goal oriented r adaptivity based on variational arguments in the physical and material spaces abstract the error in a local quantity of interest depends on the error in the corresponding dual solution or generalized green s function this fact is used in dual weighted based goal oriented error estimation techniques and h or p adaptive algorithms this contribution is concerned with a novel approach for goal oriented r adaptivity based on energy minimization principles for the primal and the dual problems the minimization of the energy of the primal problem as well as the minimization of the energy of the dual problem with respect to a design function lead to the primal and dual material residuals respectively these residuals are error indicators for the discretization error on the current mesh we propose a goal oriented mesh optimization algorithm which ends in an optimized mesh with respect to a chosen quantity of interest by means of selected computational examples we demonstrate the capability of the proposed framework

on the limiting zeros of sampled multivariable systems for time invariant linear systems with single input single output it has been shown 3 that as the sampling period goes to 0 the zeros of the corresponding discrete time system obtained by sampling converge to some specific constant values determined only be the degrees of the finite and the infinite zeros of the original continuous time system it is natural to inquire the extent to which this result may be carried over to the case of multivariable systems in this note it is shown that the result is true also for multivariable systems if the difference among the degrees of infinite elementary divisors of the pencil corresponding to the original continuous system is less than two when the last condition is not satisfied the limiting values of the zeros of the discrete system depend in general not only on the integers cited above but also on system parameters

robust linear static panel data models using e contamination abstract the paper develops a general bayesian framework for robust linear static panel data models using e contamination a two step approach is employed to derive the conditional type ii maximum likelihood ml ii posterior distribution of the coefficients and individual effects the ml ii posterior means are weighted averages of the bayes estimator under a base prior and the data dependent empirical bayes estimator two stage and three stage hierarchy estimators are developed and their finite sample performance is investigated through a series of monte carlo experiments these include standard random effects as well as mundlak type chamberlain type and hausman taylor type models the simulation results underscore the relatively good performance of the three stage hierarchy estimator within a single theoretical framework our bayesian approach encompasses a variety of specifications while conventional methods require separate estimators for each case

semiparametric nonlinear mixed effects models and their applications nonlinear mixed effects models nlmms and self modeling nonlinear regression semor models are often used to fit repeated measures data they use a common function shared by all subjects to model variation within each subject and some fixed and or random parameters to model variation between subjects the parametric nlmm may be too restrictive and the semiparametric semor model ignores correlations within each subject in this article we propose a class of semiparametric nonlinear mixed effects models snmms that extend nlmms semor models and many other existing models in a natural way a snmm assumes that the mean function depends on some parameters and nonparametric functions the parameters provide an interpretable data summary the nonparametric functions provide flexibility to allow the data to decide some unknown or uncertain components such as the shape of the mean response over time a second stage model with fixed and random effects is used to model the parameters smoothing splines are us

transitional regression models with application to environmental time series abstract environmental epidemiologists often encounter time series data in the form of discrete or other nonnormal outcomes for example in modeling the relationship between air pollution and hospital admissions or mortality rates we present a case study examining the association between pollen counts and meteorologic covariates although such time series data are inadequately described by standard methods for gaussian time series they are often autocorrelated and warrant an analysis beyond those provided by ordinary generalized linear models glms transitional regression models trms signifying nonlinear regression models expressed in terms of conditional means and variances given past observations provide a unifying framework for two mainstream approaches to extending the glm for autocorrelated data the first approach models current outcomes with a glm that incorporates past outcomes as covariates whereas the second models individual outcomes with marginal glms and then couples the error term

approaches for empirical bayes confidence intervals abstract parametric empirical bayes eb methods of point estimation date to the landmark paper by james and stein 1961 interval estimation through parametric empirical bayes techniques has a somewhat shorter history which was summarized by laird and louis 1987 in the exchangeable case one obtains a naive eb confidence interval by simply taking appropriate percentiles of the estimated posterior distribution of the parameter where the estimation of the prior parameters hyperparameters is accomplished through the marginal distribution of the data unfortunately these naive intervals tend to be too short since they fail to account for the variability in the estimation of the hyperparameters that is they do not attain the desired coverage probability in the eb sense defined by morris 1983a b they also provide no statement of conditional calibration rubin 1984 in this article we propose a conditional bias correction method for developing em intervals that corrects these deficiencies

analysis of longitudinal data random coefficient regression modelling we review random coefficient regression rcr models and methods for fitting these models from an applications perspective methods for data with exponential family distributions are presented with the gaussian distribution as a special case attention is given to interpretation of fixed effects and the correlation structures implied by rcr models estimation methods are presented wtih computational approaches problems associated with testing fixed effects include accurate variance estimation and robustness to misspecification of the covariance structure methods for model selection and assessment are presented an example is used to demonstrate recommended approaches

modified euler frobenius polynomials with application to sampled data modelling the broad class of polynomials generally known as eulerian or euler frobenius polynomials has a rich history in mathematics and engineering they have been generalised in several directions and find application in diverse areas ranging from sampled data modelling and polynomial interpolation to wavelets here we describe a modified class of euler frobenius polynomials which are functions of two independent variables we show that the sampling zero dynamics of general linear and nonlinear systems can be described using this new class of polynomials when considering several non standard sampled data modelling problems including when generalised hold functions are used to generate the input and when the continuous system has a time delay

