hierarchical generalised linear models a synthesis of generalised linear models random effect models and structured dispersions summary hierarchical generalised linear models are developed as a synthesis of generalised linear models mixed linear models and structured dispersions we generalise the restricted maximum likelihood method for the estimation of dispersion to the wider class and show how the joint fitting of models for mean and dispersion can be expressed by two interconnected generalised linear models the method allows models with i any combination of a generalised linear model distribution for the response with any conjugate distribution for the random effects ii structured dispersion components iii different link and variance functions for the fixed and random effects and iv the use of quasilikelihoods in place of likelihoods for either or both of the mean and dispersion models inferences can be made by applying standard procedures in particular those for model checking to components of either generalised linear model we also show by numerical studies that the new method gives an efficient estimation procedure for substantial class of models of practical importance likelihood type inference is extended to this wide class of models in a unified way

direct updating of damping and stiffness matrices this note has outlined an extension to the available direct methods of model updating to estimate both the damping and stiffness matrices of a structure the method minimizes the change in the damping and stiffness matrices with the constraint that the measured modal data is reproduced

sample size calculation for clinical trials with correlated count measurements based on the negative binomial distribution statistical inference based on correlated count measurements are frequently performed in biomedical studies most of existing sample size calculation methods for count outcomes are developed under the poisson model deviation from the poisson assumption equality of mean and variance has been widely documented in practice which indicates urgent needs of sample size methods with more realistic assumptions to ensure valid experimental design in this study we investigate sample size calculation for clinical trials with correlated count measurements based on the negative binomial distribution this approach is flexible to accommodate overdispersion and unequal measurement intervals as well as arbitrary randomization ratios missing data patterns and correlation structures importantly the derived sample size formulas have closed forms both for the comparison of slopes and for the comparison of time averaged responses which greatly reduces the burden of implementation in practice we conducted extensive simulation to demonstrate that the proposed method maintains the nominal levels of power and type i error over a wide range of design configurations we illustrate the application of this approach using a real epileptic trial

numerical simulation of three dimensional nonlinear water waves we present an accurate and efficient numerical model for the simulation of fully nonlinear non breaking three dimensional surface water waves on infinite or finite depth as an extension of the work of craig and sulem 19 the numerical method is based on the reduction of the problem to a lower dimensional hamiltonian system involving surface quantities alone this is accomplished by introducing the dirichlet neumann operator which is described in terms of its taylor series expansion in homogeneous powers of the surface elevation each term in this taylor series can be computed efficiently using the fast fourier transform an important contribution of this paper is the development and implementation of a symplectic implicit scheme for the time integration of the hamiltonian equations of motion as well as detailed numerical tests on the convergence of the dirichlet neumann operator the performance of the model is illustrated by simulating the long time evolution of two dimensional steadily progressing waves as well as the development of three dimensional short crested nonlinear waves both in deep and shallow water

gibbs sampling for bayesian non conjugate and hierarchical models by using auxiliary variables summary we demonstrate the use of auxiliary or latent variables for sampling non standard densities which arise in the context of the bayesian analysis of non conjugate and hierarchical models by using a gibbs sampler their strategic use can result in a gibbs sampler having easily sampled full conditionals we propose such a procedure to simplify or speed up the markov chain monte carlo algorithm the strength of this approach lies in its generality and its ease of implementation the aim of the paper therefore is to provide an alternative sampling algorithm to rejection based methods and other sampling approaches such as the metropolis hastings algorithm

correcting for nonavailability bias in surveys by weighting based on number of callbacks abstract when respondents to sample surveys differ from nonrespondents bias can result nonresponse is produced by both refusal and nonavailability here we concentrate on nonavailability clever weighting schemes to deal with nonavailability bias were proposed about 40 years ago by politz and simmons and by simmons but further theoretical development has been limited in the meantime not only have in person surveys continued to flourish but telephone surveys also have become common herein we present weighting techniques that correct for nonavailability bias yet avoid limitations of earlier methods the weights which depend on parameters are based on the number of callbacks needed to obtain the interview from the sample member and usually increase with the number of callbacks if a sample design generated sample weights that are not all the same those external weights are easily incorporated into the analysis we assume a beta distribution for p the probability or proportion of time that a sampl

