a composite likelihood approach to binary spatial data abstract conventional geostatistics addresses the problem of estimation and prediction for continuous observations but in many practical applications in public health environmental remediation or ecological research the most commonly available data are in the form of counts e g number of cases or indicator variables denoting above or below threshold values also in many situations it is less expensive to obtain an imprecise categorical observation than to obtain precise measurements of the variable of interest such as a contaminant this article proposes a computationally simple method for estimation and prediction using binary or indicator data in space the proposed method is based on pairwise likelihood contributions and the large sample properties of the estimators are obtained in a straightforward manner we illustrate the methodology through application to indicator data related to gypsy moth defoliation in massachusetts

inconsistent estimation and asymptotically equal interpolations in model based geostatistics it is shown that in model based geostatistics not all parameters in the matern class can be estimated consistently if data are observed in an increasing density in a fixed domain regardless of the estimation methods used nevertheless one quantity can be estimated consistently by the maximum likelihood method and this quantity is more important to spatial interpolation the results are established by using the properties of equivalence and orthogonality of probability measures some sufficient conditions are provided for both gaussian and non gaussian equivalent measures and necessary conditions are provided for gaussian equivalent measures two simulation studies are presented that show that the fixed domain asymptotic properties can explain some finite sample behavior of both interpolation and estimation when the sample size is moderately large

a nonparametric test for spatial isotropy using subsampling a common requirement for spatial modeling is the development of an appropriate correlation structure although the assumption of isotropy is often made for this structure it is not always appropriate a conventional practice when checking for isotropy is to informally assess plots of direction specific sample semi variograms although a useful diagnostic these graphical techniques are difficult to assess and open to interpretation formal alternatives to graphical diagnostics are valuable but have been applied to a limited class of models in this article we propose a formal approach to test for isotropy that is both objective and valid for a wide class of models this approach which is based on the asymptotic joint normality of the sample variogram can be used to compare sample variograms in multiple directions an l2 consistent subsampling estimator for the asymptotic covariance matrix of the sample variogram is derived and used to construct a test statistic a subsampling approach and a limiting

brief paper analysis of undercompensation and overcompensation of friction in 1dof mechanical systems this paper investigates the effects of undercompensation and overcompensation of friction in pd controlled 1dof mechanical systems the friction force that is acting on the mechanical system and the friction compensation term in the feedback loop are described by a class of discontinuous friction models consisting of static coulomb and viscous friction and including the stribeck effect lyapunov s stability theorem and lasalle s invariance principle are applied to prove that undercompensation of friction leads to steady state errors and the properties of the w limit set of trajectories of a two dimensional autonomous differential inclusion are used to show that overcompensation of friction may induce limit cycling furthermore the analysis also indicates that the limit cycling effect can be eliminated by tuning the pd controller gains

testing the covariance structure of multivariate random fields there is an increasing wealth of multivariate spatial and multivariate spatio temporal data appearing for such data an important part of model building is an assessment of the properties of the underlying covariance function describing variable spatial and temporal correlations in this paper we propose a methodology to evaluate the appropriateness of several types of common assumptions on multivariate covariance functions in the spatio temporal context the methodology is based on the asymptotic joint normality of the sample space time cross covariance estimators specifically we address the assumptions of symmetry separability and linear models of coregionalization we conduct simulation experiments to evaluate the sizes and powers of our tests and illustrate our methodology on a trivariate spatio temporal dataset of pollutants over california

spatio temporal covariance and cross covariance functions of the great circle distance on a sphere abstractin this article we propose stationary covariance functions for processes that evolve temporally over a sphere as well as cross covariance functions for multivariate random fields defined over a sphere for such processes the great circle distance is the natural metric that should be used to describe spatial dependence given the mathematical difficulties for the construction of covariance functions for processes defined over spheres cross time approximations of the state of nature have been proposed in the literature by using the euclidean based on map projections and the chordal distances we present several methods of construction based on the great circle distance and provide closed form expressions for both spatio temporal and multivariate cases a simulation study assesses the discrepancy between the great circle distance chordal distance and euclidean distance based on a map projection both in terms of estimation and prediction in a space time and a bivariate spatial setting where t

multivariate gaussian process emulators with nonseparable covariance structures the gaussian process regression model is a popular type of emulator used as a fast surrogate for computationally expensive simulators deterministic computer models for simulators with multivariate output common practice is to specify a separable covariance structure for the gaussian process though computationally convenient this can be too restrictive leading to poor performance of the emulator particularly when the different simulator outputs represent different physical quantities also treating the simulator outputs as independent can lead to inappropriate representations of joint uncertainty we develop nonseparable covariance structures for gaussian process emulators based on the linear model of coregionalization and convolution methods using two case studies we compare the performance of these covariance structures both with standard separable covariance structures and with emulators that assume independence between the outputs in each case study we find that only emulators with nons

pairwise meta modeling of multivariate output computer models using nonseparable covariance function gaussian process gp is a popular method for emulating deterministic computer simulation models its natural extension to computer models with multivariate outputs employs a multivariate gaussian process mgp framework nevertheless with significant increase in the number of design points and the number of model parameters building an mgp model is a very challenging task under a general mgp model framework with nonseparable covariance functions we propose an efficient meta modeling approach featuring a pairwise model building scheme the proposed method has excellent scalability even for a large number of output levels some properties of the proposed method have been investigated and its performance has been demonstrated through several numerical examples supplementary materials for this article are available online

approximate likelihood for large irregularly spaced spatial data likelihood approaches for large irregularly spaced spatial datasets are often very difficult if not infeasible to implement due to computational limitations even when we can assume normality exact calculations of the likelihood for a gaussian spatial process observed at n locations requires o n3 operations we present a version of whittle s approximation to the gaussian log likelihood for spatial regular lattices with missing values and for irregularly spaced datasets this method requires o nlog2n operations and does not involve calculating determinants we present simulations and theoretical results to show the benefits and the performance of the spatial likelihood approximation method presented here for spatial irregularly spaced datasets and lattices with missing values we apply these methods to estimate the spatial structure of sea surface temperatures using satellite data with missing values

