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

finite sample adjustments in estimating equations and covariance estimators for intracluster correlations bias corrected covariance estimators are introduced in the context of an estimating equations approach for intracluster correlations among binary outcomes simulation study results show that the bias corrected covariance estimators perform better than uncorrected sandwich estimators in terms of bias and coverage probabilities additionally introduction of a matrix based bias correction into the estimating equations considerably improves point and interval estimation for the intracluster correlations the methods are illustrated using data from a nested cross sectional cluster trial on reducing underage drinking

working correlation structure misspecification estimation and covariate design implications for generalised estimating equations performance the method of generalised estimating equations for regression modelling of clustered outcomes allows for specification of a working matrix that is intended to approximate the true correlation matrix of the observations we investigate the asymptotic relative efficiency of the generalised estimating equation for the mean parameters when the correlation parameters are estimated by various methods the asymptotic relative efficiency depends on three features of the analysis namely i the discrepancy between the working correlation structure and the unobservable true correlation structure ii the method by which the correlation parameters are estimated and iii the design by which we refer to both the structures of the predictor matrices within clusters and distribution of cluster sizes analytical and numerical studies of realistic data analysis scenarios show that choice of working covariance model has a substantial impact on regression estimator efficiency protection against avoidable loss of efficiency associated with covariance misspecification is obtained when a gaussian estimation pseudolikelihood procedure is used with an ar 1 structure

a preconditioned gmres method for nonsymmetric or indefinite problems a preconditioning technique is proposed for nonsymmetric or indefinite linear systems of equations the main idea in our theory roughly speaking is first to use some coarser mesh space to correct the nonpositive portion of the eigenvalues of the underlying operator and then switch to use a symmetric positive definite preconditioner the generality of our theory allows us to apply any known preconditioners that were orginally designed for symmetric positive definite problems to nonsymmetric or indefinite problems without losing the optimality that the original one has some numerical experiments based on gmres are reported

multi time step domain decomposition and coupling methods for nonlinear parabolic problems abstract in this paper we propose and examine a multi time step algorithm using a feti based domain decomposition method for nonlinear parabolic problems the computational domain is divided into a set of smaller subdomains that may be integrated concurrently with their own time steps the continuity condition at the interface is ensured employing local lagrange multipliers the equation of continuity of primary unknowns at the interface is written only at the so called system time step the subdomain problems are coupled together by requiring the lagrange multipliers on the interface at the intermediate time steps to match a suitable interpolation of the values at the system time steps this allows each subdomain to be solved with its own time step the rigorous nonlinear stability is performed via the energy method several numerical examples will be solved to illustrate the overall performance of the proposed coupling method

a globally uniformly convergent finite element method for a singularly perturbed elliptic problem in two dimensions we analyze a new galerkin finite element method for numerically solving a linear convection dominated convection diffusion problem in two dimensions the method is shown to be convergent uniformly in the perturbation parameter of order h1 2 in a global energy norm which is stronger than the l2 norm this order is optimal in this norm for our choice of trial functions

weighted max norms splittings and overlapping additive schwarz iterations summary weighted max norm bounds are obtained for algebraic additive schwarz iterations with overlapping blocks for the solution of ax b when the coefficient matrix a is an m matrix the case of inexact local solvers is also covered these bounds are analogous to those that exist using a norms when the matrix a is symmetric positive definite a new theorem concerningp regular splittings is presented which provides a useful tool for the a norm bounds furthermore a theory of splittings is developed to represent algebraic additive schwarz iterations this representation makes a connection with multisplitting methods with this representation and using a comparison theorem it is shown that a coarse grid correction improves the convergence of additive schwarz iterations when measured in weighted max norm

the calculation of thermoacoustic oscillations thermoacoustic oscillations occur in a wide variety of practical applications in which heat is supplied to an acoustic resonator a simple geometry is investigated systematically to determine the importance of various flow parameters on the frequency of the oscillations detailed consideration of elementary examples shows that the form of the coupling between the heat input and the unsteady flow has a crucial effect on the frequency of oscillation the same elementary examples are used to compare how well if at all different calculation methods in the literature account for this influence a mean flow and a distributed region of heat input significantly complicate the analysis of thermoacoustic oscillations and are often neglected model problems are used to illustrate that mean flow effects can become significant even at modest inlet mach numbers and to indicate circumstances under which a distributed heat input may be treated as concentrated

correlated binary regression using a quadratic exponential model summary a model of quadratic exponential form is parameterized in terms of marginal means and pairwise correlations for the regression analysis of correlated binary data pseudo maximum likelihood methods using a special case termed the multiplicative model are proposed but are noted to be computationally unattractive if the blocks of correlated responses are at all large on the other hand score estimating functions for mean and correlation parameters are shown to be of a particularly simple form under the quadratic exponential family special cases of such estimating functions having attractive computational properties are identified and illustrated

estimating equations for removal data analysis we consider the problem of estimating a population size from successive catches taken during a removal experiment and propose two estimating functions approaches the traditional quasi likelihood tql approach for dependent observations and the conditional quasi likelihood cql approach using the conditional mean and conditional variance of the catch given previous catches asymptotic covariance of the estimates and the relationship between the two methods are derived simulation results and application to the catch data from smallmouth bass show that the proposed estimating functions perform better than other existing methods especially in the presence of overdispersion