gibbs sampling methods for stick breaking priors a rich and flexible class of random probability measures which we call stick breaking priors can be constructed using a sequence of independent beta random variables examples of random measures that have this characterization include the dirichlet process its two parameter extension the two parameter poisson dirichlet process finite dimensional dirichlet priors and beta two parameter processes the rich nature of stick breaking priors offers bayesians a useful class of priors for nonparametric problems while the similar construction used in each prior can be exploited to develop a general computational procedure for fitting them in this article we present two general types of gibbs samplers that can be used to fit posteriors of bayesian hierarchical models based on stick breaking priors the first type of gibbs sampler referred to as a polya urn gibbs sampler is a generalized version of a widely used gibbs sampling method currently employed for dirichlet process computing this method applies t

new methods for finite element model updating problems we consider two finite element model updating problems which incorporate the measured modal data into the analytical finite element model producing an adjusted model on the mass damping and stiffness that closely matches the experimental modal data we develop two efficient numerical algorithms for solving these problems the new algorithms are direct methods that require o nk2 and o nk2 k6 flops respectively and employ sparse matrix techniques when the analytic model is sparse here n is the dimension of the coefficient matrices defining the analytical model and k is the number of measured eigenpairs

combined hybridizable discontinuous galerkin hdg and runge kutta discontinuous galerkin rk dg formulations for green naghdi equations on unstructured meshes abstract in this paper we introduce some new high order discrete formulations on general unstructured meshes especially designed for the study of irrotational free surface flows based on partial differential equations belonging to the family of fully nonlinear and weakly dispersive shallow water equations working with a recent family of optimized asymptotically equivalent equations we benefit from the simplified analytical structure of the linear dispersive operators to conveniently reformulate the models as the classical nonlinear shallow water equations supplemented with several algebraic source terms which globally account for the non hydrostatic effects through the introduction of auxiliary coupling variables high order discrete approximations of the main flow variables are obtained with a rk dg method while the trace of the auxiliary variables are approximated on the mesh skeleton through the resolution of second order linear elliptic sub problems with high order hdg formulations the combined use of hybrid unknowns and local post processing significantly helps to reduce the number of globally coupled unknowns in comparison with previous approaches the proposed formulation is then extended to a more complex family of three parameters enhanced green naghdi equations the resulting numerical models are validated through several benchmarks involving nonlinear waves transformations and propagation over varying topographies showing good convergence properties and very good agreements with several sets of experimental data

a high order spectral method for nonlinear water waves over moving bottom topography we present a numerical method for simulations of nonlinear surface water waves over variable bathymetry it is applicable to either two or three dimensional flows as well as to either static or moving bottom topography the method is based on the reduction of the problem to a lower dimensional hamiltonian system involving boundary quantities alone a key component of this formulation is the dirichlet neumann operator which in light of its joint analyticity properties with respect to surface and bottom deformations is computed using its taylor series representation we present new stabilized forms for the taylor terms each of which is efficiently computed by a pseudospectral method using the fast fourier transform physically relevant applications are displayed to illustrate the performance of the method comparisons with analytical solutions and laboratory experiments are provided

quadratic model updating with no spill over and incomplete measured data existence and computation of solution abstract quadratic finite element model updating problem qfemup to be studied in this paper is concerned with updating a symmetric nonsingular quadratic pencil in such a way that a small set of measured eigenvalues and eigenvectors is reproduced by the updated model if in addition the updated model preserves the large number of unupdated eigenpairs of the original model the model is said to be updated with no spill over qfemup is in general a difficult and computationally challenging problem due to the practical constraint that only a very small number of eigenvalues and eigenvectors of the associated quadratic eigenvalue problem are available from computation or measurement additionally for practical effectiveness engineering concerns such as nonorthogonality and incompleteness of the measured eigenvectors must be considered most of the existing methods including those used in industrial settings deal with updating a linear model only ignoring damping only in the last few years a small number of papers been published on the quadratic model updating several of the above issues have been dealt with both from theoretical and computational point of views however mathematical criterion for existence of solution has not been fully developed in this paper we first i prove a set of necessary and sufficient conditions for the existence of a solution of the no spill over qfemup then ii present a parametric representation of the solution assuming a solution exists and finally iii propose an algorithm for qfemup with no spill over and incomplete measured eigenvectors interestingly it is shown that the parametric representation can be constructed with the knowledge of only the few eigenvalues and eigenvectors that are to be updated and the corresponding measured eigenvalues and eigenvectors complete knowledge of eigenvalues and eigenvectors of the original pencil is not needed which makes the solution readily applicable to real life structures