methods for combining rates from several studies when several independent groups have conducted studies to estimate a procedure s success rate it is often of interest to combine the results of these studies in the hopes of obtaining a better estimate for the true unknown success rate of the procedure in this paper we present two hierarchical methods for estimating the overall rate of success both methods take into account the within study and between study variation and assume in the first stage that the number of successes within each study follows a binomial distribution given each study s own success rate they differ however in their second stage assumptions the first method assumes in the second stage that the rates of success from individual studies form a random sample having a constant expected value and variance generalized estimating equations gee are then used to estimate the overall rate of success and its variance the second method assumes in the second stage that the success rates from different studies follow a beta distribution both methods use the maximum likelihood approach to derive an estimate for the overall success rate and to construct the corresponding confidence intervals we also present a two stage bootstrap approach to estimating a confidence interval for the success rate when the number of studies is small we then perform a simulation study to compare the two methods finally we illustrate these two methods and obtain bootstrap confidence intervals in a medical example analysing the effectiveness of hyperdynamic therapy for cerebral vasospasm

paper zeros of sampled systems the zeros of the discrete time system obtained when sampling a continuous time system are explored theorems for the limiting zeros for large and small sampling periods are given conditions which guarantee that the sampled system has stable zeros are also presented

estimating a population of parameter values using bayes and empirical bayes methods abstract in standard bayes and empirical bayes component decision problems estimating inidividual parameters is the primary goal in multiple comparison problems and in comparisons of histograms of estimates however the primary goal is to produce parameter estimates that can be considered as an ensemble for example the histogram of estimates should be a good estimate of the histogram of parameters standard methods of estimating by the posterior expectation do minimize symmetric componentwise losses such as squared error but they produce ensembles of estimates with a sample variance smaller than the posterior expected sample variance for parameters in this article we propose new bayes and empirical bayes estimates that minimize a distance function between the empirical cdf of the estimates and the true parameters these estimators are weighted averages of the prior mean and the data with weight on the data being approximately the square root of that for the posterior expectation we give theoreti

hierarchical poisson regression modeling abstract the poisson model and analyses here feature nonexchangeable gamma distributions although exchangeable following a scale transformation for individual parameters with standard deviations proportional to means a relatively uninformative prior distribution for the shrinkage values eliminates the ill behavior of maximum likelihood estimators of the variance components when tested in simulation studies the resulting procedure provides better coverage probabilities and smaller risk than several other published rules and thus works well from bayesian and frequentist perspectives alike the computations provide fast accurate density approximations to individual parameters and to structural regression coefficients the computer program is publicly available through statlib

error estimation and adaptive meshing in strongly nonlinear dynamic problems we present work aimed at developing a general framework for mesh adaption in strongly nonlinear possibly dynamic problems we begin by showing that the solutions of the incremental boundary value problem for a wide class of materials including nonlinear elastic materials compressible newtonian fluids and viscoplastic solids obey a minimum principle provided that the constitutive updates are formulated appropriately this minimum principle can be taken as a basis for asymptotic error estimation in particular we chose to monitor the error of a lower order projection of the finite element solution the optimal mesh size distribution then follows from a posteriori error indicators which are purely local i e can be computed element by element we demonstrate the robustness and versatility of the computational framework with the aid of convergence studies and selected examples of application

a quasi empirical bayes method for small area estimation abstract this article develops an empirical bayes type approach for small area estimation based only on the specification of a set of conditionally independent hierarchical mean and variance functions describing the first two moments of the process generating the data the objective of the analysis is to draw inference about the intermediate or the random means we combine the quasi likelihood functions to construct the quasi posterior density of the random means conditional on the data and the marginal parameters we describe a method for estimating the marginal parameters that are then substituted in the quasi posterior density of the random means the empirical quasi posterior density so derived is used to obtain the quasi empirical bayes estimates of the random parameters we apply the methodology to estimate the utilization rates of cancer chemotherapy for the selected counties in the state of washington

analytic study on the intrinsic zeros of sampled data systems this paper investigates the properties of the mapping from the simple zero spl gamma of a scalar continuous time system to the corresponding zero spl gamma t of the sampled data system that results by its discretization using a zero order hold where t is the sampling period it is shown that spl gamma t admits a taylor expansion with respect to t and that it coincides with that of exp spl gamma t at least up to the second order term in general and at least up to the third order term if the relative degree of the continuous time system is greater than or equal to two the result is applied to derive a new stability condition of spl gamma t for sufficiently small sampling periods

brief paper inversion of sampled data system approximates the continuous time counterpart in a noncausal framework although correspondence between the poles of a continuous time and sampled data system with a piecewise constant input is simple and desirable from the stability viewpoint the relationship between zeros is intricate inversion of a sampled data system is mostly unstable irrespective of the stability of the continuous time counterpart this makes it difficult to apply inversion based control techniques such as perfect tracking transient response shaping or iterative learning control to sampled data systems although recently developed noncausal inversion techniques help us to circumvent unboundedness of the inversion caused by unstable zeros whether the inversion of sampled data systems approximates the continuous time counterpart or not as the sample period is shortened is still to be determined this article gives a positive conclusion to this problem

random effects models with non parametric priors we discuss the performance of non parametric maximum likelihood npml estimators for the distribution of a univariate random effect in the analysis of longitudinal data for continuous data we analyse generated and real data sets and compare the npml method to those that assume a gaussian random effects distribution and to ordinary least squares for binary outcomes we use generated data to study the moderate and large sample performance of the npml compared with a method based on a gaussian random effect distribution in logistic regression we find that estimated fixed effects are compatible for all approaches but that appropriate standard errors for the npml require adjusting the likelihood based standard errors we conclude that the non parametric approach provides an attractive alternative to gaussian based methods though additional evaluations are necessary before it can be recommended for general use

random effects models for combining results from controlled and uncontrolled studies in a meta analysis abstract a random effects model is used to analyze meta analyses containing both controlled and uncontrolled studies a noniterative estimator of the treatment effect is derived using least squares with the between study variance substituted by an empirical bayes estimator the estimator is shown to be strongly consistent when the between study variance is known and the variance estimator is also shown to be strongly consistent the estimator is shown to have desirable heuristic properties