computer model calibration using high dimensional output this work focuses on combining observations from field experiments with detailed computer simulations of a physical process to carry out statistical inference of particular interest here is determining uncertainty in resulting predictions this typically involves calibration of parameters in the computer simulator as well as accounting for inadequate physics in the simulator the problem is complicated by the fact that simulation code is sufficiently demanding that only a limited number of simulations can be carried out we consider applications in characterizing material properties for which the field data and the simulator output are highly multivariate for example the experimental data and simulation output may be an image or may describe the shape of a physical object we make use of the basic framework of kennedy and o hagan however the size and multivariate nature of the data lead to computational challenges in implementing the framework to overcome these challenges we make use of basis repre

on the existence of caratheodory solutions in mechanical systems with friction it is shown that the differential equation with discontinuous right hand side which describes the dynamic behavior of a mechanical system with friction has a caratheodory solution this result supports theoretically the prior work on the control of mechanical systems with friction which assumes the existence of caratheodory solutions without proof

joint composite estimating functions in spatiotemporal models summary modelling of spatiotemporal processes has received considerable attention in recent statistical research however owing to the high dimensionality of the data the joint modelling of spatial and temporal processes presents a great computational challenge in both likelihood based and bayesian approaches we propose a joint composite estimating function approach to estimating spatiotemporal covariance structures this substantially reduces the computational complexity and is more efficient than existing composite likelihood methods the novelty of the proposed joint composite estimating function is rooted in the construction of three sets of estimating functions from spatial temporal and spatiotemporal cross pairs which results in overidentified estimating functions thus we form a joint inference function in a spirit that is similar to hansen s generalized method of moments we show that under practical scenarios the estimator proposed is consistent and asymptotically normal simulation studies prove that our method performs well in finite samples finally we illustrate the joint composite estimating function method by estimating the spatiotemporal dependence structure of airborne particulates pm10 in the north eastern usa over a 32 month period

pairwise likelihood methods for inference in image models summary we consider parameter estimation for certain random set models for image data for the spatial models considered here a full likelihood based approach to this problem is often difficult since the likelihood generally cannot be computed for images of typical size this has motivated the consideration of various less computationally demanding parameter estimation techniques we discuss one method based on likelihoods for small subsets of the data consideration of the basic technique within the framework of the theory of estimating functions leads to a weighted version of the basic approach results of a simulation study are reported for some variants of the boolean model and excursion sets of random fields the methods are illustrated for some data on the spatial incidence of heather

a bayesian analysis of kriging this article is concerned with predicting for gaussian random fields in a way that appropriately deals with uncertainty in the covariance function to this end we analyze the best linear unbiased prediction procedure within a bayesian framework particular attention is paid to the treatment of parameters in the covariance structure and their effect on the quality both real and perceived of the prediction these ideas are implemented using topographical data from davis

the use of subseries values for estimating the variance of a general statistic from a stationary sequence let z i infty i infty be a strictly stationary infty mixing sequence without specifying the dependence model giving rise to z i and without specifying the marginal distribution of z i we address the question of variance estimation for a general statistic t n t n z 1 z n for estimating var t n from just the available data z 1 z n we propose computing subseries values t m z i 1 z i 2 z i m 0 leq i i m leq n these subseries values are used as replicates to model the sampling variability of t n in particular we use adjacent nonoverlapping subseries of length m m n with m rightarrow infty and m n n rigtharrow 0 our variance estimator is just the usual sample variance computed amongst these subseries values after appropriate standardization this estimator is shown to be consistent under mild integrability conditions we present optimal i e minimum m s e choices of m n for the special case where t n overset z n and z i is a normal ar 1 sequence a simulation study is conducted showing that those same choices of m n are effective when t n is a robust estimator of location and z i is subject to contamination

bayesian prediction of deterministic functions with applications to the design and analysis of computer experiments abstract this article is concerned with prediction of a function y t over a multidimensional domain t given the function values at a set of sites t 1 t 2 t n in t and with the design that is with the selection of those sites the motivating application is the design and analysis of computer experiments where t determines the input to a computer model of a physical or behavioral system and y t is a response that is part of the output or is calculated from it following a bayesian formulation prior uncertainty about the function y is expressed by means of a random function y which is taken here to be a gaussian stochastic process the mean of the posterior process can be used as the prediction function t and the variance can be used as a measure of uncertainty this kind of approach has been used previously in bayesian interpolation and is strongly related to the kriging methods used in geostatistics here emphasis is placed on product linear and product cubic correlation func

necessary and sufficient conditions for the two point phase probability function of two phase random media constructing realizations of random media with a specified two point phase probability function s2 has attracted considerable attention in the recent literature however little is known about cond

random fields on a network modeling statistics and applications the theory of spatial models over lattices or random fields as they are known has developed significantly over recent years this book provides a graduate level introduction to the subject which assumes only a basic knowledge of probability and statistics finite markov chains and the spectral theory of second order processes a particular strength of this book is its emphasis on examples both to motivate the theory which is being developed and to demonstrate the applications which range from statistical mechanics to image analysis and from statistics to stochastic algorithms

using convex quadratic programming to model random media with gaussian random fields excursion sets of gaussian random fields grfs have been frequently used in the literature to model two phase random media with measurable phase autocorrelation functions the goal of successful modeling is finding the optimal field autocorrelation function that best approximates the prescribed phase autocorrelation function in this paper we present a technique which uses convex quadratic programming to find the best admissible field autocorrelation function under a prescribed discretization unlike previous methods this technique efficiently optimizes over all admissible field autocorrelation functions instead of optimizing only over a predetermined parametrized family the results from using this technique indicate that the grf model is significantly more versatile than observed in previous studies an application to modeling a base catalyzed tetraethoxysilane aerogel system given small angle neutron scattering data is also presented