preconditioning indefinite discretization matrices the finite element discretization of many elliptic boundary value problems leads to linear systems with positive definite and symmetric coefficient matrices many efficient preconditioners are known for these systems we show that these preconditioning matrices can also be used for the linear systems arising from boundary value problems which are potentially indefinite due to lower order terms in the partial differential equation our main tool is a careful algebraic analysis of the condition numbers and the spectra of perturbed matrices which are preconditioned by the same matrices as in the unperturbed case

the solution of singularly perturbed semilinear elliptic problems by iterative domain decomposition algorithms abstract parallel domain decomposition algorithms for the solution of singularly perturbed semilinear elliptic problems are considered convergence properties and numerical stability of these iterative algorithms are established numerical experiments are provided

meta analytical synthesis of regression coefficients under different categorization scheme of continuous covariates recently the number of clinical prediction models sharing the same regression task has increased in the medical literature however evidence synthesis methodologies that use the results of these regression models have not been sufficiently studied particularly in meta analysis settings where only regression coefficients are available one of the difficulties lies in the differences between the categorization schemes of continuous covariates across different studies in general categorization methods using cutoff values are study specific across available models even if they focus on the same covariates of interest differences in the categorization of covariates could lead to serious bias in the estimated regression coefficients and thus in subsequent syntheses to tackle this issue we developed synthesis methods for linear regression models with different categorization schemes of covariates a 2 step approach to aggregate the regression coefficient estimates is proposed the first step is to estimate the joint distribution of covariates by introducing a latent sampling distribution which uses one set of individual participant data to estimate the marginal distribution of covariates with categorization the second step is to use a nonlinear mixed effects model with correction terms for the bias due to categorization to estimate the overall regression coefficients especially in terms of precision numerical simulations show that our approach outperforms conventional methods which only use studies with common covariates or ignore the differences between categorization schemes the method developed in this study is also applied to a series of who epidemiologic studies on white blood cell counts

an approach to the analysis of repeated measurements summary a linear model for repeated measurements is proposed in which the correlation structure within each time sequence of measurements includes parameters for measurement error variation between experimental units and serial correlation within units an approach to data analysis is presented which involves preliminary analysis by ordinary least squares use of the empirical semi variogram of residuals to suggest a suitable correlation structure and formal inference using likelihood based methods applications to two biological data sets are described

a latent process regression model for spatially correlated count data summary this paper proposes a regression model for spatially correlated count data that generalizes the work spatially correlated count data arise in a variety of settings frequently it is of interest to make marginal inferences about spatial trends and effects of explanatory variables on spatially correlated counts an example application described in this paper involves an examination of the distribution of neuronal cells in a laboratory culture well our motivation for examining the distribution of cells was due to the implications of the distribution for the choice of an efficient sampling method to estimate total cell count total neuronal cell counts in a culture well are ordinarily estimated using data from multiple sampled subregions viewed under the microscope or with the aid of an image analysis system because counting all cells in a culture well is prohibitively time consuming as routine practice these sampling methods typically involve recording from multiple randomly selected fields the area of the field and number of cells visible in the field a cell per unit area density is estimated from the data and the total cell count estimate for the well is obtained by multiplication by the total well area these methods implicitly assume that cells are distributed completely at random throughout the well experience would suggest that there could be trends in neuron density and clustering tendencies for example neurons can tend to a higher density in the center of a well due to a slight vortex that occurs when the cultures are moved before the neurons have attached themselves to the substratum neurons also may distribute in higher density around the edges of a culture well due to a meniscus and slightly greater depth of medium at the edge of a well spatial clustering may result if neural cell bodies migrate along the cell body s neuritic processes or if the tissue culture tray is

spatial modeling of regional variables abstract in this article accumulated sudden infant death syndrome sids data from 1974 1978 and 1979 1984 for the counties of north carolina are analyzed after a spatial exploratory data analysis markov random field models are fit to the data the spatial trend is meant to capture the large scale variation in the data and the variance and spatial dependence are meant to capture the small scale variation the trend could be a function of other explanatory variables or could simply be modeled as a function of spatial location both models are fit and compared the results give an excellent illustration of a phenomenon already well known in time series that autocorrelation in data can be due to an undiscovered explanatory variable indeed for 1974 1978 we confirm a dependence of sids rate on proportion of nonwhite babies born along with insignificant spatial correlation without this regressor variable however the spatial correlation is significant in 1979 1984 perhaps due to reporting bias o

a regression modeling approach for describing patterns of hiv genetic variation we introduce a novel approach for describing patterns of hiv genetic variation using regression modeling techniques parameters are defined for describing genetic variation within and between viral populations by generalizing simpson s index of diversity regression models are specified for these variation parameters and the generalized estimating equation framework is used for estimating both the regression parameters and their corresponding variances conditions are described under which the usual asymptotic approximations to the distribution of the estimators are met this approach provides a formal statistical framework for testing hypotheses regarding the changing patterns of hiv genetic variation over time within an infected patient the application of these methods for testing biologically relevant hypotheses concerning hiv genetic variation is demonstrated in an example using sequence data from a subset of patients from the multicenter aids cohort study