general methods for analysing repeated measures we present an overview of issues and methods for analysing repeated measures of a continuous random variable we discuss modelling the mean vector and covariance structure statistical efficiency regression diagnostics and discrepancies between longitudinal and cross sectional methods we illustrate key points with examples and discuss areas requiring further development

the relationship between real poles and real zeros in siso sampled data systems a relationship between real poles and real zeros of siso single input single output sampled data systems is presented which is independent of the sampling period the relation is stated in terms of a parity property involving the number of real zeros between any two real poles this property allows the investigation of conditions for the preservation of stable or unstable zeros under sampling a sufficient condition for stability of a sampled system with a continuous time plant having all real zeros and a sufficient condition for instability of a two sampled system with an unstable plant is developed

properties of zeros in digital control systems with computational time delay abstract a digital control system with computational time delay is considered in which the controlled plant is a continuous time linear system and the control input is calculated by a digital computer based on the data of the output measured before a certain time not greater than the sampling period some qualitative properties of the zeros such as the characteristics of the limiting zeros the parity relation between real poles and zeros and the behaviour of the zeros with respect to the computational time delay are investigated and the parity interlacing property and its dual are derived a method of stabilization by a stable digital compensator using the inter sample data is also proposed finally the first order hold case is discussed

empirical bayes estimation of finite population means from complex surveys abstract estimation of finite population means is considered when samples are collected using a stratified sampling design finite populations for different strata are assumed to be realizations from different superpopulations the true means of the observations lie on a regression surface with random intercepts for different strata the true sampling variances are also different and random for different strata the strata are connected through two common prior distributions one for the intercepts and another for the sampling variances for all the strata the model is appropriate in two important survey situations first it can be applied to repeated surveys where the physical characteristics of the sampling units change slowly over time second the model is appropriate in small area estimation problems where a very few samples are available for any particular area empirical bayes estimators of the finite population means are shown to be asymptotically optimal in the sense of robbins the proposed emp

natural exponential families with quadratic variance functions statistical theory the normal poisson gamma binomial negative binomial and nefghs distributions are the six univariate natural exponential families nef with quadratic variance functions qvf this sequel to morris 1982 treats certain statistical topics that can be handled within this unified nef qvf formulation including unbiased estimation bhattacharyya and cramer rao lower bounds conditional distributions and moments quadratic regression conjugate prior distributions moments of conjugate priors and posterior distributions empirical bayes and g 2 minimax marginal distributions and their moments parametric empirical bayes and characterizations

mesh motion techniques for the ale formulation in 3d large deformation problems efficient mesh motion techniques are a key issue to achieve satisfactory results in the arbitrary lagrangian eulerian ale finite element formulation when simulating large deformation problems such as metal forming in the updated lagrangian ul formulation mesh and material movement are attached and an excessive mesh distortion usually appears by uncoupling mesh movement from material movement the ale formulation can relocate the mesh to avoid distortion to facilitate the calculation process the ale operator is split into two steps at each analysis time step ul step where deformation due to loading is calculated without convective terms and eulerian step where mesh motion is applied in this work mesh motion is performed by new nodal relocation methods developed for eight node hexahedral elements which can move internal and boundary nodes improving and concentrating the mesh in critical zones after mesh motion data is transferred from the ul mesh to the relocated mesh using an expansion of stresses in a taylor s series two numerical applications are presented comparing results of ul and ale formulation with results found in the literature copyright 2004 john wiley sons ltd

empirical bayes analysis for systems of mixed models with linked autocorrelated random effects abstract empirical bayes concepts are implemented in a simultaneous analysis of a system of mixed linear models having linked and serially correlated random effects emphasis is placed on the estimation of the random effects and exploration of the relationships between them application is made to the investigation of several series of laboratory assay data that were observed during overlapping time intervals and were therefore subjected to common systematic errors or daily effects the motivation for this work was the need to investigate methods of adjustment for such daily effects and to estimate the degree to which concurrently run series are impacted in common attention is given to the construction of confidence intervals for daily effects tractable methods are proposed that yield approximately correct coverage for large samples although derived within a bayes empirical bayes framework these intervals are somewhat similar to intervals constructed by the method of kackar and harville implement

singular element construction using a mapping technique conformal mapping regularizes in the new plane the singular stress field around the crack tip so conventional finite elements can be used in the transformed plane the inverse mapping of the above elements gives another class of mapped elements the crack tip mapped element is a singular element thus using various elements the parent elements in the mapped plane we obtain an infinity of singular elements the product elements these singular elements are introduced naturally and have no defect as many other singular elements have

a stability condition of zeros of sampled multivariable systems this note derives a new condition for zeros of sampled multivariable systems to be stable for sufficiently small sampling periods it is a natural extension of hagiwara s result for single input single output systems 1993 to multivariable systems

adaptive mesh refinement in strain localization problems an adaptive meshing method tailored to problems of strain localization is given the adaption strategy consists of equi distributing the variation of the velocity field over the elements of the mesh a heuristic justification for the use of variations as indicators is advanced and possible connections with interpolation error bounds are discussed meshes are constructed by delaunay triangulation it is shown how the hu washizu principle determines a consistent transfer operator for the state variables examples of application are given which demonstrate the versatility of the method