robust inference in the negative binomial regression model with an application to falls data summary a popular way to model overdispersed count data such as the number of falls reported during intervention studies is by means of the negative binomial nb distribution classical estimating methods are well known to be sensitive to model misspecifications taking the form of patients falling much more than expected in such intervention studies where the nb regression model is used we extend in this article two approaches for building robust m estimators of the regression parameters in the class of generalized linear models to the nb distribution the first approach achieves robustness in the response by applying a bounded function on the pearson residuals arising in the maximum likelihood estimating equations while the second approach achieves robustness by bounding the unscaled deviance components for both approaches we explore different choices for the bounding functions through a unified notation we show how close these approaches may actually be as long as the bounding functions are chosen and tuned appropriately and provide the asymptotic distributions of the resulting estimators moreover we introduce a robust weighted maximum likelihood estimator for the overdispersion parameter specific to the nb distribution simulations under various settings show that redescending bounding functions yield estimates with smaller biases under contamination while keeping high efficiency at the assumed model and this for both approaches we present an application to a recent randomized controlled trial measuring the effectiveness of an exercise program at reducing the number of falls among people suffering from parkinsons disease to illustrate the diagnostic use of such robust procedures and their need for reliable inference

estimation of the negative binomial parameter κ by maximum quasi likelihood we investigate estimation of the parameter k of the negative binomial distribution for small samples using a method of moments estimate mme and a maximum quasi likelihood estimate mqle previous work is reviewed the importance of indirect estimation of k through its reciprocal a and of allowance for negative estimates of k or a are discussed samples of size 50 are simulated 10 000 times for each of several parameter combinations to examine the properties of the estimates samples of sizes 10 20 30 and 50 are simulated 1 000 times to investigate the effect of sample size both estimators perform reasonably well except when the mean is small and the sample size does not exceed 20 three examples are given one of a designed experiment for which the mqle is especially suited confidence limits are derived for the mqle further work along these lines is required for adequate assessment of the usual maximum likelihood estimate

arbitrary order exactly divergence free central discontinuous galerkin methods for ideal mhd equations ideal magnetohydrodynamic mhd equations consist of a set of nonlinear hyperbolic conservation laws with a divergence free constraint on the magnetic field neglecting this constraint in the design of computational methods may lead to numerical instability or nonphysical features in solutions in our recent work f li l xu s yakovlev central discontinuous galerkin methods for ideal mhd equations with the exactly divergence free magnetic field journal of computational physics 230 2011 4828 4847 second and third order exactly divergence free central discontinuous galerkin methods were proposed for ideal mhd equations in this paper we further develop such methods with higher order accuracy the novelty here is that the well established h div conforming finite element spaces are used in the constrained transport type framework and the magnetic induction equations are extensively explored in order to extract sufficient information to uniquely reconstruct an exactly divergence free magnetic field the overall algorithm is local and it can be of arbitrary order of accuracy numerical examples are presented to demonstrate the performance of the proposed methods especially when they are fourth order accurate

tests of hypotheses in overdispersed poisson regression and other quasi likelihood models abstract test statistics for evaluating the significance of added variables in a regression equation are developed for mixed poisson models where the structural parameter that determines the mean variance relationship var 2 is estimated by the method of moments and the regression coefficients are estimated by quasi likelihood the formulas presented for test statistics and related estimating equations are applicable generally to quasi likelihood models specified by an arbitrary mean value function x together with a variance function v that contains one or more unknown parameters two versions of the wald and score tests are investigated one calculated from the usual model based covariance matrix whose validity depends on correct specification of the variance function and another using an empirical covariance matrix that has a more general asymptotic justification monte carlo simulations demonstrate that the quasi likelihood method of moments ql m procedures yield ap

a modified pseudolikelihood approach for analysis of longitudinal data we consider the analysis of longitudinal data when the covariance function is modeled by additional parameters to the mean parameters in general inconsistent estimators of the covariance variance correlation parameters will be produced when the working correlation matrix is misspecified which may result in great loss of efficiency of the mean parameter estimators albeit the consistency is preserved we consider using different working correlation models for the variance and the mean parameters in particular we find that an independence working model should be used for estimating the variance parameters to ensure their consistency in case the correlation structure is misspecified the designated working correlation matrices should be used for estimating the mean and the correlation parameters to attain high efficiency for estimating the mean parameters simulation studies indicate that the proposed algorithm performs very well we also applied different estimation procedures to a data set from a clinical trial for illustration