feedback control of combustion instabilities from within limit cycle oscillations using h loop shaping and the ν gap metric combustion instabilities arise owing to a two way coupling between acoustic waves and unsteady heat release oscillation amplitudes successively grow until nonlinear effects cause saturation into limit cycle oscillations feedback control in which an actuator modifies some combustor input in response to a sensor measurement can suppress combustion instabilities linear feedback controllers are typically designed using linear combustor models however when activated from within limit cycle the linear model is invalid and such controllers are not guaranteed to stabilize this work develops a feedback control strategy guaranteed to stabilize from within limit cycle oscillations a low order model of a simple combustor exhibiting the essential features of more complex systems is presented linear plane acoustic wave modelling is combined with a weakly nonlinear describing function for the flame the latter is determined numerically using a level set approach its implication is that the open loop transfer function oltf needed for controller design varies with oscillation level the difference between the mean and the rest of the oltfs is characterized using the gap metric providing the minimum required robustness margin for an formula see text loop shaping controller such controllers are designed and achieve stability both for linear fluctuations and from within limit cycle oscillations

empirical bayes estimates of age standardized relative risks for use in disease mapping there have been many attempts in recent years to map incidence and mortality from diseases such as cancer such maps usually display either relative rates in each district as measured by a standardized mortality ratio smr or some similar index or the statistical significance level for a test of the difference between the rates in that district and elsewhere neither of these approaches is fully satisfactory and we propose a new approach using empirical bayes estimation the resulting estimators represent a weighted compromise between the smr the overall mean relative rate and a local mean of the relative rate in nearby areas the compromise solution depends on the reliability of each individual smr and on estimates of the overall amount of dispersion of relative rates over different districts

on an uniform multidomain decomposition method applied to a singularly perturbed problem with regular boundary layers this paper deals with an iterative algorithm for multidomain decomposition applied to the solution of a singularly perturbed convection diffusion problem uniform convergent properties of the algorithm are established numerical results are presented

power and sample size requirements for gee analyses of cluster randomized crossover trials the cluster randomized crossover design has been proposed to improve efficiency over the traditional parallel cluster randomized design which often involves a limited number of clusters in recent years the cluster randomized crossover design has been increasingly used to evaluate the effectiveness of health care policy or programs and the interest often lies in quantifying the population averaged intervention effect in this paper we consider the two treatment two period crossover design and develop sample size procedures for continuous and binary outcomes corresponding to a population averaged model estimated by generalized estimating equations accounting for both within period and interperiod correlations in particular we show that the required sample size depends on the correlation parameters through an eigenvalue of the within cluster correlation matrix for continuous outcomes and through two distinct eigenvalues of the correlation matrix for binary outcomes we demonstrate that the empirical power corresponds well with the predicted power by the proposed formulae for as few as eight clusters when outcomes are analyzed using the matrix adjusted estimating equations for the correlation parameters concurrently with a suitable bias corrected sandwich variance estimator

performance of analytical methods for overdispersed counts in cluster randomized trials sample size degree of clustering and imbalance many different methods have been proposed for the analysis of cluster randomized trials crts over the last 30 years however the evaluation of methods on overdispersed count data has been based mostly on the comparison of results using empiric data i e when the true model parameters are not known in this study we assess via simulation the performance of five methods for the analysis of counts in situations similar to real community intervention trials we used the negative binomial distribution to simulate overdispersed counts of crts with two study arms allowing the period of time under observation to vary among individuals we assessed different sample sizes degrees of clustering and degrees of cluster size imbalance the compared methods are i the two sample t test of cluster level rates ii generalized estimating equations gee with empirical covariance estimators iii gee with model based covariance estimators iv generalized linear mixed models glmm and v bayesian hierarchical models bayes hm variation in sample size and clustering led to differences between the methods in terms of coverage significance power and random effects estimation glmm and bayes hm performed better in general with bayes hm producing less dispersed results for random effects estimates although upward biased when clustering was low gee showed higher power but anticonservative coverage and elevated type i error rates imbalance affected the overall performance of the cluster level t test and the gee s coverage in small samples important effects arising from accounting for overdispersion are illustrated through the analysis of a community intervention trial on solar water disinfection in rural bolivia

overlapping schwarz methods for a singularly perturbed semilinear elliptic problem and their parallel implementation domain decomposition algorithms based on the schwarz alternating method are applied to the numerical solution of a singularly perturbed semilinear elliptic problem the emphasis is given to the description of the algorithms multidomain schwarz alternating method and two level schwarz method as well as their computer realization on a distributed memory multiprocessor computer numerical experiments related to a model problem illustrate the performance of the algorithms on parallel environment as well as their behavior with respect to the critical parameters such as the perturbation parameter the amount of overlapping and sizes of subdomains application of the two level schwarz method to a model semiconductor problem is also discussed

a second order parameter uniform overlapping schwarz method for reaction diffusion problems with boundary layers the problem of constructing a parameter uniform numerical method for a singularly perturbed self adjoint ordinary differential equation is considered it is shown that a suitably designed discrete schwarz method based on a standard finite difference operator with a uniform mesh on each subdomain gives numerical approximations which converge in the maximum norm to the exact solution uniformly with respect to the singular perturbation parameter this parameter uniform convergence is shown to be essentially second order that this new discrete schwarz method is efficient in practice is demonstrated by numerical experiments

multigrid convergence for nonsymmetric indefinite variational problems and one smoothing step we prove that the multigrid method for linear systems arising from nonsymmetric and indefinite elliptic variational problems converges for all sufficiently small h with one smoothing step only previous proofs required that the number of smoothing steps be within certain bounds which were quite difficult to compute our theory is based on sharp energy norm convergence estimates for the symmetric definite case and lower order terms are treated as perturbations the resulting estimates are so sharp that we obtain even the convergence of the v cycle