a method of grid optimization for finite element methods a computationally useful criterion for grid optimization is derived based on a measure of the interpolation error associated with the finite element model the result is intended to be used to improve the quality of finite element solutions by changing the location of the nodes within a fixed number of degrees of freedom examples of the application of the criterion are provided the finite element method has become an important tool of engineering analysis and design much of the popularity of the method is due to the freedom that it allows in the construction of the discretized model it has long been realized however that this freedom must be carefully exercised since the quality of the finite element solution greatly depends on how the discretization is performed several methods have been proposed to improve the discretized model in an iterative manner one such method is presented in this paper a natural way of improving the quality of finite element solutions is to increase the number of degrees of freedom the process is normally performed after an initial solution is already available several schemes have been devised to introduce the new degrees of freedom in a selective manner in order to produce the greatest possible improvement of the previous solution this calls for the definition of criteria to identify the regions of the domain where the finite element approximation is poorer the new degrees of freedom are added in these regions by either increasing the order of polynomial approximation inside elements the so called p method or by subdivision of elements or h method the process is continued until a specified accuracy is achieved the quality of the finite element solution may be improved also by optimizing the disposition of the nodes analysts often rely on their experience to construct grids that make an efficient use of the available degrees of freedom it is also possible to improve the quality of existing meshes iteratively using predefined guidelines for the redistribution of the nodes this paper considers the development of such guidelines

on the rates of convergence of the finite element method abstract the rate of convergence of the finite element method is a function of the strategy by which the number of degrees of freedom are increased alternative strategies are examined in the light of recent theoretical results and computational experience author

bayesian estimates of disease maps how important are priors in the fully bayesian fb approach to disease mapping the choice of the hyperprior distribution of the dispersion parameter is a key issue in this context we investigated the sensitivity of the rate ratio estimates to the choice of the hyperprior via a simulation study we also compared the performance of the fb approach to mapping disease risk to the conventional approach of mapping maximum likelihood ml estimates and p values the study was modelled on the incidence data of insulin dependent diabetes mellitus iddm as observed in the communes of sardinia

parametric empirical bayes inference theory and applications abstract this article reviews the state of multiparameter shrinkage estimators with emphasis on the empirical bayes viewpoint particularly in the case of parametric prior distributions some successful applications of major importance are considered recent results concerning estimates of error and confidence intervals are described and illustrated with data

stability of the limiting zeros of sampled data systems with zero and first order holds this paper is concerned with the zeros of sampled data systems resulting from continuous time systems preceded by a hold and followed by a sampler the holds we shall consider are a zero order hold and a first order hold for sufficiently small or large sampling periods such zeros are called limiting zeros for sufficiently small sampling periods they are known to consist of two different types of zeros the zeros of the first type correspond to the zeros of the original continuous time system while those of the second type have no continuous time counterparts we first show basic properties of the zeros of sample data systems for sufficiently small sampling periods next we clarify in more detail the correspondence between the former type zeros of the sampled data systems and the zeros of the original continuous time system including the stability property of these zeros we also study stability properties of the latter type zeros in addition we study limiting zeros for sufficiently large sampli

standard errors of prediction in generalized linear mixed models abstract the unconditional mean squared error of prediction umsep is widely used as a measure of prediction variance for inferences concerning linear combinations of fixed and random effects in the classical normal theory mixed model but the umsep is inappropriate for generalized linear mixed models where the conditional variance of the random effects depends on the data when the random effects describe variation between independent small domains and domain specific prediction is of interest we propose a conditional mean squared error of prediction cmsep as a general measure of prediction variance the cmsep is shown to be the sum of the conditional variance and a positive correction that accounts for the sampling variability of parameter estimates we derive a second order correct estimate of the cmsep that consists of three components a a plug in estimate of the conditional variance b a plug in estimate of a taylor series approximation to the correction term and c a bootstrap estimate of

approximate bayesian inference with the weighted likelihood bootstrap we introduce the weighted likelihood bootstrap wlb as a way to simulate approximately from a posterior distribution this method is often easy to implement requiring only an algorithm for calculating the maximum likelihood estimator such as iteratively reweighted least squares in the generic weighting scheme the wlb is first order correct under quite general conditions inaccuracies can be removed by using the wlb as a source of samples in the sampling importance resampling sir algorithm which also allows incorporation of particular prior information the sir adjusted wlb can be a competitive alternative to other integration methods in certain models asymptotic expansions elucidate the second order properties of the wlb which is a generalization of rubin s bayesian bootstrap the calculation of approximate bayes factors for model comparison is also considered we note that given a sample simulated from the posterior distribution the required marginal likelihood may be simulation consistently estimated by the harmonic mean of the associated likelihood values a modification of this estimator that avoids instability is also noted these methods provide simple ways of calculating approximate bayes factors and posterior model probabilities for a very wide class of models

extension of the stein estimating procedure through the use of estimating functions abstract this article extends the stein method through the use of estimating functions godambe 1960 to address the simultaneous estimation of k population parameters 1 k in a mixed model setting the procedure generalizes the stein method by a allowing us to deal effectively with complications such as inequality of population variances that may arise in non gaussian mixed models b being appropriate for estimating i in populations of varying sizes and in particular populations of small sizes and c applying to situations where it cannot be assumed that the i s have unbiased estimators or even estimators of finite moment the focus of the article is on the quadratic variance function exponential family morris 1983b estimators for the parameters of the mixed model are developed in a regression model setting in which the i s are allowed to vary with a vector of covariates an application to incidence rates for the iceland breast cancer incidence data is presented for illustra