analysis of one way layout of count data with negative binomial variation on derive deux statistiques c neyman 1959 pour tester l egalite des moyennes de plusieurs groupes de donnees de comptage en presence d un parametre de dispersion commun on compare leurs performances avec celles de la statistique du rapport de vraisemblance et de deux autres statistiques basees sur des donnees transformees anscombe 1948

combinatorial clustering and the beta negative binomial process we develop a bayesian nonparametric approach to a general family of latent class problems in which individuals can belong simultaneously to multiple classes and where each class can be exhibited multiple times by an individual we introduce a combinatorial stochastic process known as the negative binomial process rm nbp as an infinite dimensional prior appropriate for such problems we show that the rm nbp is conjugate to the beta process and we characterize the posterior distribution under the beta negative binomial process rm bnbp and hierarchical models based on the rm bnbp the rm hbnbp we study the asymptotic properties of the rm bnbp and develop a three parameter extension of the rm bnbp that exhibits power law behavior we derive mcmc algorithms for posterior inference under the rm hbnbp and we present experiments using these algorithms in the domains of image segmentation object recognition and document analysis

hierarchical generalized linear models we consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models the distribution of these components is not restricted to be normal this allows a broader class of models which includes generalized linear mixed models we use a generalization of henderson s joint likelihood called a hierarchical or h likelihood for inferences from hierarchical generalized linear models this avoids the integration that is necessary when marginal likelihood is used under appropriate conditions maximizing the h likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors an adjusted profile h likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components a scaled deviance test for the goodness of fit a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed the ideas of quasi likelihood and extended quasi likelihood are generalized to the new class we give examples of the poisson gamma binomial beta and gamma inverse gamma hierarchical generalized linear models a resolution is proposed for the apparent difference between population averaged and subject specific models a unified framework is provided for viewing and extending many existing methods

nonparametric bayes estimators based on beta processes in models for life history data the article studies the problem of finding bayes estimators for cumulative hazard rates and related quantities w r t prior distributions that correspond to cumulative hazard rate processes with nonnegative independent increments a particular class of prior processes termed beta processes is introduced and is shown to constitute a conjugate class an important bonus of the approach based on cumulative hazards is that more complicated models for life history data than the simple life table situation can be treated for example time inhomogeneous markov chains we find posterior distributions and derive bayes estimators in such models and present a semiparametric bayesian analysis of the cox regression model

analysis of two way layout of count data involving multiple counts in each cell abstract multiple counts may occur in each cell of an a b two way layout balanced or unbalanced of two fixed factors a and b standard log linear model analysis based on a poisson distribution assumption of the cell counts is not applicable here because of the unbalanced nature of the table or because the poisson distribution assumption is not valid we develop c tests for interaction and main effects assuming data to be poisson distributed and also assuming that data within the cells have extra over under dispersion beyond that explained by a poisson distribution for this we consider an extended negative binominal distribution and a semiparametric model using the quasi likelihood we show that in all situations the c tests for interaction are of very simple forms for c tests for the main effect in presence of no interaction such simplification is possible only under certain conditions a score test for detecting extra dispersion in presence of interaction is also obtained and is of sim

a pseudo spectral algorithm and test cases for the numerical solution of the two dimensional rotating green naghdi shallow water equations a pseudo spectral algorithm is presented for the solution of the rotating green naghdi shallow water equations in two spatial dimensions the equations are first written in vorticity divergence form in order to exploit the fact that time derivatives then appear implicitly in the divergence equation only a nonlinear equation must then be solved at each time step in order to determine the divergence tendency the nonlinear equation is solved by means of a simultaneous iteration in spectral space to determine each fourier component the key to the rapid convergence of the iteration is the use of a good initial guess for the divergence tendency which is obtained from polynomial extrapolation of the solution obtained at previous time levels the algorithm is therefore best suited to be used with a standard multi step time stepping scheme e g leap frog two test cases are presented to validate the algorithm for initial value problems on a square periodic domain the first test is to verify cnoidal wave speeds in one dimension against analytical results the second test is to ensure that the miles salmon potential vorticity is advected as a parcel wise conserved tracer throughout the nonlinear evolution of a perturbed jet subject to shear instability the algorithm is demonstrated to perform well in each test the resulting numerical model is expected to be of use in identifying paradigmatic behavior in mesoscale flows in the atmosphere and ocean in which both vortical nonlinear and dispersive effects are important