domain decomposition for an advection diffusion problem with parabolic layers this paper deals with multidomain domain decomposition algorithms applied to the solution of a singularly perturbed advection diffusion problem with parabolic layers our purpose is to study the algorithms applied to finite difference approximations of the problem the finite difference approximations make use of special piecewise uniform meshes we consider two algorithms the first one is based on decomposition of the computational domain into nonoverlapping vertical subdomains and second uses decomposition into nonoverlapping horizontal subdomains convergence properties of the algorithms are established numerical results for a test problem are presented

algebraic theory of multiplicative schwarz methods the convergence of multiplicative schwarz type methods for solving linear systems when the coefficient matrix is either a nonsingular m matrix or a symmetric positive definite matrix is studied using classical and new results from the theory of splittings the effect on convergence of algorithmic parameters such as the number of subdomains the amount of overlap the result of inexact local solves and of coarse grid corrections global coarse solves is analyzed in an algebraic setting results on algebraic additive schwarz are also included

regular article a pde based fast local level set method we develop a fast method to localize the level set method of osher and sethian 1988 j comput phys 79 12 and address two important issues that are intrinsic to the level set method a how to extend a quantity that is given only on the interface to a neighborhood of the interface b how to reset the level set function to be a signed distance function to the interface efficiently without appreciably moving the interface this fast local level set method reduces the computational effort by one order of magnitude works in as much generality as the original one and is conceptually simple and easy to implement our approach differs from previous related works in that we extract all the information needed from the level set function or functions in multiphase flow and do not need to find explicitly the location of the interface in the space domain the complexity of our method to do tasks such as extension and distance reinitialization is o n where n is the number of points in space not o n log n as in works by sethian 1996 proc nat acad sci 93 1591 and helmsen and co workers 1996 spie microlithography ix p 253 this complexity estimation is also valid for quite general geometrically based front motion for our localized method

maximum norm stability of difference schemes for parabolic equations on overset nonmatching space time grids in this paper theoretical results are described on the maximum norm stability and accuracy of finite difference discretizations of parabolic equations on overset nonmatching space time grids we consider parabolic equations containing a linear reaction term on a space time domain 0 t which is decomposed into an overlapping collection of cylindrical subregions of the form l 0 t for l 1 p each of the space time domains l 0 t are assumed to be independently grided in parallel according to the local geometry and space time regularity of the solution yielding space time grids with mesh parameters hl and l in particular the different space time grids need not match on the regions of overlap and the time steps l can differ from one grid to the next we discretize the parabolic equation on each local grid by employing an explicit or implicit scheme in time and a finite difference scheme in space satisfying a discrete maximum principle the local discretizations are coupled together without the use of lagrange multipliers by requiring the boundary values on each space time grid to match a suitable interpolation of the solution on adjacent grids the resulting global discretization yields a large system of coupled equations which can be solved by a parallel schwarz iterative procedure requiring some communication between adjacent subregions our analysis employs a contraction mapping argument applications of the results are briefly indicated for reaction diffusion equations with contractive terms and heterogeneous hyperbolic parabolic approximations of parabolic equations

empirical bayes estimates of cancer mortality rates using spatial models we give results of empirical bayes eb estimation of mortality rates designed to smooth observed smr when random fluctuation of the observed deaths is important we have specially studied the case where the prior distributions of the eb method have a spatial structure the need for spatial modelling of cancer mortality rates in france is first shown with testing autocorrelation and fitting autoregressive spatial models conditional car or simultaneous sar a positive autocorrelation of the rates is shown for most cancer sites studied as expected eb estimates of mortality rates for common tumours are similar to smrs for rare tumours the eb method identifies the extreme rates more clearly than smrs by smoothing the smrs with large variances car or sar models are adequate prior distributions for autocorrelated rates and produce quite similar rate estimates

using second order generalized estimating equations to model heterogeneous intraclass correlation in cluster randomized trials in cluster randomized trials it is commonly assumed that the magnitude of the correlation among subjects within a cluster is constant across clusters however the correlation may in fact be heterogeneous and depend on cluster characteristics accurate modeling of the correlation has the potential to improve inference we use second order generalized estimating equations to model heterogeneous correlation in cluster randomized trials using simulation studies we show that accurate modeling of heterogeneous correlation can improve inference when the correlation is high or varies by cluster size we apply the methods to a cluster randomized trial of an intervention to promote breast cancer screening

convergence theory of restricted multiplicative schwarz methods convergence results for the restricted multiplicative schwarz rms method the multiplicative version of the restricted additive schwarz ras method for the solution of linear systems of the form ax b are provided an algebraic approach is used to prove convergence results for nonsymmetric m matrices several comparison theorems are also established these theorems compare the asymptotic rate of convergence with respect to the amount of overlap the exactness of the subdomain solver and the number of domains moreover comparison theorems are given between the rms and ras methods as well as between the rms and the classical multiplicative schwarz method

high order numerical methods to two dimensional delta function integrals in level set methods in this paper we design and analyze a class of high order numerical methods to delta function integrals appearing in level set methods in two dimensional case the methods comprise approximating the mesh cell restrictions of the delta function integral in each mesh cell the two dimensional delta function integral can be rewritten as a one dimensional ordinary integral with the smooth integrand being a one dimensional delta function integral and thus is approximated by applying standard one dimensional high order numerical quadratures and high order numerical methods to one dimensional delta function integrals proposed in x wen high order numerical methods to a type of delta function integrals j comput phys 226 2007 1952 1967 we establish error estimates for the method which show that the method can achieve any desired accuracy by assigning the corresponding accuracy to the sub algorithms and has better accuracy under an assumption on the zero level set of the level set function which holds generally numerical examples are presented showing that the second to fourth order methods implemented in this paper achieve or exceed the expected accuracy and demonstrating the advantage of using our high order numerical methods