binary mosaics and the spatial pattern of heather an idealized model for the spatial pattern of heather in a planar region is proposed in this model the subregiorl occupied by heather is represented by the union of randomly located discs of randomly varying radii some previous applications of the model are noted techniques for parameter estimation and for testing goodness of fit are suggested these techniques are applied to data showing the incidence of heather in a lomx20m rectangle at jadraas sweden thereby demonstrating the extension to binary mosaics of methodology previously illustrated with spatial point processes

nonseparable stationary covariance functions for space time data geostatistical approaches to spatiotemporal prediction in environmental science climatology meteorology and related fields rely on appropriate covariance models this article proposes general classes of nonseparable stationary covariance functions for spatiotemporal random processes the constructions are directly in the space time domain and do not depend on closed form fourier inversions the model parameters can be associated with the data s spatial and temporal structures respectively and a covariance model with a readily interpretable space time interaction parameter is fitted to wind data from ireland

matern cross covariance functions for multivariate random fields we introduce a flexible parametric family of matrix valued covariance functions for multivariate spatial random fields where each constituent component is a matern process the model parameters are interpretable in terms of process variance smoothness correlation length and colocated correlation coefficients which can be positive or negative both the marginal and the cross covariance functions are of the matern type in a data example on error fields for numerical predictions of surface pressure and temperature over the north american pacific northwest we compare the bivariate matern model to the traditional linear model of coregionalization

hidden symmetries and exact solutions of integro differential jaulent miodek evolution equation use of the adjoint method to obtain optimal lie vectors a reduction of the jm equation to ordinary differential equations and detection of lie symmetries test if these symmetries are hidden analysis and plot of results comparison with previous work in the field analytical solutions of a 2 1 dimensional nonlinear model using the jaulent miodek hierarchy are investigated following a similarity reduction procedure for this adjoint lie matrices are first evaluated and an extensive list of optimal lie vectors is obtained the systematic reduction of jaulent miodek evolution equation to lower number of variables leads to hidden symmetries and new solutions

stochastic modeling of groundwater flow by unconditional and conditional probabilities the inverse problem the inverse problem is defined here as follows determine the transmissivity at varius points given the shape and boundary of the aquifer and recharge intensity and given a set of measured log transmissivity y and head h values at a few points the log transmissivity distribution is regarded as a realization of a random function of normal and stationary unconditional probability density function pdf the solution of the inverse problem is the conditional normal pdf of y conditioned on measured h and y which is expressed in terms of the unconditional joint pdf of y and h the problem is reduced to determining the unconditional head log transmissivity covariance and head variogram for a selected y covariance which depends on a few unknown parameters this is achieved by solving a first order approximation of the flow equations the method is illustrated for an exponential y covariance and the effect of head and transmissivity measurements upon the reduction of uncertainty of y is investigated systematically it is shown that measurement of h has a lesser impact than those of y but a judicious combination may lead to significant reduction of the predicted variance of y possible applications to real aquifers are outlined

gaussian process modeling of a functional output with information from boundary and initial conditions and analytical approximations a partial differential equation pde models a physical quantity as a function of space and time these models are often solved numerically with the finite element fe method and the computer outp

testing for a signal with unknown location and scale in a stationary gaussian random field we suppose that our observations can be decomposed into a fixed signal plus random noise where the noise is modelled as a particular stationary gaussian random field in n dimensional euclidean space the signal has the form of a known function centered at an unknown location and multiplied by an unknown amplitude and we are primarily interested in a test to detect such a signal there are many examples where the signal scale or width is assumed known and the test is based on maximising a gaussian random field over all locations in a subset of n dimensional euclidean space the novel feature of this work is that the width of the signal is also unknown and the test is based on maximising a gaussian random field in n 1 dimensions n dimensions for the location plus one dimension for the width two convergent approaches are used to approximate the null distribution one based on the method of knowles and siegmund which uses a version of weyl s tube formula for manifolds with boundaries and the other based on some recent work by worsley which uses the hadwiger characteristic of excursion sets as introduced by adler finally we compare the power of our method with one based on a fixed but perhaps incorrect signal width

modeling complex systems by generalized factor analysis we propose a new modeling paradigm for large dimensional aggregates of stochastic systems by generalized factor analysis gfa models these models describe the data as the sum of a flocking plus an uncorrelated idiosyncratic component the flocking component describes a sort of collective orderly motion which admits a much simpler mathematical description than the whole ensemble while the idiosyncratic component describes weakly correlated noise we first discuss static gfa representations and characterize in a rigorous way the properties of the two components the extraction of the dynamic flocking component is discussed for time stationary linear systems and for a simple classes of separable random fields

computer model validation with functional output a key question in evaluation of computer models is does the computer model adequately represent reality a six step process for computer model validation is set out in bayarri et al technometrics 49 2007 138 154 and briefly summarized below based on comparison of computer model runs with field data of the process being modeled the methodology is particularly suited to treating the major issues associated with the validation process quantifying multiple sources of error and uncertainty in computer models combining multiple sources of information and being able to adapt to different but related scenarios two complications that frequently arise in practice are the need to deal with highly irregular functional data and the need to acknowledge and incorporate uncertainty in the inputs we develop methodology to deal with both complications a key part of the approach utilizes a wavelet representation of the functional data applies a hierarchical version of the scalar validation methodology to the wavelet coefficients and transforms back to ultimately compare computer model output with field output the generality of the methodology is only limited by the capability of a combination of computational tools and the appropriateness of decompositions of the sort wavelets employed here the methods and analyses we present are illustrated with a test bed dynamic stress analysis for a particular engineering system