analysis of a discontinuous galerkin method for the biot s consolidation problem in this paper a fully discrete stabilized discontinuous galerkin method is proposed to solve the biot s consolidation problem the existence and uniqueness of the finite element solution are obtained the stability of the fully discrete solution is discussed the corresponding error estimates for the approximation of displacement and pressure in a mesh dependent norm are obtained the error estimate for the approximation of pressure in l 2 norm is also obtained

on linear and quadratic estimating functions summary in some cases maximum quasi likelihood estimation which is at the core of glim can fail to give reasonable results a more general class of estimating functions is investigated which avoids such failure and also is not restricted to the particular forms of mean and variance function of glim

a conditional likelihood approach to residual maximum likelihood estimation in generalized linear models summary residual maximum likelihood reml estimation is often preferred to maximum likelihood estimation as a method of estimating covariance parameters in linear models because it takes account of the loss of degrees of freedom in estimating the mean and produces unbiased estimating equations for the variance parameters in this paper it is shown that reml has an exact conditional likelihood interpretation where the conditioning is on an appropriate sufficient statistic to remove dependence on the nuisance parameters this interpretation clarifies the motivation for reml and generalizes directly to non normal models in which there is a low dimensional sufficient statistic for the fitted values the conditional likelihood is shown to be well defined and to satisfy the properties of a likelihood function even though this is not generally true when conditioning on statistics which depend on parameters of interest using the conditional likelihood representation the concept of reml is extended to generalized linear models with varying dispersion and canonical link explicit calculation of the conditional likelihood is given for the one way lay out a saddlepoint approximation for the conditional likelihood is also derived

estimation for zero inflated over dispersed count data model with missing response in this paper we develop estimation procedure for the parameters of a zero inflated over dispersed under dispersed count model in the presence of missing responses in particular we deal with a zero inflated extended negative binomial model in the presence of missing responses a weighted expectation maximization algorithm is used for the maximum likelihood estimation of the parameters involved some simulations are conducted to study the properties of the estimators robustness of the procedure is shown when count data follow other over dispersed models such as the log normal mixture of the poisson distribution or even from a zero inflated poisson model an illustrative example and a discussion leading to some conclusions are given copyright 2016 john wiley sons ltd

a discontinuous galerkin method for wave propagation in orthotropic poroelastic media with memory terms abstract poroelastic materials play an important role in biomechanical and geophysical research in this paper we investigate wave propagation in orthotropic poroelastic media by studying the time domain poroelastic wave equations both the low frequency biot s lf biot equations and the biot johnson koplik dashen biot jkd model are considered in lf biot equations the dissipation terms are proportional to the relative velocity between the fluid and the solid by a constant contrast to this the dissipation terms in the biot jkd model are in the form of time convolution memory as a result of the frequency dependence of fluid solid interaction at the underlying microscopic scale in the frequency domain the dynamic tortuosity and permeability described by darcy s law are two crucial factors in this problem and highly linked to the viscous force in the biot model the key difficulty is to handle the viscous term when the pore fluid is viscous in the biot jkd model the convolution operator involves order 1 2 shifted fractional derivatives in the time domain which is challenging to discretize in this work a new method of the multipoint pade or rational approximation for stieltjes function is applied to approximate the jkd dynamic tortuosity and then an augmented system of biot jkd model is obtained where the kernel of the memory term is replaced by the finite auxiliary variables satisfying a local system of ordinary differential equations the runge kutta discontinuous galerkin rkdg method with the un splitting method is used to compute the numerical solution and numerical examples are presented to demonstrate the high order accuracy and stability of the method compared with the existing approaches for solving the biot jkd equations the augmented system presented here require neither the storage of solution history nor the computation of the flux of the auxiliary variables

extended generalized estimating equations for clustered data abstract typically analysis of data consisting of multiple observations on a cluster is complicated by within cluster correlation estimating equations for generalized linear modeling of clustered data have recently received much attention this article proposes an extension to the generalized estimating equation method proposed by liang and zeger which treats within cluster correlations as nuisance parameters using ideas from extended quasi likelihood estimating equations for regression and association parameters are provided simultaneously the resulting estimators are proven to be asymptotically normal and consistent under certain conditions the consistency of regression estimators allows incorrect modeling of the correlation among repeated responses the method is illustrated with an analysis of data from a developmental toxicity study