uniform convergence of the schwarz alternating method for solving singularly perturbed advection diffusion equations our purpose in this paper is to study the convergence rate of some variants of the schwarz alternating method for solving two types of singularly perturbed advection diffusion equations one in which the advection term first order term dominates and the other in which the lowest order term zeroth order term dominates for such problems boundary or other layer regions may be present for singular perturbation problems in which the advection dominates we choose two overlapping subregions one corresponding to an outer or elliptic region and the other corresponding to an inner or hyperbolic region our main result for this problem shows that if the subdomains can be chosen to follow the flow i e if the boundary interface of one of the subdomains corresponds to an outflow boundary for the streamlines of the flow then the schwarz iterates converge in the maximum norm with an error reduction factor per iteration that exponentially decays with increasing overlap or decreasing diffusion for the singular perturbation problem in which the lowest order term dominates we consider many overlapping subregions with no special requirement on outflow or inflow boundaries our main result here which is valid for two variants of the classical schwarz algorithm shows that the error reduction factor per iteration decays exponentially in the maximum norm with increasing overlap and increasing dominance of the zeroth order term for both problems our proofs rely on the maximum principle and the construction of barrier functions

a regression model for time series of counts summary this paper discusses a model for regression analysis with a time series of counts correlation is assumed to arise from an unobservable process added to the linear predictor in a log linear model an estimating equation approach used for parameter estimation leads to an iterative weighted and filtered least squares algorithm asymptotic properties for the regression coefficients are presented we illustrate the technique with an analysis of trends in u s polio incidence since 1970

correlated binary regression with covariates specific to each binary observation regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates it is argued that binary response models that condition on some or all binary responses in a given block are useful for studying certain types of dependencies but not for the estimation of marginal response probabilities or pairwise correlations fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data hence a generalized estimating equation approach is advocated for inference on response probabilities and correlations illustrations involving both small and large block sizes are provided

a survey of model reduction by balanced truncation and some new results balanced truncation is one of the most common model reduction schemes in this note we present a survey of balancing related model reduction methods and their corresponding error norms and also introduce some new results five balancing methods are studied 1 lyapunov balancing 2 stochastic balancing 3 bounded real balancing 4 positive real balancing and 5 frequency weighted balancing for positive real balancing we introduce a multiplicative type error bound moreover for a certain subclass of positive real systems a modified positive real balancing scheme with an absolute error bound is proposed we also develop a new frequency weighted balanced reduction method with a simple bound on the error system based on the frequency domain representations of the system gramians two numerical examples are illustrated to verify the efficiency of the proposed methods

on the problem of permissible covariance and variogram models the covariance and variogram models ordinary or generalized are important statistical tools used in various estimation and simulation techniques which have been recently applied to diverse hydrologic problems for example the efficacy of kriging a method for interpolating filtering or averaging spatial phenomena depends to a large extent on the covariance or variogram model chosen the aim of this article is to provide the users of these techniques with convenient criteria that may help them to judge whether a function which arises in a particular problem and is not included among the known covariance or variogram models is permissible as such a model this is done by investigating the properties of the candidate model in both the space and frequency domains in the present article this investigation covers stationary random functions as well as intrinsic random functions i e nonstationary functions for which increments of some order are stationary then based on the theoretical results obtained a procedure is outlined and successfully applied to a number of candidate models in order to give to this procedure a more practical context we employ stereological equations that essentially transfer the investigations to one dimensional space together with approximations in terms of polygonal functions and fourier bessel series expansions there are many benefits and applications of such a procedure polygonal models can be fit arbitrarily closely to the data also the approximation of a particular model in the frequency domain by a fourier bessel series expansion can be very effective this is shown by theory and by example

geometry related convergence results for domain decomposition algorithms for general second order elliptic partial differential equations the schwarz alternating procedure is proved to converge at a rate independent of the aspect ratio for l shaped t shaped and c shaped domains these results cover both continuous and discrete versions of the schwarz algorithm moreover they apply to the nonoverlapping schur complement algorithms with the preconditioner proposed in chan siam j numer anal 24 1987 pp 382 390 in particular it is shown that the condition number of the preconditioned interface operator is bounded by 2 for all l shaped and t shaped domains this improves similar geometry independent convergence results for the schur complement algorithms obtained previously by chan and resasco advances in computer methods for partial differential equations vi r vichnevetsky and r s stepleman eds pp 317 322

estimating equations for spatially correlated data in multi dimensional space summary we use the quasilikelihood concept to propose an estimating equation for spatial data with correlation across the study region in a multi dimensional space with appropriate mixing con ditions we develop a central limit theorem for a random field under various lp metrics the consistency and asymptotic normality of quasilikelihood estimators can then be derived we also conduct simulations to evaluate the performance of the proposed estimating equation and a dataset from east lansing woods is used to illustrate the method

convergence estimates for product iterative methods with applications to domain decomposition in this paper we consider iterative methods for the solution of symmetric positive definite problems on a space which are defined in terms of products of operators defined with respect to a number of subspaces the simplest algorithm of this sort has an error reducing operator which is the product of orthogonal projections onto the complement of the subspaces new normreduction estimates for these iterative techniques will be presented in an abstract setting applications are given for overlapping schwarz algorithms with many subregions for finite element approximation of second order elliptic problems