a note on composite likelihood inference and model selection a composite likelihood consists of a combination of valid likelihood objects usually related to small subsets of data the merit of composite likelihood is to reduce the computational complexity so that it is possible to deal with large datasets and very complex models even when the use of standard likelihood or bayesian methods is not feasible in this paper we aim to suggest an integrated general approach to inference and model selection using composite likelihood methods in particular we introduce an information criterion for model selection based on composite likelihood we also describe applications to the modelling of time series of counts through dynamic generalised linear models and to the analysis of the well known old faithful geyser dataset

reduced dimensional gaussian process emulators of parametrized partial differential equations based on isomap in this paper isomap and kernel isomap are used to dramatically reduce the dimensionality of the output space to efficiently construct a gaussian process emulator of parametrized partial differential equations the output space consists of spatial or spatio temporal fields that are functions of multiple input variables for such problems standard multi output gaussian process emulation strategies are computationally impractical and or make restrictive assumptions regarding the correlation structure the method we develop can be applied without modification to any problem involving vector valued targets and vector valued inputs it also extends a method based on linear dimensionality reduction to response surfaces that cannot be described accurately by a linear subspace of the high dimensional output space comparisons to the linear method are made through examples that clearly demonstrate the advantages of nonlinear dimensionality reduction

gaussian process models for computer experiments with qualitative and quantitative factors modeling experiments with qualitative and quantitative factors is an important issue in computer modeling we propose a framework for building gaussian process models that incorporate both types of factors the key to the development of these new models is an approach for constructing correlation functions with qualitative and quantitative factors an iterative estimation procedure is developed for the proposed models modern optimization techniques are used in the estimation to ensure the validity of the constructed correlation functions the proposed method is illustrated with an example involving a known function and a real example for modeling the thermal distribution of a data center

a comparison of three methods for selecting values of input variables in the analysis of output from a computer code two types of sampling plans are examined as alternatives to simple random sampling in monte carlo studies these plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function

approximating likelihoods for large spatial data sets summary likelihood methods are often difficult to use with large irregularly sited spatial data sets owing to the computational burden even for gaussian models exact calculations of the likelihood for n observations require o n3 operations since any joint density can be written as a product of conditional densities based on some ordering of the observations one way to lessen the computations is to condition on only some of the past observations when computing the conditional densities we show how this approach can be adapted to approximate the restricted likelihood and we demonstrate how an estimating equations approach allows us to judge the efficacy of the resulting approximation previous work has suggested conditioning on those past observations that are closest to the observation whose conditional density we are approximating through theoretical numerical and practical examples we show that there can often be considerable benefit in conditioning on some distant observations as well

aberrant crypt foci and semiparametric modeling of correlated binary data motivated by the spatial modeling of aberrant crypt foci acf in colon carcinogenesis we consider binary data with probabilities modeled as the sum of a nonparametric mean plus a latent gaussian spatial process that accounts for short range dependencies the mean is modeled in a general way using regression splines the mean function can be viewed as a fixed effect and is estimated with a penalty for regularization with the latent process viewed as another random effect the model becomes a generalized linear mixed model in our motivating data set and other applications the sample size is too large to easily accommodate maximum likelihood or restricted maximum likelihood estimation reml so pairwise likelihood a special case of composite likelihood is used instead we develop an asymptotic theory for models that are sufficiently general to be used in a wide variety of applications including but not limited to the problem that motivated this work the splines have penalty parameters that must converge to zero asymptotically we derive theory for this along with a data driven method for selecting the penalty parameter a method that is shown in simulations to improve greatly upon standard devices such as likelihood crossvalidation finally we apply the methods to the data from our experiment acf we discover an unexpected location for peak formation of acf

global asymptotic stability of a pid control system with coulomb friction for a point mass subject to coulomb friction in feedback with a pid controller we consider a model based on a differential inclusion comprising all the possible magnitudes of static friction during the stick phase and having unique solutions we study the set of all equilibria and we establish its global asymptotic stability using a discontinuous lyapunov like function and a suitable lasalle s invariance principle the well posedness of the proposed model allows to establish useful robustness results including an iss property from a suitable input in a perturbed context simulation results are also given to illustrate our statements

a test for stationarity for irregularly spaced spatial data summary the analysis of spatial data is based on a set of assumptions which in practice need to be checked a commonly used assumption is that the spatial random field is second order stationary in the paper a test for spatial stationarity for irregularly sampled data is proposed the test is based on a transformation of the data a type of fourier transform where the correlations between the transformed data are close to 0 if the random field is second order stationary however if the random field were second order non stationary this property does not hold using this property a test for second order stationarity is constructed the test statistic is based on measuring the degree of correlation in the transformed data the asymptotic sampling properties of the test statistic are derived under both stationarity and non stationarity of the random field these results motivate a graphical tool which allows a visual representation of the non stationary features the method is illustrated with simulations and a real data example

multilevel latent class models with dirichlet mixing distribution summary latent class analysis lca and latent class regression lcr are widely used for modeling multivariate categorical outcomes in social science and biomedical studies standard analyses assume data of different respondents to be mutually independent excluding application of the methods to familial and other designs in which participants are clustered in this article we consider multilevel latent class models in which subpopulation mixing probabilities are treated as random effects that vary among clusters according to a common dirichlet distribution we apply the expectation maximization em algorithm for model fitting by maximum likelihood ml this approach works well but is computationally intensive when either the number of classes or the cluster size is large we propose a maximum pairwise likelihood mpl approach via a modified em algorithm for this case we also show that a simple latent class analysis combined with robust standard errors provides another consistent robust but less efficient inferential procedure simulation studies suggest that the three methods work well in finite samples and that the mpl estimates often enjoy comparable precision as the ml estimates we apply our methods to the analysis of comorbid symptoms in the obsessive compulsive disorder study our models random effects structure has more straightforward interpretation than those of competing methods thus should usefully augment tools available for lca of multilevel data