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

mesh smoothing using a posteriori error estimates we develop a simple mesh smoothing algorithm for adaptively improving finite element triangulations the algorithm makes use of a posteriori error estimates which are now widely used in finite element calculations in this paper we derive the method present some numerical illustrations and give a brief analysis of the issue of uniqueness

taylor series expansion for zeros of sampled data systems this paper introduces key properties that are useful for the computation of a taylor expansion of discretization zeros or single intrinsic zeros of sampled data systems furthermore regularity is shown to exist in the suffixes of the coefficients of the expansion expressions which implies that the sampling zeros or every coefficient in the numerator of the transfer function of the sampled data systems is dominated by the coefficients of higher order terms in the numerator and denominator of the continuous time counterpart moreover it is shown that the regularity can reduce the calculation effort for expansions of higher order systems

a bootstrap comparison of genetic covariance matrices summary an important problem in evolutionary biology is how population bottlenecks affect additive genetic variance va when only additive effects are present a decrease in va is predicted whereas with many forms of nonadditive interactions an increase is predicted we present an analysis of the changes in variance that occur as a result of a bottleneck in a population of the red flour beetle tribolium castaneum in this experiment the additive genetic covariance matrix for four traits in two sexes was measured in the ancestral population the population then went through a bottleneck and the genetic covariance matrix was again measured these data were analyzed by first examining the univariate estimates for va and second examining the covariance matrices for the univariate measures the statistic we used was the change in va for the multivariate comparisons we used three measures the difference in rank the difference in the number of positive eigenvalues to test changes in the number of heritable traits a multivariate equivalent of bartlett s statistic to test changes in the size of the matrices and a modification of mantel s correlation to test for changes in the correlation structure of the matrices because the distribution of all of these measures is complex and dependent on the specifics of the particular matrices being compared we chose to use a bootstrap analysis to test for significance for females we found that following the population bottleneck va was significantly decreased and that the correlation structure of the matrix was significantly changed for males we found that following the population bottleneck va significantly increased but that the correlation structure was unchanged

a sample reuse method for accurate parametric empirical bayes confidence intervals abstract parametric empirical bayes methods of point estimation for a vector of unknown parameters date to the landmark paper of james and stein 1961 the usual approach is to use the mean of the estimated posterior distribution of each parameter where the estimation of the prior parameters hyperparameters is accomplished through the marginal distribution of the data while point estimates computed this way usually perform well interval estimates based on the estimated posterior called naive eb intervals are not they fail to account for the variability in the estimation of the hyperparameters generally resulting in sub nominal coverage probability in the eb sense defined in morris 1983a in this paper we extend the work of carlin and gelfand 1989 who proposed a conditional bias correction method for developing eb intervals which corrects the deficiencies in the naive intervals we show how bias correction can be implemented in general via a type iii parametric bootstrap procedure a sample reuse method first employed by laird and louis 1987

grid optimization for the boundary element method the quality of solution obtained using the boundary element method bem is dependent on how the boundary is discretized this is particularly true in domains of complex geometry a rule for grid optimization for the bem is derived on the bases of an asymptotic measure of the boundary element error that preserves the number of elements degrees of freedom three example problems are provided to show the advantages of grid optimization in terms of accuracy and cost

regression analysis of case k interval censored failure time data in the presence of informative censoring summary interval censored failure time data occur in many fields such as demography economics medical research and reliability and many inference procedures on them have been developed sun 2006 chen sun and peace 2012 however most of the existing approaches assume that the mechanism that yields interval censoring is independent of the failure time of interest and it is clear that this may not be true in practice zhang et al 2007 ma hu and sun 2015 in this article we consider regression analysis of case k interval censored failure time data when the censoring mechanism may be related to the failure time of interest for the problem an estimated sieve maximum likelihood approach is proposed for the data arising from the proportional hazards frailty model and for estimation a two step procedure is presented in the addition the asymptotic properties of the proposed estimators of regression parameters are established and an extensive simulation study suggests that the method works well finally we apply the method to a set of real interval censored data that motivated this study

validation of a posteriori error estimators by numerical approach abstract a numerical methodology which determines the quality or robustness of a posteriori error estimators is described the methodology accounts precisely for the factors which affect the quality of error estimators for finite element solutions of linear elliptic problems namely the local geometry of the grid and the structure of the solution the methodology can be employed to check the robustness of any estimator for the complex grids which are used in engineering computations

three dimensional adaptive meshing by subdivision and edge collapse in finite deformation dynamic plasticity problems with application to adiabatic shear banding this paper is concerned with the development of a general framework for adaptive mesh refinement and coarsening in three dimensional finite deformation dynamic plasticity problems mesh adaption is driven by a posteriori global error bounds derived on the basis of a variational formulation of the incremental problem the particular mesh refinement strategy adopted is based on rivara s longest edge propagation path lepp bisection algorithm our strategy for mesh coarsening or unrefinement is based on the elimination of elements by edge collapse the convergence characteristics of the method in the presence of strong elastic singularities are tested numerically an application to the three dimensional simulation of adiabatic shear bands in dynamically loaded tantalum is also presented which demonstrates the robustness and versatility of the method copyright c 2001 john wiley sons ltd

some improvements of the finite element solution for one dimensional problems new algorithms which improve the finite element solution on a fixed mesh of the domain are developed for this objective functions which depend on a positive parameter to be determined are proposed these functions lead to criteria which combine in several ways the residual of the solution the approximation in the euclidean norm of the value of the solution at the nodes and the approximations in the energy and hk norms some aspects of optimality are studied and finally numerical results are given

empirical bayes confidence intervals based on bootstrap samples abstract consider the model with data generated by the following two stage process first a parameter is sampled from a prior distribution g and then an observation is sampled from the conditional distribution f y if the prior distribution is known then the bayes estimate under squared error loss is the posterior expectation of conditional on the data y for example if g is gaussian with mean and variance 2 and f y is gaussian with mean and variance 2 then the posterior distribution is gaussian with mean b 1 b y and variance 2 1 b where b 2 2 2 inferences about are based on this distribution we study the application of the bootstrap to situations where the prior must be estimated from the data empirical bayes methods for this model we observe data y t y 1 y k t each independent y k following the compound model described previously as first shown by james and stein 1961 setting each k equal to its estimated posterior mean where and pr

rejection control and sequential importance sampling abstract we discuss ways of combining rejection sampling and importance sampling methods in monte carlo computations and demonstrate their usefulness in updating dynamic systems specifically we propose the rejection controlled sequential importance sampling rc sis algorithm which is designed to simultaneously reduce monte carlo variation and retain independent samples in sequential importance sampling the proposed method is demonstrated by three examples taken from econometrics hierarchical bayes analysis and digital telecommunications they all show significant improvements over previous results