convergence analysis of the schwarz algorithm and multilevel decomposition iterative methods ii nonselfadjoint and indefinite elliptic problems convergence estimate for the schwarz alternating algorithm applied to nonselfadjoint and indefinite elliptic problems is established for a certain overlapping domain decomposition multilevel iterative algorithms are proposed and analyzed for the finite element method for the same problem with locally refined grids the author shows that the algorithm based on the hierarchical basis decomposition converges with rate bounded by 1 cj 2 where j is the number of levels the author also analyzes the algorithm based on the full multigrid decomposition and shows that the algorithm converges with rate 1 cj 1 for problems of any dimension all the results are established without regularity assumption for the differential equation

a schwarz alternating procedure for singular perturbation problems we show that the schwarz alternating procedure offers a good algorithm for the numerical solution of singular perturbation problems provided the domain decomposition is properly designed to resolve the boundary and transition layers we give sharp estimates for the optimal position of the domain boundaries and study the convergence rates of the algorithm for various linear second order singular perturbation problems we report on implementation results for a turning point problem and a combustion problem

correlation structure and variable selection in generalized estimating equations via composite likelihood information criteria the method of generalized estimating equations gee is popular in the biostatistics literature for analyzing longitudinal binary and count data it assumes a generalized linear model for the outcome variable and a working correlation among repeated measurements in this paper we introduce a viable competitor the weighted scores method for generalized linear model margins we weight the univariate score equations using a working discretized multivariate normal model that is a proper multivariate model because the weighted scores method is a parametric method based on likelihood we propose composite likelihood information criteria as an intermediate step for model selection the same criteria can be used for both correlation structure and variable selection simulations studies and the application example show that our method outperforms other existing model selection methods in gee from the example it can be seen that our methods not only improve on gee in terms of interpretability and efficiency but also can change the inferential conclusions with respect to gee copyright 2016 john wiley sons ltd

control of combustion oscillations via h loop shaping µ analysis and integral quadratic constraints certain combustion processes are inherently unstable due to the coupling of the flame and the acoustic modes of the combustion chamber such instabilities lead to oscillating heat release and pressure which are undesirable a means to eliminate these oscillations is to design a controller to monitor the fluctuating pressure upstream and modulate the fuel injection accordingly making use of a recently developed nonlinear model for a premixed ducted flame we demonstrate in this paper advances in robust control can be used to methodically synthesize a controller and analyse the resulting closed loop system precisely h loop shaping is employed to obtain a controller and m analysis and integral quadratic constraints are applied to prove the closed loop stability of the nonlinear model open and closed loop simulations are also provided

maximum norm analysis of overlapping nonmatching grid discretizations of elliptic equations in this paper we provide a maximum norm analysis of a finite difference scheme defined on overlapping nonmatching grids for second order elliptic equations we consider a domain which is the union of p overlapping subdomains where each subdomain has its own independently generated grid the grid points on the subdomain boundaries need not match the grid points from adjacent subdomains to obtain a global finite difference discretization of the elliptic problem we employ standard stable finite difference discretizations within each of the overlapping subdomains and the different subproblems are coupled by enforcing continuity of the solutions across the boundary of each subdomain by interpolating the discrete solution on adjacent subdomains if the subdomain finite difference schemes satisfy a strong discrete maximum principle and if the overlap is sufficiently large we show that the global discretization converges in optimal order corresponding to the largest truncation errors of the local interpolation maps and discretizations our discretization scheme and the corresponding theory allows any combination of lower order and higher order finite difference schemes in different subdomains we describe also how the resulting linear system can be solved iteratively by a parallel schwarz alternating method or a schwarz preconditioned krylov subspace iterative method several numerical results are included to support the theory

efficient pairwise composite likelihood estimation for spatial clustered data spatial clustered data refer to high dimensional correlated measurements collected from units or subjects that are spatially clustered such data arise frequently from studies in social and health sciences we propose a unified modeling framework termed as geocopula to characterize both large scale variation and small scale variation for various data types including continuous data binary data and count data as special cases to overcome challenges in the estimation and inference for the model parameters we propose an efficient composite likelihood approach in that the estimation efficiency is resulted from a construction of over identified joint composite estimating equations consequently the statistical theory for the proposed estimation is developed by extending the classical theory of the generalized method of moments a clear advantage of the proposed estimation method is the computation feasibility we conduct several simulation studies to assess the performance of the proposed models and estimation methods for both gaussian and binary spatial clustered data results show a clear improvement on estimation efficiency over the conventional composite likelihood method an illustrative data example is included to motivate and demonstrate the proposed method

a brief survey on numerical methods for solving singularly perturbed problems in the present paper a brief survey on computational techniques for the different classes of singularly perturbed problems is given this survey is a continuation of work performed earlier by the first author and contains the literature of the work done by the researchers during the years 2000 2009 however some older important relevant papers are also included in this survey we also mentioned those papers which are not surveyed in the previous survey papers by the first author of this paper see appl math comput 30 1989 223 259 130 2002 457 510 134 2003 371 429 for details thus this survey paper contains a surprisingly large amount of literature on singularly perturbed problems and indeed can serve as an introduction to some of the ideas and methods for the singular perturbation problems

schwarz alternating algorithms for a convection diffusion problem abstract this paper deals with iterative domain decomposition algorithms for solving a singularly perturbed convection diffusion problem the algorithms are based on schwarz alternating procedure applied to a discrete approximations of the continuous problem convergence properties of the algorithms are established and their parallel implementations are discussed numerical results for a test singularly perturbed problem are presented