a nonparametric assessment of properties of space time covariance functions we propose a unified framework for testing various assumptions commonly made for covariance functions of stationary spatio temporal random fields the methodology is based on the asymptotic normality of space time covariance estimators we focus on tests for full symmetry and separability in this article but our framework naturally covers testing for isotropy and taylor s hypothesis our test successfully detects the asymmetric and nonseparable features in two sets of wind speed data we perform simulation experiments to evaluate our test and conclude that our method is reliable and powerful for assessing common assumptions on space time covariance functions

pairwise estimation of multivariate gaussian process models with replicated observations application to multivariate profile monitoring abstractprofile monitoring is often conducted when the product quality is characterized by profiles although existing methods almost exclusively deal with univariate profiles observations of multivariate profile data are increasingly encountered in practice these data are seldom analyzed in the area of statistical process control due to lack of effective modeling tools in this article we propose to analyze them using the multivariate gaussian process model which offers a natural way to accommodate both within profile and between profile correlations to mitigate the prohibitively high computation in building such models a pairwise estimation strategy is adopted asymptotic normality of the parameter estimates from this approach has been established comprehensive simulation studies are conducted in the case study the method has been demonstrated using transmittance profiles from low emittance glass supplementary materials for this article are available online

towards reconciling two asymptotic frameworks in spatial statistics summary two asymptotic frameworks increasing domain asymptotics and infill asymptotics have been advanced for obtaining limiting distributions of maximum likelihood estimators of covariance parameters in gaussian spatial models with or without a nugget effect these limiting distributions are known to be different in some cases it is therefore of interest to know for a given finite sample which framework is more appropriate we consider the possibility of making this choice on the basis of how well the limiting distri butions obtained under each framework approximate their finite sample counterparts we investigate the quality of these approximations both theoretically and empirically showing that for certain consistently estimable parameters of exponential covariograms approximations corresponding to the two frameworks perform about equally well for those parameters that cannot be estimated consistently however the infill asymptotic approximation is preferable

a hybrid pairwise likelihood method a modification to the pairwise likelihood method is proposed which aims to improve the estimation of the marginal distribution parameters this is achieved by replacing the pairwise likelihood score equations for estimating such parameters by the optimal linear combinations of the marginal score functions a further advantage of the proposed estimator of marginal parameters over pairwise likelihood is that it is robust to misspecification of the bivariate distributions as long as the univariate marginal distributions are correctly specified while alternating logistic regression can be seen as a special case of the proposed method it is shown that an existing generalization of alternating logistic regression applicable to ordinal data is not the same as and is inferior to the proposed method because it replaces certain conditional densities by pseudodensities that assume working independence the fitting of the multivariate negative binomial distribution is another scenario involving intractable likelihood that calls for the use of pairwise likelihood methods and the superiority of the modified method is demonstrated in a simulation study two examples based on the analyses of salamander mating and patient controlled analgesia data demonstrate the usefulness of the proposed method the possibility of combining optimally the pairwise rather than marginal scores is also considered and its difficulty and potential are discussed

multivariate versus univariate kriging metamodels for multi response simulation models to analyze the input output behavior of simulation models with multiple responses we may apply either univariate or multivariate kriging gaussian process metamodels in multivariate kriging we face a major problem the covariance matrix of all responses should remain positive definite we therefore use the recently proposed nonseparable dependence model to evaluate the performance of univariate and multivariate kriging we perform several monte carlo experiments that simulate gaussian processes these monte carlo results suggest that the simpler univariate kriging gives smaller mean square error

the direct symmetry method and its application in variable coefficients schrodinger equation by using a direct transformation the variable coefficients schrodinger equation is changed to two nonlinear partial differential equations with variable coefficients we consider the two differential equations and derive different forms of symmetry by the direct symmetry method at last some symmetry reductions and explicit solutions of the variable coefficients schrodinger equation are obtained in terms of similarity solutions of the two differential equations

pid control in the presence of static friction a comparison of algebraic and describing function analysis pid position control in the presence minimal coulomb friction and non zero static friction is shown to lead to a frictional limit cycle for all stabilizing combinations of p i and d parameters an idealized coulomb static friction model dimensional analysis and the study of all possible solutions of the equations of motion are used to achieve rigorous and general results for this nonlinear problem the algebraic prediction of stick slip for this system is contrasted with predictions of the describing function the predictions of the describing function are shown to be unreliable for this problem of friction and control

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

a note on pseudolikelihood constructed from marginal densities for likelihood based inference involving distributions in which high dimensional dependencies are present it may be useful to use approximate likelihoods based for example on the univariate or bivariate marginal distributions the asymptotic properties of formal maximum likelihood estimators in such cases are outlined in particular applications in which only a single q x i vector of observations is observed are examined conditions under which consistent estimators of parameters result from the approximate likelihood using only pairwise joint distributions are studied some examples are analysed in detail

a generalized g g expansion method and its applications to nonlinear evolution equations in this paper a generalized g g expansion method and its algorithm are proposed by studying wang s g g expansion method and constructing a first order nonlinear ordinary differential equation with a third degree nonlinear term being concise and straightforward the method is applied to combined kdv mkdv equation and coupled jaulent miodek equation as a result some new exact travelling wave solutions are obtained which include solitary wave solutions triangular periodic wave solutions exponential solutions complex travelling solutions and rational solutions this method can also be applied to other nonlinear evolution equations in mathematical physics