interval estimation of the over dispersion parameter in the analysis of one way layout of count data the over dispersion parameter is an important and versatile measure in the analysis of one way layout of count data in biological studies for example it is commonly used as an inverse measure of aggregation in biological count data its estimation from finite data sets is a recognized challenge many simulation studies have examined the bias and efficiency of different estimators of the over dispersion parameter for finite data sets see for example clark and perry biometrics 1989 45 309 316 and piegorsch biometrics 1990 46 863 867 but little attention has been paid to the accuracy of the confidence intervals cis of it in this paper we first derive asymptotic procedures for the construction of confidence limits for the over dispersion parameter using four estimators that are specified by only the first two moments of the counts we also obtain closed form asymptotic variance formulae for these four estimators in addition we consider the asymptotic ci based on the maximum likelihood ml estimator using the negative binomial model it appears from the simulation results that the asymptotic cis based on these five estimators have coverage below the nominal coverage probability to remedy this we also study the properties of the asymptotic cis based on the restricted estimates of ml extended quasi likelihood and double extended quasi likelihood by eliminating the nuisance parameter effect using their adjusted profile likelihood and quasi likelihoods it is shown that these cis outperform the competitors by providing coverage levels close to nominal over a wide range of parameter combinations two examples to biological count data are presented copyright 2010 john wiley sons ltd

residuals in generalized linear models abstract generalized linear models are regression type models for data not normally distributed appropriately fitted by maximum likelihood rather than least squares typical examples are models for binomial or poisson data with a linear regression model for a given ordinarily nonlinear function of the expected values of the observations use of such models has become very common in recent years and there is a clear need to study the issue of appropriate residuals to be used for diagnostic purposes several definitions of residuals are possible for generalized linear models the statistical package glim baker and nelder 1978 routinely prints out residuals where v is the function relating the variance to the mean of y and is the maximum likelihood estimate of the ith mean as fitted to the regression model these residuals are the signed square roots of the contributions to the pearson goodness of fit statistic another choice of residual is the signed square root of the contribution to the devia

econometric models for count data with an application to the patents r d relationship this paper focuses on developing and adapting statistical models of counts nonnegative integers in the context of panel data and using them to analyze the relationship between patents and r d expenditures since a variety of other economic data come in the form of repeated counts of some individual actions or events the methodology should have wide applications the statistical models we develop are applications and generalizations of the poisson distribution two important issues are i given the panel nature of our data how can we allow for separate persistent individual fixed or random effects ii how does one introduce the equivalent of disturbances in the equation into the analysis of poisson and other discrete probability functions the first problem is solved by conditioning on the total sum of outcomes over the observed years while the second problem is solved by introducing an additional source of randomness allowing the poisson parameter to be itself randomly distributed and compounding the two distributions lastly we develop a test statistic for the presence of serial correlation when fixed effects estimators are used in nonlinear conditional models

robust inference for generalized linear models by starting from a natural class of robust estimators for generalized linear models based on the notion of quasi likelihood we define robust deviances that can be used for stepwise model selection as in the classical framework we derive the asymptotic distribution of tests based on robust deviances and we investigate the stability of their asymptotic level under contamination the binomial and poisson models are treated in detail two applications to real data and a sensitivity analysis show that the inference obtained by means of the new techniques is more reliable than that obtained by classical estimation and testing procedures

bias corrected maximum likelihood estimator of the negative binomial dispersion parameter nous decrivons un estimateur du maximum de vraisemblance avec correction du premier ordre pour le biais sur le parametre de dispersion d une distribution binomiale negative cet estimateur est compare en terme debiais et d efficacite avec l estimateur du maximum de vraisemblance etudie par piegorsch 1990 biometrics 46 863 867 les estimateurs de moment et du maximum de quasi vraisemblance etendue de clark et perry 1989 biometrics 45 309 316 et un estimateur de double quasi vraisemblance etendue l estimateur du maximum de vraisemblance avec correction du biais a des proprietes de biais et d efficacite superieures dans la plupart des cas pour faciliter la comparaison nous donnons les resultats pour le modele binomial negatif a deux parametres cependant un exemple impliquant la regression binomiale negative est donne

testing for overdispersion in poisson and binomial regression models abstract in this article a method for obtaining tests for overdispersion with respect to a natural exponential family is derived the tests are designed to be powerful against arbitrary alternative mixture models where only the first two moments of the mixed distribution are specified various tests for extra poisson and extra binomial variation are obtained as special cases the use of a particular test may be motivated by a consideration of the mechanism through which the overdispersion may arise the common occurrence of extra poisson and extra binomial variation has been noted by several authors however the poisson and binomial models remain valid in many instances and because of their simplicity and appeal it is of real interest to ascertain when they apply this paper develops a unifying theory for testing for overdispersion and generalizes tests previously derived including those by fisher 1950 collings and margolin 1985 and prentice 1986 it also shows the pearson statistic to be a sc