on optimal triangular meshes for minimizing the gradient error construction of optimal triangular meshes for controlling the errors in gradient estimation for piecewise linear interpolation of data functions in the plane is discussed using an appropriate linear coordinate transformation rigorously optimal meshes for controlling the error in quadratic data functions are constructed it is shown that the transformation can be generated as a curvilinear coordinate transformation for anyc data function with nonsingular hessian matrix using this transformation a construction of nearly optimal meshes for general data functions is described and the error equilibration properties of these meshes discussed in particular it is shown that equilibration of errors is not a sufficient condition for optimality a comparison of meshes generated under several different criteria is made and their equilibrating properties illustrated

empirical bayes estimation for the finite population mean on the current occasion abstract many finite populations which are sampled repeatedly change slowly over time then estimation of finite population characteristics for the current occasion l may be improved by the use of data from previous surveys in this article we investigate the use of empirical bayes procedures based on two superpopulation models each model has the same first stage the values of the population units on the ith occasion are a random sample from the normal distribution with mean i and variance 2 i at the second stage we assume that either a 1 l are a random sample from the normal distribution with mean and variance 2 or b given 2 i and i has the normal distribution with mean and variance 2 i independently for each i whereas the 2 i are a random sample from the inverse gamma distribution with parameters 2 and 2 in a the 2 i and 2 are assumed to be unknown whereas in b and are unknown we develop empirical bayes point estimators and confide

an adaptive h r boundary element algorithm for the laplace equation in this paper the combination of the h method mesh refinement and the r method mesh redistribution is employed to solve the laplace equation using the boundary element procedure the key in this approach is to derive on upper bound for the residual associated with the boundary element solution and minimize this bound with respect to an unknown grading function the latter part is achieved by employing techniques of the calculus of variations

approximate bayesian inference in conditionally independent hierarchical models parametric empirical bayes models abstract we consider two stage models of the kind used in parametric empirical bayes peb methodology calling them conditionally independent hierarchical models we suppose that there are k units which may be experimental subjects cities study centers etcetera at the first stage the observation vectors yi for units i 1 k are independently distributed with densities p yi i or more generally p yi i at the second stage the unit specific parameter vectors i are iid with densities p i the peb approach proceeds by regarding the second stage distribution as a prior and noting that if were known inference about could be based on its posterior since is not known the simplest peb methods estimate the parameter by maximum likelihood or some variant and then treat as if it were known to be equal to this estimate although this procedure is sometimes satisfactory a well known defect is that it neglects the uncertainty due to the estimation of in this article w

four bootstrap confidence intervals for the binomial error model confidence intervals for the mean function of the true proportion score x where andx respectively denote the true proportion and observed test scores can be approximated by the efron bayesian and parametric empirical bayes peb bootstrap procedures the similarity of results yielded by all the bootstrap methods suggests the following the unidentifiability problem of the prior distributiong can be bypassed with respect to the construction of confidence intervals for the mean function and a beta distribution forg is a reasonable assumption for the test scores in compliance with a negative hypergeometric distribution the peb bootstrap which reflects the construction of morris intervals is introduced for computing predictive confidence bands for x it is noted that the effect of test reliability on the precision of interval estimates varies with the two types of confidence statements concerned

some bayesian and non bayesian procedures for the analysis of comparative experiments and for small area estimation computational aspects frequentist properties and relationships abstract the estimation of a treatment contrast from experimental data and the estimation of a small area mean are special cases of the prediction of the realization of a linear combination of fixed and random effects in a possibly unbalanced two part mixed linear model in this article a bayesian approach to point and interval prediction is presented and its computational requirements are examined differences between the bayesian approach and the traditional classical approach are discussed in general terms and in addition in terms of two examples taken from the literature 1 the comparison of drug formulations in a bioavailability trial westlake and 2 the estimation of corn crop areas using satellite data battese harter and fuller some deficiencies in the classical approach are pointed out and the bayesian approach is considered from a frequentist perspective it is shown via a monte carlo study that for certain noninformative choices of the prior distribution the frequentist prop

on an h type mesh refinement strategy based on minimization of interpolation errors abstract an adaptive finite element method is proposed which involves an automatic mesh refinement in areas of the mesh where local errors are determined to exceed a pre assigned limit the estimation of local errors is based on interpolation error bounds and extraction formulas for highly accurate estimates of second derivatives applications to several two dimensional model problems are discussed the results indicate that the method can be very effective for both regular problems and problems with strong singularities

a model study of the quality of a posteriori error estimators for linear elliptic problems error estimation in the interior of patchwise uniform grids of triangles abstract this paper is the first in a series in which we discuss computational methodologies for checking the quality of a posteriori error estimators for finite element approximations of linear elliptic problems in this first part we study the asymptotic properties of error estimators in the interior of patchwise uniform grids of triangles a completely numerical methodology for the analysis of the quality of estimators is presented results from the application of the methodology to the study of the quality of several well known error estimators are reported in subsequent papers we shall discuss methods to study the properties of estimators for meshes of quadrilaterals non uniform grids at boundaries grid interfaces and near singular points

design of a stable state feedback controller based on the multirate sampling of the plant output a new type of controller is proposed which detects the ith plant output n sub i times during a period of t sub 0 and changes the plant inputs once during t sub 0 it is shown that an arbitrary state feedback can be realized by such controllers if the plant is observable this implies for instance that arbitrary symmetric pole assignment is possible if the plant is controllable it is also shown that if the plant has no zeros at the origin the state transition matrix of the controller itself can be set arbitrarily without changing the state feedback to be realized that is to say inversely expressed any state feedback can be equivalently realized by a controller with any prescribed degree of stability