probabilistic sensitivity analysis of complex models a bayesian approach summary in many areas of science and technology mathematical models are built to simulate complex real world phenomena such models are typically implemented in large computer programs and are also very complex such that the way that the model responds to changes in its inputs is not transparent sensitivity analysis is concerned with understanding how changes in the model inputs influence the outputs this may be motivated simply by a wish to understand the implications of a complex model but often arises because there is uncertainty about the true values of the inputs that should be used for a particular application a broad range of measures have been advocated in the literature to quantify and describe the sensitivity of a model s output to variation in its inputs in practice the most commonly used measures are those that are based on formulating uncertainty in the model inputs by a joint probability distribution and then analysing the induced uncertainty in outputs an approach which is known as probabilistic sensitivity analysis we present a bayesian framework which unifies the various tools of prob abilistic sensitivity analysis the bayesian approach is computationally highly efficient it allows effective sensitivity analysis to be achieved by using far smaller numbers of model runs than standard monte carlo methods furthermore all measures of interest may be computed from a single set of runs

cross covariance functions for multivariate random fields based on latent dimensions summary the problem of constructing valid parametric cross covariance functions is challenging we propose a simple methodology based on latent dimensions and existing covariance models for univariate random fields to develop flexible interpretable and computationally feasible classes of cross covariance functions in closed form we focus on spatio temporal cross covariance functions that can be nonseparable asymmetric and can have different covariance structures for instance different smoothness parameters in each component we discuss estimation of these models and perform a small simulation study to demonstrate our approach we illustrate our methodology on a trivariate spatio temporal pollution dataset from california and demonstrate that our cross covariance performs better than other competing models

an interval finite element approach for the calculation of envelope frequency response functions this paper focusses on the application of the interval finite element method in dynamic analyses it describes a methodology for calculating frequency response function envelopes from a finite element model containing imprecise parameters defined as interval uncertainties the resulting envelope functions give a conservative approximation of the possible range of the frequency response function taking into account that the uncertain parameters in the model can adopt any value in their presumed uncertainty intervals the methodology is based on the modal superposition principle it consists of an interval aritmethic algorithm which processes the results of a preliminary global optimization performed on the modal parameters the algorithm is constructed such that it optimally combines the advantages of both the anti optimization and the interval arithmetic strategy for general numerical interval calculations in the first stage of the development the modal parameter ranges of each individual mode are independently combined in the modal response contributions this yields the modal rectangle mr method in order to remedy the high conservatism inherent to the mr method the exact eigenfrequency ranges are added to the analysis this results in the modal rectangle method with eigenfrequency interval correction mre a second improvement consists of adding extra delimiters to the mre modal parameter range approximation this is achieved by performing an extra optimization on the modal response contributions at discrete frequencies the method is referred to as the locally optimized modal rectangle method with eigenfrequency interval correction omre finally a numerical example illustrates the different algorithms copyright 2004 john wiley sons ltd

physical experimental design in support of computer model development computer models of physical systems are often written based on known theory or first principles of a system reflecting substantial knowledge of each component or subsystem but also the need to use a numerical approach to mimic the more complex behavior of the entire system of interest however in some cases there is insufficient known theory to encode all necessary aspects of the system and empirical studies are required to generate approximate functional forms we consider the question of how a physical experiment might be designed to approximate one module or subroutine of a computer model that can otherwise be written from first principles the concept of preposterior analysis is used to suggest an approach to generating a kind of i optimal design for this purpose when the remainder of the computer model is a composition of nonlinear functions that can be directly evaluated as part of the design process extensions are then described for situations in which one or more known components must the

full scale multi output gaussian process emulator with nonseparable auto covariance functions gaussian process emulator with separable covariance function has been utilized extensively in modeling large computer model outputs the assumption of separability imposes constraints on the emulator and may negatively affect its performance in some applications where separability may not hold we propose a multi output gaussian process emulator with a nonseparable auto covariance function to avoid limitations of using separable emulators in addition to facilitate the computation of nonseparable emulator we introduce a new computational method referred to as the full scale approximation method with block modulating function fsa block approach the fsa block is an effective and accurate covariance approximation method to reduce computations for gaussian process models which applies to both nonseparable and partially separable covariance models we illustrate the effectiveness of our method through simulation studies and compare it with emulators with separable covariances we also apply our method to a real computer code of the carbon capture system

predicting the output from a complex computer code when fast approximations are available s we consider prediction and uncertainty analysis for complex computer codes which can be run at different levels of sophistication in particular we wish to improve efficiency by combining expensive runs of the most complex versions of the code with relatively cheap runs from one or more simpler approximations a bayesian approach is described in which prior beliefs about the codes are represented in terms of gaussian processes an example is presented using two versions of an oil reservoir simulator 1 c complex mathematical models implemented in large computer codes have been used to study real systems in many areas of scientific research sacks et al 1989 usually because physical experimentation is too costly and sometimes impossible as in the case of large environmental systems a computer experiment involves running the code with various input values for the purpose of learning something about the real system often a simulator can be run at different levels of complexity with versions ranging from the most sophisticated high level code to the most basic for example in 4 we consider two codes which simulate oil pressure at a well of a hydrocarbon reservoir both codes use finite element analysis in which the rocks comprising the reservoir are represented by small interacting grid blocks the flow of oil within the reservoir can be simulated by considering the interaction between the blocks the two codes differ in the resolution of the grid so that we have a very accurate slow version using many small blocks and a crude approximation using large blocks which runs much faster alternatively a mathematical model could be expanded to include more of the scientific laws underlying the physical processes simple fast versions of the code may well include the most important features and are useful for preliminary investigations in real time applications the number of runs from a high level simulator may be limited by expense then there is a need to trade off the complexity of the expensive code with the availability of the simpler approximations the purpose of the current paper is to explore ways in which runs from several levels of a code can be used to make inference about the output from the most complex code we may also have uncertainty about values for the input parameters which apply in any given application uncertainty analysis of computer codes describes how this uncertainty on the inputs affects our uncertainty about the output

