the evolution of hydrodynamic wavepackets in a spatially evolving jet the latter problem shows the potential of the method to offer a systematic convergent alternative to ad hoc regularizations such as the parabolized stability equations

a finite element alternative to infinite elements abstract in this paper a simple idea based on midpoint integration rule is utilized to solve a particular class of mechanics problems namely static problems defined on unbounded domains where the solution is required to be accurate only in an interior and not in the far field by developing a finite element mesh that approximates the stiffness of an unbounded domain directly without approximating the far field displacement profile first the current formulation provides a superior alternative to infinite elements ies that have long been used to incorporate unbounded domains into the finite element method fem in contrast to most ies the present formulation a requires no new shape functions or special integration rules b is proved to be both accurate and efficient and c is versatile enough to handle a large variety of domains including those with anisotropic stratified media and convex polygonal corners in addition to this the proposed model leads to the derivation of a simple error expression that provides an explicit correlation between the mesh parameters and the accuracy achieved this error expression can be used to calculate the accuracy of a given mesh a priori this in turn allows one to generate the most efficient mesh capable of achieving a desired accuracy by solving a mesh optimization problem we formulate such an optimization problem solve it and use the results to develop a practical mesh generation methodology this methodology does not require any additional computation on the part of the user and can hence be used in practical situations to quickly generate an efficient and near optimal finite element mesh that models an unbounded domain to the required accuracy numerical examples involving practical problems are presented at the end to illustrate the effectiveness of this method

efficient computation of dispersion curves for multilayered waveguides and half spaces abstract motivated by the need to compute dispersion curves for layered media in the contexts of geophysical inversion and nondestructive testing a novel discretization approach termed complex length finite element method cfem is developed and shown to be more efficient than the existing finite element approaches the new approach is exponentially convergent based on two key features unconventional stretching of the mesh into complex space and midpoint integration for evaluating the contribution matrices for modeling the layered half spaces of infinite depth we couple cfem with the method of perfectly matched discrete layers pmdl to minimize the errors due to mesh truncation a number of numerical examples are used to investigate the efficiency of the proposed methods it is shown that the suggested combination of cfem and pmdl drastically reduces the number of elements while requiring minor modifications to the existing finite element codes it is concluded that the methods exponential convergence and sparse computation associated with linear finite elements result in significant reduction in the overall computational cost

stationary max stable fields associated to negative definite functions let wi i be independent copies of a zero mean gaussian process w t t d with stationary increments and variance 2 t independently of wi let i 1 ui be a poisson point process on the real line with intensity e y dy we show that the law of the random family of functions vi i where vi t ui wi t 2 t 2 is translation invariant in particular the process t i 1 vi t is a stationary max stable process with standard gumbel margins the process arises as a limit of a suitably normalized and rescaled pointwise maximum of n i i d stationary gaussian processes as n if and only if w is a nonisotropic fractional brownian motion on d under suitable conditions on w the process has a mixed moving maxima representation

estimation of husler reiss distributions and brown resnick processes summary estimation of extreme value parameters from observations in the max domain of attraction of a multivariate max stable distribution commonly uses aggregated data such as block maxima multivariate peaks over threshold methods in contrast exploit additional information from the non aggregated large observations we introduce an approach based on peaks over thresholds that provides several new estimators for processes in the max domain of attraction of the frequently used husler reiss model and its spatial extension brown resnick processes the method relies on increments t0 conditional on t0 exceeding a high threshold where t0 is a fixed location when the marginals are standardized to the gumbel distribution these increments asymptotically form a gaussian process resulting in computationally simple estimates of the husler reiss parameter matrix and particularly enables parametric inference for brown resnick processes based on high dimensional multivariate densities this is a major advantage over composite likelihood methods that are commonly used in spatial extreme value statistics since they rely only on bivariate densities a simulation study compares the performance of the new estimators with other commonly used methods as an application we fit a non isotropic brown resnick process to the extremes of 12 year data of daily wind speed measurements

efficient inference and simulation for elliptical pareto processes recent advances in extreme value theory have established ell pareto processes as the natural limits for extreme events defined in terms of exceedances of a risk functional here we provide methods for the practical modelling of data based on a tractable yet flexible dependence model we introduce the class of elliptical ell pareto processes which arise as the limit of threshold exceedances of certain elliptical processes characterized by a correlation function and a shape parameter an efficient inference method based on maximizing a full likelihood with partial censoring is developed novel procedures for exact conditional and unconditional simulation are proposed these ideas are illustrated using precipitation extremes in switzerland

higher order paraxial wave equation approximations in heterogenous media a new family of paraxial wave equation approximations is derived these approximations are of higher order accuracy than the parabolic approximation and they can be applied to the same computationa

efficient inference for spatial extreme value processes associated to log gaussian random functions max stable processes arise as the only possible nontrivial limits for maxima of affinely normalized identically distributed stochastic processes and thus form an important class of models for the extreme values of spatial processes until recently inference for max stable processes has been restricted to the use of pairwise composite likelihoods due to intractability of higher dimensional distributions in this work we consider random fields that are in the domain of attraction of a widely used class of max stable processes namely those constructed via manipulation of log gaussian random functions for this class we exploit limiting d dimensional multivariate poisson process intensities of the underlying process for inference on all d vectors exceeding a high marginal threshold in at least one component employing a censoring scheme to incorporate information below the marginal threshold we also consider the d dimensional distributions for the equivalent max stable process and perform full likelihood inference by exploiting the methods of stephenson tawn 2005 where information on the occurrence times of extreme events is shown to dramatically simplify the likelihood the stephenson tawn likelihood is in fact simply a special case of the censored poisson process likelihood we assess the improvements in inference from both methods over pairwise likelihood methodology by simulation

on the likelihood function of gaussian max stable processes summary wederiveaclosedformexpressionforthelikelihoodfunctionofagaussianmax stableprocessindexed by r d at p d 1 sites d 1 we demonstrate the gain in efficiency in the maximum composite likelihood estimators of the covariance matrix from p 2t op 3 sites in r 2 by means of a monte carlo