adaptive s method for linear elastostatics abstract a methodology has been developed to simultaneously treat phenomena at several scales the key features of the method are i a detailed error diagnosis which identifies critical regions and ii a feedback procedure which overlays portions of the finite element mesh where unacceptable errors have been identified by local finite element mesh es and then subsequently improves the quality of the solution in the global and local response until the desired level of accuracy is achieved the method can be routinely used as a global local method and or as an adaptive technique which provides a measure of reliability of global and local computations numerical experiments for problems in homogeneous and heterogeneous laminated composites media are presented to validate the present formulation

error indicators for adaptive mesh refinement in the boundary element method a new approach in this paper a new approach to the development of a posteriori error indicators for the direct boundary element method bem is presented it takes advantage of a unique opportunity offered by the collocation bem that is the possibility of obtaining more than one numerical solution from a given boundary element mesh unlike other approaches the error indicator introduced in the present paper does not require any explicit evaluation of the residual of the approximate solution in order to test the capability of the proposed error indicators to actually control a selective mesh refinement process an h adaptive refinement strategy is also described together with the criteria for refinement and for the termination of the adaptive process full details on the whole numerical implementation for two dimensional problems are provided in particular there is described a direct method for the numerical evaluation of cauchy principal value integrals numerical examples show that pointwise convergence is always obtained in a few steps and the final meshes look nearly as if they were designed by an expert analyst

smoothing spline models for the analysis of nested and crossed samples of curves abstract we introduce a class of models for an additive decomposition of groups of curves stratified by crossed and nested factors generalizing smoothing splines to such samples by associating them with a corresponding mixed effects model the models are also useful for imputation of missing data and exploratory analysis of variance we prove that the best linear unbiased predictors blups from the extended mixed effects model correspond to solutions of a generalized penalized regression where smoothing parameters are directly related to variance components and we show that these solutions are natural cubic splines the model parameters are estimated using a highly efficient implementation of the em algorithm for restricted maximum likelihood reml estimation based on a preliminary eigenvector decomposition variability of computed estimates can be assessed with asymptotic techniques or with a novel hierarchical bootstrap resampling scheme for nested mixed effects models our methods are applied to me

using empirical bayes methods in biopharmaceutical research a compound sampling model where a unit specific parameter is sampled from a prior distribution and then observed are generated by a sampling distribution depending on the parameter underlies a wide variety of biopharmaceutical data for example in a multi centre clinical trial the true treatment effect varies from centre to centre observed treatment effects deviate from these true effects through sampling variation knowledge of the prior distribution allows use of bayesian analysis to compute the posterior distribution of clinic specific treatment effects frequently summarized by the posterior mean and variance more commonly with the prior not completely specified observed data can be used to estimate the prior and use it to produce the posterior distribution an empirical bayes or variance component analysis in the empirical bayes model the estimated prior mean gives the typical treatment effect and the estimated prior standard deviation indicates the heterogeneity of treatment effects in both the bayes and empirical bayes approaches estimated clinic effects are shrunken towards a common value from estimates based on single clinics this shrinkage produces more efficient estimates in addition the compound model helps structure approaches to ranking and selection provides adjustments for multiplicity allows estimation of the histogram of clinic specific effects and structures incorporation of external information this paper outlines the empirical bayes approach coverage will include development and comparison of approaches based on parametric priors for example a gaussian prior with unknown mean and variance and non parametric priors discussion of the importance of accounting for uncertainty in the estimated prior comparison of the output and interpretation of fixed and random effects approaches to estimating population values estimating histograms and identification of key considerations in the use and interpretation of empirical bayes methods

sharp simultaneous confidence intervals for the means of selected populations with application to microarray data analysis simultaneous inference for a large number n of parameters is a challenge in some situations such as microarray experiments researchers are only interested in making inference for the k parameters corresponding to the k most extreme estimates hence it seems important to construct simultaneous confidence intervals for these k parameters the naive simultaneous confidence intervals for the k means applied directly without taking into account the selection have low coverage probabilities we take an empirical bayes approach or an approach based on the random effect model to construct simultaneous confidence intervals with good coverage probabilities for n 10 000 and k 100 typical for microarray data our confidence intervals could be 77 shorter than the naive k dimensional simultaneous intervals

the optimal confidence region for a random parameter suppose that under a two level hierarchical model the distribution of the vector of random parameters is known or can be estimated well the data are generated via a fixed but unobservable realisation of the vector we derive the smallest confidence region for a specific component of this random vector under a joint bayesian frequentist paradigm on average this optimal region can be much smaller than the corresponding bayesian highest posterior density region the new estimation procedure is especially appealing when one deals with data generated under a highly parallel structure the new proposal is illustrated with a dataset from a multi centre clinical study and also with one from a typical microarray experiment the performance of our procedure is examined via simulation studies

a semi bayes approach to the analysis of correlated multiple associations with an application to an occupational cancer mortality study thomas et al presented the application of empirical bayes methods to the problem of multiple inference in epidemiologic studies one limitation of their approach which they noted was the need to assume exchangeable log relative risk parameters and independent relative risk estimates numerical integration was also required here i generalize their approach to allow for non exchangeable parameters and non independent estimates the resulting method is bayesian in so far as some feature of the prior distribution are specified from prior information but is empirical bayes in so far as some explicit parameters in the prior distribution are estimated from the data estimation is based on approximations to the posterior distribution this allows one to implement the approach with standard software packages for matrix algebra the method is illustrated in an occupational mortality study of 84 exposure cancer associations