calibration and uncertainty analysis for computer simulations with multivariate output model calibration analysis is concerned with the estimation of unobservable modeling parameters using observations of system response when the model being calibrated is an expensive computer simulation special techniques such as surrogate modeling and bayesian inference are often fruitful in this paper we show how the flexibility of the bayesian calibration approach can be exploited to account for a wide variety of uncertainty sources in the calibration process we propose a straightforward approach for simultaneously handling gaussian and non gaussian errors as well as a framework for studying the effects of prescribed uncertainty distributions for model inputs that are not treated as calibration parameters further we discuss how gaussian process surrogate models can be used effectively when simulator response may be a function of time and or space multivariate output the proposed methods are illustrated through the calibration of a simulation of thermally decomposing foam

information transfer for small amplitude signals we study the optimality conditions of information transfer in systems with memory in the low signal to noise ratio regime of vanishing input amplitude we find that the optimal mutual information is represented by a maximum variance of the signal time course with correlation structure determined by the fisher information matrix we provide illustration of the method on a simple biologically inspired model of electrosensory neuron our general results apply also to the study of information transfer in single neurons subject to weak stimulation with implications to the problem of coding efficiency in biological systems

multivariate environmental statistics preface multivariate environmental statistics in agriculture v barnett a study of the relationship between diversity indices of benthic communities and heavy metal concentrations of northwest atlantic sediments n c bolgiano r n reid g p patil multivariate non normal statistics in site characterization and evaluation j h carson jr a k gupta spatial prediction in a multivariate setting n cressie needs and developments in multivariate environmental monitoring statistics g t flatman certain multivariate considerations in ranked set sampling and composite sampling designs s d gore et al relating two sets of variables in environmental studies r h green statistical analysis of biological monitoring data p guttorp using entropy in the redesign of an environmental monitoring network p guttorp et al graphical techniques for enhancing the utility of multivariate environmental statistics w a huber carcinogenicity tests involving multiple tumor sites r l kodell e o george errors in variables analysis of extrapolation procedures in environmental toxicology e linder g p patil g suter ii a unified linear model for estimation with composite sample data g lovison change point methods for spatial data i b macneill v k jandkyala a review of computer intensive multivariate methods in ecology b f j manly spatial temporal statistical analysis of multivariate environmental monitoring data k v mardia c r goodall correspondence analysis applied to environmental data sets d e myers a meta network approach to higher order spatial constructs and scale effects w l myers estimation of trend in chesapeake bay water quality data n k nagaraj s l brunenmeister the complexities and scenarios of ecosystem analysis l orloci multivariate methods in nuclear waste remediation needs and applications b a pulsipher omnibus robust procedures for assessment of multivariate normality and detection of multivariate outliers a singh multivariate assessment of trend in environmental variables e p smith s rheem g i holtzman multivariate chemometrics a case study applying and developing receptor models for the 1990 el paso winter pm10 receptor modeling scoping study c h spiegelman s dattner weighted averaging partial least squares regression wa pls definition and comparison with other methods for species environment calibration c j f ter braak et al multivariate aspects of adaptive cluster sampling s k thompson approximating multivariate distributions in stochastic models of insect population dynamics t e wehrly j h matis g w otis

the finite band solution of the jaulent miodek equation a method to construct the finite band solution to the soliton equation is presented we take the jaulent miodek equation as an example with the use of the nonlinearization of lax pair the jaulent miodek equation is decomposed into two finite dimensional integrable systems whose properties are studied from the view of an r matrix then through solving these finite dimensional integrable systems the finite band solution of the jaulent miodek equation is obtained

strictly proper scoring rules prediction and estimation scoring rules assess the quality of probabilistic forecasts by assigning a numerical score based on the predictive distribution and on the event or value that materializes a scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distributionf if he or she issues the probabilistic forecast f rather than g f it is strictly proper if the maximum is unique in prediction problems proper scoring rules encourage the forecaster to make careful assessments and to be honest in estimation problems strictly proper scoring rules provide attractive loss and utility functions that can be tailored to the problem at hand this article reviews and develops the theory of proper scoring rules on general probability spaces and proposes and discusses examples thereof proper scoring rules derive from convex functions and relate to information measures entropy functions and bregman divergences in the case of categorical variables we prove a rigorous version of the

a composite likelihood approach in fitting spatial point process models we propose a new likelihood based approach in fitting spatial point process models a composite likelihood is first formed by adding some pairwise composite likelihood functions that are defined in terms of the second order intensity function of the underlying process and then used for estimating the unknown parameters the estimation procedure is computationally simple and yields consistent and asymptotically normal estimators under some mild conditions we demonstrate through a simulation study and applications to two real data examples that the proposed approach may lead to improved estimations compared with the commonly used minimum contrast estimation approach

a generalized gaussian process model for computer experiments with binary time series non gaussian observations such as binary responses are common in some computer experiments motivated by the analysis of a class of cell adhesion experiments we introduce a generalized gaussian pr

analyzing spatially distributed binary data using independent block estimating equations summary we estimate the relation between binary responses and corresponding covariate vectors both observed over a large spatial lattice we assume a hierarchical generalized linear model with probit link function partition the lattice into blocks and adopt the working assumption of independence between the blocks to obtain an easily solved estimating equation standard errors are obtained using the sandwich estimator together with window subsampling sherman 1996 journal of the royal statistical society series b 58 509 523 we apply this to a large data set describing long term vegetation growth together with two other approximate likelihood approaches pairwise composite likelihood cl and estimation under a working assumption of independence the independence and cl methods give similar point estimates and standard errors while the independent block approach gives considerably smaller standard errors as well as more easily interpretable point estimates we present numerical evidence suggesting this increased efficiency may hold more generally

maximum likelihood estimation of models for residual covariance in spatial regression we describe the maximum likelihood method for fitting the linear model when residuals are correlated and when the covariance among the residuals is determined by a parametric model containing unknown parameters observations are assumed to be gaussian we give conditions which ensure consistency and asymptotic normality of the estimators our main concern is with the analysis of spatial data and in this context we describe some simulation experiments to assess the small sample behaviour of estimators we also discuss an application of the spectral approximation to the likelihood for processes on a lattice