a cdg fe method for the two dimensional green naghdi model with the enhanced dispersive property abstract in this work we investigate numerical solutions of the two dimensional shallow water wave using a fully nonlinear green naghdi model with an improved dispersive effect for numerics the green naghdi model is rewritten into a formulation coupling a pseudo conservative system and a set of pseudo elliptic equations since the pseudo conservative system is no longer hyperbolic and its riemann problem can only be approximately solved we consider the utilization of the central discontinuous galerkin method which possesses an important feature of the needlessness of riemann solvers meanwhile the stationary elliptic part will be solved using the finite element method both the well balanced and the positivity preserving features which are highly desirable in the simulation of the shallow water wave will be embedded into the proposed numerical scheme the accuracy and efficiency of the numerical model and method will be illustrated through numerical tests

a numerical scheme for the green naghdi model abstract in this paper a hybrid numerical method using a godunov type scheme is proposed to solve the green naghdi model describing dispersive shallow water waves the corresponding equations are rewritten in terms of new variables adapted for numerical studies in particular the numerical scheme preserves the dynamics of solitary waves some numerical results are shown and compared to exact and or experimental ones in different and significant configurations a dam break problem and an impact problem where a liquid cylinder is falling to a rigid wall are solved numerically this last configuration is also compared with experiments leading to a good qualitative agreement

estimating intraclass correlation for binary data summary this paper reviews many different estimators of intraclass correlation that have been proposed for binary data and compares them in an extensive simulation study some of the estimators are very specific while others result from general methods such as pseudo likelihood and extended quasi likelihood estimation the simulation study identifies several useful estimators one of which does not seem to have been considered previously for binary data estimators based on extended quasi likelihood are found to have a substantial bias in some circumstances

orthogonality and partial pole assignment for the symmetric definite quadratic pencil abstract the eigenvectors of a symmetric matrix can be chosen to form an orthogonal set with respect to the identity and to the matrix itself similarly the eigenvectors of a symmetric definite linear pencil can be chosen to be orthogonal with respect to the pair this paper presents the three sets of matrix weights with respect to which the eigenvectors of the symmetric definite quadratic pencil are orthogonal one of these is used to derive an explicit solution of the partial pole assignment problem by state feedback control for a control system modeled by a system of second order differential equations the solution may be of particular interest in the stabilization and control of flexible large space structures where only a small part of the spectrum is to be reassigned and the rest of the spectrum is required to remain unchanged

modeling discrete choice with response error food stamp participation abstract validation of food stamp program participation by marquis and moore revealed net bias of 13 in mean estimates of participation in the 1984 survey of income and program participation we extend the analysis incorporating demographic and economic covariates in models for underreporting and overreporting we use the resulting models of response error to refine estimates of participation models using pseudo maximum likelihood estimation methods we find that the probability of underreporting rises with increased family income estimates of the participation model indicate the presence of substantial bias in income and asset related parameters compared to values obtained without incorporating response error

an extended quasi likelihood function summary wedderburn s original definition of quasi likelihood for generalized linear models is extended to allow the comparison of variance functions as well as those of linear predictors and link functions the relationship between generalized linear models and the use of transformations of the response variable is explored and the ideas are illustrated by three examples generalized linear models by allowing the full distributional assumption about the random component in the model to be replaced by a much weaker assumption in which only the first and second moments were defined in making this extension wedderburn widened the scope of generalized linear models in a way very similar to that of gauss when he replaced the assumption of normality in classical linear models by that of equal variance for generalized linear models with distributions in the exponential family likelihood ratio and score tests are used for testing hypotheses concerning nested subsets of covariates in the linear predictor and for assessing hypothesized link functions these methods are also applicable with wedderburn s form of quasi likelihood however neither of these methods is suitable for the comparison of different variance functions in this paper we introduce an extended quasi likelihood function which allows for the comparison of various forms of all the components of a generalized linear model i e the linear predictor the link function and the variance function we then apply the ideas to the analysis of several sets of data