an approximate bivariate bayesian method for analyzing small frequencies an approximate bayesian method is developed to study the joint mortality rates of two cancer sites over several geographic areas a conditionally independent two stage hierarchical model is used to model the sources of variability in these data at the first stage conditional on area specific parameters the within area variation in the joint frequencies of death from two sites is modeled by a bivariate poisson distribution with means proportional to the populations at risk at the second stage conditional on parameters for the prior the between area variation in the joint logits of true mortality rates is modeled by a bivariate normal distribution the prior distribution in estimating area mortality rates of one site it is shown that the simultaneous use of data on both sites is superior to that based on a single site only the relation between two sites is studied using the correlation between the logits of true mortality rates a monte carlo simulation is conducted to investigate the performance of this method as a function of the prior correlation the method is applied to two data sets

approximations for standard errors of estimators of fixed and random effects in mixed linear models abstract best linear unbiased estimators of the fixed and random effects of mixed linear models are available when the true values of the variance ratios are known if the true values are replaced by estimated values the mean squared errors of the estimators of the fixed and random effects increase in size the magnitude of this increase is investigated and a general approximation is proposed the performance of this approximation is investigated in the context of a the estimation of the effects of the balanced one way random model and b the estimation of treatment contrasts for balanced incomplete block designs

estimation of multivariate frailty models using penalized partial likelihood summary there exists a growing literature on the estimation of gamma distributed multiplicative shared frailty models there is however often a need to model more complicated frailty structures but attempts to extend gamma frailties run into complications motivated by hip replacement data with a more complicated dependence structure we propose a model based on multiplicative frailties with a multivariate log normal joint distribution we give a justification and an estimation procedure for this generally structured frailty model which is a generalization of the one presented by mcgilchrist 1993 biometrics49 221 225 the estimation is based on laplace approximation of the likelihood function this leads to estimating equations based on a penalized fixed effects partial likelihood where the marginal distribution of the frailty terms determines the penalty term the tuning parameters of the penalty function i e the frailty variances are estimated by maximizing an approximate profile likelihood the performance of the approximation is evaluated by simulation and the frailty model is fitted to the hip replacement data

empirical bayes confidence intervals shrinking both means and variances summary we construct empirical bayes intervals for a large number p of means the existing intervals in the literature assume that variances are either equal or unequal but known when the variances are unequal and unknown the suggestion is typically to replace them by unbiased estimators however when p is large there would be advantage in borrowing strength from each other we derive double shrinkage intervals for means on the basis of our empirical bayes estimators that shrink both the means and the variances analytical and simulation studies and application to a real data set show that compared with the t intervals our intervals have higher coverage probabilities while yielding shorter lengths on average the double shrinkage intervals are on average shorter than the intervals from shrinking the means alone and are always no longer than the intervals from shrinking the variances alone also the intervals are explicitly defined and can be computed immediately

an adaptive finite element method for linear elliptic problems on propose une methode adaptative d elements finis basee sur une estimation d erreur optimale de norme maxima pour les problemes elliptiques lineaires

empirical bayes methods for combining likelihoods abstract suppose that several independent experiments are observed each one yielding a likelihood l k k for a real valued parameter of interest k for example k might be the log odds ratio for a 2 2 table relating to the kth population in a series of medical experiments this article concerns the following empirical bayes question how can we combine all of the likelihoods l k to get an interval estimate for any one of the k s say 1 the results are presented in the form of a realistic computational scheme that allows model building and model checking in the spirit of a regression analysis no special mathematical forms are required for the priors or the likelihoods this scheme is designed to take advantage of recent methods that produce approximate numerical likelihoods l k k even in very complicated situations with all nuisance parameters eliminated the empirical bayes likelihood theory is extended to situations where the k s have a regression structure as well as an empiri

multi level finite element solution algorithms based on multiplicative and additive correction procedures owing to the failure of the finite element analyst to employ a properly refined computational model the accuracy of preliminary finite element computations is often low thus it is useful to introduce a computational procedure for improving the results obtained from a preliminary finite element solution such a procedure is presented in this paper in this procedure the solution error components are decomposed into two parts one of the error components is assumed to have a long period variation the other component is assumed to have a short period variation multiplicative and additive correction procedures are introduced to iteratively eliminate the two error components the multiplicative and additive correction procedures are implemented using multi level solution techniques

adaptive multigroup confidence intervals with constant coverage summarycommonly used interval procedures for multigroup data attain their nominal coverage rates across a population of groups on average but their actual coverage rate for a given group will be above or below the nominal rate depending on the group mean while correct coverage for a given group can be achieved with a standard t interval this approach is not adaptive to the available information about the distribution of group specific means in this article we construct confidence intervals that have a constant frequentist coverage rate and that make use of information about across group heterogeneity resulting in constant coverage intervals that are narrower than standard t intervals on average across groups such intervals are constructed by inverting biased bayes optimal tests for the mean of each group where the prior distribution for a given group is estimated with data from the other groups

detection of significant disease risks using a spatial conditional autoregressive model summary the conditional autoregressive car model is widely used to describe the geographical distribution of a specific disease risk in lattice mapping successful developments based on frequentist and bayesian procedures have been extensively applied to obtain two stage disease risk predictions at the subregional level bayesian procedures are preferred for making inferences as the posterior standard errors se of the two stage prediction account for the variability in the variance component estimates however some recent work based on frequentist procedures and the use of bootstrap adjustments for the se has been undertaken in this article we investigate the suitability of an analytical adjustment for disease risk inference that provides accurate interval predictions by using the penalized quasilikelihood pql technique to obtain model parameter estimates the method is a first order approximation of the naive se based on a taylor expansion and is interpreted as a conditional measure of variability providing conditional calibrated prediction intervals given the data we conduct a simulation study to demonstrate how the method can be used to estimate the specific subregion risk by interval we evaluate the proposed methodology by analyzing the commonly used example data set of lip cancer incidence in the 56 counties of scotland for the period 1975 1980 this evaluation reveals a close similarity between the solutions provided by the method proposed here and those of its fully bayesian counterpart