a generalized estimating equations approach for spatially correlated binary data applications to the analysis of neuroimaging data this paper proposes a generalized estimating equations approach for the analysis of spatially correlated binary data when there are large numbers of spatially correlated observations on a moderate number of subjects this approach is useful when the scientific focus is on modeling the marginal mean structure proper modeling of the spatial correlation structure is shown to provide large efficiency gains along with precise standard error estimates for inference on mean structure parameters generalized estimating equations for estimating the parameters of both the mean and spatial correlation structure are proposed the use of semivariogram models for parameterizing the correlation structure is discussed and estimation of the sample semivariogram is proposed as a technique for choosing parametric models and starting values for generalized estimating equations estimation the methodology is illustrated with neuroimaging data collected as part of the national institute of neurological disorders and stroke ninds stroke data bank a simulation study demonstrates the importance of accurate modeling of the spatial correlation structure in data with large numbers of spatially correlated observations such as those found in neuroimaging studies

schwarz methods of neumann neumann type for three dimensional elliptic finite element problems several domain decomposition methods of neumann neumann type are considered for solving the large linear systems of algebraic equations that arise from discretizations of elliptic problems by finite elements we will only consider problems in three dimensions several new variants of the basic algorithm are introduced in a schwarz method framework that provides tools which have already proven very useful in the design and analysis of other domain decomposition and multi level methods the neumann neumann algorithms have several advantages over other domain decomposition methods the subregions which define the subproblems only share the boundary degrees of freedom with their neighbors the subregions can also be of quite arbitrary shape and many of the major components of the preconditioner can be constructed from subprograms available in standard finite element program libraries in its original form however the algorithm lacks a mechanism for global transportation of information and its performance therefore suffers when the number of subregions increases in the new variants of the algorithms considered in this paper the preconditioners include global components of low rank to overcome this difficulty bounds are established for the condition number of the iteration operator which are independent of the number of subregions and depend only polylogarithmically on the number of degrees of freedom of individual local subproblems results are also given for problems with arbitrarily large jumps in the coefficients across the interfaces separating the subregions 1995 john wiley sons inc

semiparametric time varying coefficient model for matched case crossover studies in matched case crossover studies it is generally accepted that the covariates on which a case and associated controls are matched cannot exert a confounding effect on independent predictors included in the conditional logistic regression model this is because any stratum effect is removed by the conditioning on the fixed number of sets of the case and controls in the stratum hence the conditional logistic regression model is not able to detect any effects associated with the matching covariates by stratum however some matching covariates such as time often play an important role as an effect modification leading to incorrect statistical estimation and prediction therefore we propose three approaches to evaluate effect modification by time the first is a parametric approach the second is a semiparametric penalized approach and the third is a semiparametric bayesian approach our parametric approach is a two stage method which uses conditional logistic regression in the first stage and then estimates polynomial regression in the second stage our semiparametric penalized and bayesian approaches are one stage approaches developed by using regression splines our semiparametric one stage approach allows us to not only detect the parametric relationship between the predictor and binary outcomes but also evaluate nonparametric relationships between the predictor and time we demonstrate the advantage of our semiparametric one stage approaches using both a simulation study and an epidemiological example of a 1 4 bi directional case crossover study of childhood aseptic meningitis with drinking water turbidity we also provide statistical inference for the semiparametric bayesian approach using bayes factors copyright 2016 john wiley sons ltd

the one dimensional acoustic field in a duct with arbitrary mean axial temperature gradient and mean flow abstract this paper presents an analytical solution for the one dimensional acoustic field in a duct with arbitrary mean temperature gradient and mean flow a wave equation for the pressure perturbation is derived which relies on very few assumptions an analytical solution for this is derived using an adapted wkb approximation the solution is a superposition of waves travelling in either direction and thus provides physical insight it is also very easy to calculate the proposed solution is applied to ducts with a mean temperature profile which varies axially with i a linear and ii a partial sine wave profile predictions are compared to those obtained by numerically solving the linearised euler equations lees the analytical solution reproduces the acoustic field very accurately across a wide range of flow conditions which span both low and moderate to high subsonic mach numbers it always performs well when the frequency exceeds a certain value when the mean temperature profile is linear it also performs well to very low frequencies this increased frequency range for linear mean temperature profiles leads to its application to more complicated profiles in a piecewise linear manner axially segmenting the temperature profile into regions that can be approximated as linear the acoustic field is predicted very accurately as long as enough segmentation points are used and the condition for the linear mean temperature profile is satisfied k 0 where k0 is the local wave number when there is no mean flow and is the normalised mean density gradient the proposed solution is extensively compared to previous analytical solutions and is found to be more accurate and reliable especially at higher mach numbers the entropy wave generated by communication between the acoustic waves and the distributed mean temperature zone is calculated using the lees it is found to remain very small across all operating conditions such that both the entropy wave and its impact on the acoustic field can be neglected

overlapping additive and multiplicative schwarz iterations for h matrices abstract in recent years an algebraic framework was introduced for the analysis of convergence of schwarz methods for the solution of linear systems of the form ax b within this framework additive and multiplicative schwarz were shown to converge when the coefficient matrix a is a nonsingular m matrix or a symmetric positive definite matrix in this paper many of these results are extended to the case of a being an h matrix the case of inexact local solves is also considered in addition the two level scheme is studied i e when a coarse grid correction is used in conjunction with the additive or the multiplicative schwarz iterations