on sample reuse methods for dependent data we suggest a sample reuse method for dependent data based on a cross between the block bootstrap and richardson extrapolation instead of simulating a same size resample by resampling blocks and placing them end to end it analyses the blocks directly and employs a variant of richardson extrapolation to adjust for block size a simple empirical rule also based on richardson extrapolation is suggested for empirically selecting the block size performance in the contexts of distribution and bias estimation is discussed via theoretical analysis and numerical simulation

estimating the number of peaks in a random field using the hadwiger characteristic of excursion sets with applications to medical images excursion sets has been studied by adler who defined the ig integral geometry characteristic of excursion sets as a multidimensional analogue of the number of upcrossings of the threshold by a unidimensional process the ig characteristic equals the euler characteristic of an excursion set provided that the set does not touch the boundary of the volume and adler found the expected ig characteristic for a stationary random field inside a fixed volume worsley evans marrett and neelin used the ig characteristic as an estimator of the number of regions of activation of positron emission tomography pet images of blood flow in the brain unfortunately the ig characteristic is only defined on intervals it is not invariant under rotations and it can fail to count connected regions that touch the boundary this is important since activation often occurs in the cortical regions near the boundary of the brain in this paper we study the hadwiger characteristic which is defined on arbitrary sets is invariant under rotations and does count connected regions whether they touch the boundary or not our main result is a simple expression for the expected hadwiger characteristic for an isotropic stationary random field in two and three dimensions and on a smooth surface embedded in three dimensions results are applied to pet studies of pain perception and word recognition

bayesian calibration of computer models we consider prediction and uncertainty analysis for systems which are approximated using complex mathematical models such models implemented as computer codes are often generic in the sense that by a suitable choice of some of the model s input parameters the code can be used to predict the behaviour of the system in a variety of specific applications however in any specific application the values of necessary parameters may be unknown in this case physical observations of the system in the specific context are used to learn about the unknown parameters the process of fitting the model to the observed data by adjusting the parameters is known as calibration calibration is typically effected by ad hoc fitting and after calibration the model is used with the fitted input values to predict the future behaviour of the system we present a bayesian calibration technique which improves on this traditional approach in two respects first the predictions allow for all sources of uncertainty including the remaining uncertainty over the fitted parameters second they attempt to correct for any inadequacy of the model which is revealed by a discrepancy between the observed data and the model predictions from even the best fitting parameter values the method is illustrated by using data from a nuclear radiation release at tomsk and from a more complex simulated nuclear accident exercise

on the relative importance of input factors in mathematical models safety assessment for nuclear waste disposal this article deals with global quantitative sensitivity analysis of the level e model a computer code used in safety assessment for nuclear waste disposal the level e code has been the subject of two international benchmarks of risk assessment codes and monte carlo methods and is well known in the literature we discuss the level e model with reference to two different settings in the first setting the objective is to find the input factor that drives most of the output variance in the second setting we strive to achieve a preestablished reduction in the variance of the model output by fixing the smallest number of factors the emphasis of this work is on how to define the concept of importance in an unambiguous way and how to assess it in the simultaneous occurrence of correlated input factors and non additive models

statistical inference for max stable processes in space and time max stable processes have proved to be useful for the statistical modelling of spatial extremes several families of max stable random fields have been proposed in the literature one such representation is based on a limit of normalized and rescaled pointwise maxima of stationary gaussian processes that was first introduced by kabluchko and co workers this paper deals with statistical inference for max stable space time processes that are defined in an analogous fashion we describe pairwise likelihood estimation where the pairwise density of the process is used to estimate the model parameters for regular grid observations we prove strong consistency and asymptotic normality of the parameter estimates as the joint number of spatial locations and time points tends to furthermore we discuss extensions to irregularly spaced locations a simulation study shows that the method proposed works well for these models

manifold learning for the emulation of spatial fields from computational models repeated evaluations of expensive computer models in applications such as design optimization and uncertainty quantification can be computationally infeasible for partial differential equation pde models the outputs of interest are often spatial fields leading to high dimensional output spaces although emulators can be used to find faithful and computationally inexpensive approximations of computer models there are few methods for handling high dimensional output spaces for gaussian process gp emulation approximations of the correlation structure and or dimensionality reduction are necessary linear dimensionality reduction will fail when the output space is not well approximated by a linear subspace of the ambient space in which it lies manifold learning can overcome the limitations of linear methods if an accurate inverse map is available in this paper we use kernel pca and diffusion maps to construct gp emulators for very high dimensional output spaces arising from pde model simulations for diffusion maps we develop a new inverse map approximation several examples are presented to demonstrate the accuracy of our approach

a pairwise likelihood based approach for changepoint detection in multivariate time series models this paper develops a composite likelihood based approach for multiple changepoint estimation in multivariate time series we derive a criterion based on pairwise likelihood and minimum description length for estimating the number and locations of changepoints and for performing model selection in each segment the number and locations of the changepoints can be consistently estimated under mild conditions and the computation can be conducted efficiently with a pruned dynamic programming algorithm simulation studies and real data examples demonstrate the statistical and computational efficiency of the proposed method

calibration of computational models with categorical parameters and correlated outputs via bayesian smoothing spline anova it has become commonplace to use complex computer models to predict outcomes in regions where data do not exist typically these models need to be calibrated and validated using some experimental data which often consists of multiple correlated outcomes in addition some of the model parameters may be categorical in nature such as a pointer variable to alternate models or submodels for some of the physics of the system here we present a general approach for calibration in such situations where an emulator of the computationally demanding models and a discrepancy term from the model to reality are represented within a bayesian smoothing spline bss anova framework the bss anova framework has several advantages over the traditional gaussian process including ease of handling categorical inputs and correlated outputs and improved computational efficiency finally this framework is then applied to the problem that motivated its design a calibration of a computational fluid dynamics cfd model of