singularly perturbed problems in partial differential equations a survey this survey paper contains a surprisingly large amount of material on singularly perturbed partial differential equations and indeed can serve as an introduction to some of the ideas and methods of the singular perturbation theory starting from prandtl s work a large amount of work has been done in the area of singular perturbations this paper limits its coverage to some standard singular perturbation models considered by various workers and the methods developed by numerous researchers after 1980 2000 in this review we have covered singularly perturbed partial differential equations about odes the survey has already been done by us see m k kadalbajoo k c patidar appl math comput 130 2002 457 510

parallel schwarz methods for convection dominated semilinear diffusion problems parallel two level schwarz methods are proposed for the numerical solution of convection diffusion problems with the emphasis on convection dominated problems two variants of the methodology are investigated they differ from each other by the type of boundary conditions dirichlet or neumann type posed on a part of the second level subdomain interfaces convergence properties of the two level schwarz methods are experimentally compared with those of a variant of the standard multi domain schwarz alternating method numerical experiments performed on a distributed memory multiprocessor computer illustrate parallel efficiency of the methods

models for longitudinal data a generalized estimating equation approach this article discusses extensions of generalized linear models for the analysis of longitudinal data two approaches are considered subject specific ss models in which heterogeneity in regression parameters is explicitly modelled and population averaged pa models in which the aggregate response for the population is the focus we use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes when the subject specific parameters are assumed to follow a gaussian distribution simple relationships between the pa and ss parameters are available the methods are illustrated with an analysis of data on mother s smoking and children s respiratory disease

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

unbiased estimating equations from working correlation models for irregularly timed repeated measures the method of generalized estimating equations gees has been criticized recently for a failure to protect against misspecification of working correlation models which in some cases leads to loss of efficiency or infeasibility of solutions however the feasibility and efficiency of gee methods can be enhanced considerably by using flexible families of working correlation models we propose two ways of constructing unbiased estimating equations from general correlation models for irregularly timed repeated measures to supplement and enhance gee the supplementary estimating equations are obtained by differentiation of the cholesky decomposition of the working correlation or as score equations for decoupled gaussian pseudolikelihood the estimating equations are solved with computational effort equivalent to that required for a first order gee full details and analytic expressions are developed for a generalized markovian model that was evaluated through simulation large sample sandwich standard errors for working correlation parameter estimates are derived and shown to have good performance the proposed estimating functions are further illustrated in an analysis of repeated measures of pulmonary function in children

domain decomposition for a singularly perturbed parabolic problem with a convection dominated term this paper deals with an iterative algorithm for domain decomposition applied to the solution of a singularly perturbed parabolic problem with a convection dominated term convergence properties of the algorithm are established numerical results are presented

analysis of binary spatial data by quasi likelihood estimating equations the goal of this paper is to describe the application of quasi likelihood estimating equations for spatially correlated binary data in this paper a logistic function is used to model the marginal probability of binary responses in terms of parameters of interest with mild assumptions on the correlations the leonov shiryaev formula combined with a comparison of characteristic functions can be used to establish asymptotic normality for linear combinations of the binary responses the consistency and asymptotic normality for quasi likelihood estimates can then be derived by modeling spatial correlation with a variogram we apply these asymptotic results to test independence of two spatially correlated binary outcomes and illustrate the concepts with a well known example based on data from lansing woods the comparison of generalized estimating equations and the proposed approach is also discussed

multivariate regression analyses for categorical data summary it is common to observe a vector of discrete and or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes the response vector can comprise repeated observations on one variable as in longitudinal studies or genetic studies of families or can include observations for different variables this paper discusses a class of models for the marginal expectations of each response and for pairwise associations the marginal models are contrasted with log linear models two generalized estimating equation approaches are compared for parameter estimation the first focuses on the regression parameters the second simultaneously estimates the regression and association parameters the robustness and efficiency of each is discussed the methods are illustrated with analyses of two data sets from public health research

iterative domain decomposition algorithms for a convection diffusion problem abstract this paper deals with iterative algorithms for domain decomposition applied to the solution of a singularly perturbed convection diffusion problem with regular boundary layers these algorithms are based on a finite difference domain decomposition approach and on a modified schwarz alternating method convergence properties of the algorithm are established and their parallel implementations are discussed numerical results for a test singularly perturbed problem are presented

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

a comparison of several approaches for choosing between working correlation structures in generalized estimating equation analysis of longitudinal binary data the method of generalized estimating equations gee models the association between the repeated observations on a subject with a patterned correlation matrix correct specification of the underlying structure is a potentially beneficial goal in terms of improving efficiency and enhancing scientific understanding we consider two sets of criteria that have previously been suggested respectively for selecting an appropriate working correlation structure and for ruling out a particular structure s in the gee analysis of longitudinal studies with binary outcomes the first selection criterion chooses the structure for which the model based and the sandwich based estimator of the covariance matrix of the regression parameter estimator are closest while the second selection criterion chooses the structure that minimizes the weighted error sum of squares the rule out criterion deselects structures for which the estimated correlation parameter violates standard constraints for binary data that depend on the marginal means in addition we remove structures from consideration if their estimated parameter values yield an estimated correlation structure that is not positive definite we investigate the performance of the two sets of criteria using both simulated and real data in the context of a longitudinal trial that compares two treatments for major depressive episode practical recommendations are also given on using these criteria to aid in the efficient selection of a working correlation structure in gee analysis of longitudinal binary data