isospectral vibrating systems part 1 the spectral method as tudy is made of inverse problems forn n systems of the form l m 2 d k t his paper concerns the determination of systems in an equivalence class def ined by afi xed 2n 2n admissible jordan matrix i e a class of isospectral systems constructive methods are obtained for complex or real systems with no symmetry constraints it is also shown how isospectral families of complex hermitian matrices can be formed the case of real symmetric matrices is more difficult some partial solutions are obtained but in this case the theory remains incomplete examples are given 2 005 elsevier inc all rights reserved

a variance components approach to categorical data models with heterogeneous cell populations analysis of spatial gradients in lung cancer mortality rates in north carolina counties a mixed categorical continuous variable model is proposed for the analysis of mortality rates this model differs from other available models such as weighted least squares and loglinear models in that the within cell populations are assumed to be heterogeneous in their levels of mortality risk heterogeneity implies that in addition to the sampling variance considered in other available models there will be a second component of variance due solely to within cell heterogeneity maximum likelihood procedures are presented for the estimation of the model parameters these procedures are based on the assumption that the distribution function for each cell death count is the negative binomial probability function this assumption is shown to be equivalent to assuming a mixture of poisson processes with the differential risk levels among individuals within each cell being governed by a two parameter gamma distribution the model is applied to data on lung cancer mortality for 1970 1975 for the 100 counties of north carolina the analysis shows that though a gradient in lung cancer mortality rates exist in space the gradient is restricted to specific demographic categories identified by race age and sex

diagnostics for overdispersion abstract diagnostic tools are proposed for assessing the dependence of extrabinomial or extra poisson variation on explanatory variables and for comparing several common models for overdispersion these tools are based on tests for regression terms in the dispersion parameter of a generalized linear model using double exponential family and pseudolikelihood formulations score tests do not require the full fitting of models for variation and lead to easy graphical and numerical procedures based on squared residuals deviance or pearson robust modifications of these are motivated by levene s test in linear models the diagnostic tools are intended primarily to ensure prudent modeling of the variance to make correct inferences about parameters in the mean

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

maximum principle satisfying and positivity preserving high order central discontinuous galerkin methods for hyperbolic conservation laws maximum principle or positivity preserving property holds for many mathematical models when the models are approximated numerically it is preferred that these important properties can be preserved by numerical discretizations for the robustness and the physical relevance of the approximate solutions in this paper we investigate such discretizations of high order accuracy within the central discontinuous galerkin framework more specifically we design and analyze high order maximum principle satisfying central discontinuous galerkin methods for scalar conservation laws and high order positivity preserving central discontinuous galerkin for compressible euler systems the performance of the proposed methods will be demonstrated through a set of numerical experiments

a note on extended quasi likelihood abstract we study the method of extended quasi likelihood estimation and inference of a variance function recently proposed by nelder pregibon 1987 the estimates are inconsistent in general and the test levels can be biased but in many cases such as the exponential family the inconsistency and bias will not be a major concern extended quasi likelihood is compared with carroll ruppert s 1982 pseudo likelihood method which gives consistent estimates and when slightly modified asymptotically unbiased tests we quantify the showing in this instance that the two estimates are closely related and may be asymptotically equivalent in many important cases however in some cases outside the exponential family an asymptotic bias can persist heteroscedastic regression model

markov chain monte carlo in approximate dirichlet and beta two parameter process hierarchical models summary we present some easy to construct random probability measures which approximate the dirichlet process and an extension which we will call the beta two parameter process the nature of these constructions makes it simple to implement markov chain monte carlo algorithms for fitting nonparametric hierarchical models and mixtures of nonparametric hierarchical models for the dirichlet process we consider a truncation approximation as well as a weak limit approximation based on a mixture of dirichlet processes the same type of truncation approximation can also be applied to the beta two parameter process both methods lead to posteriors which can be fitted using markov chain monte carlo algorithms that take advantage of blocked coordinate updates these algorithms promote rapid mixing of the markov chain and can be readily applied to normal mean mixture models and to density estimation problems we prefer the truncation approximations since a simple device for monitoring the adequacy of the approximation can be easily computed from the output of the gibbs sampler furthermore for the dirichlet process the truncation approximation offers an exponentially higher degree of accuracy over the weak limit approximation for the same computational effort we also find that a certain beta two parameter process may be suitable for finite mixture modelling because the distinct number of sampled values from this process tends to match closely the number of components of the underlying mixture distribution

poisson gamma random field models for spatial statistics summary doubly stochastic bayesian hierarchical models are introduced to account for uncertainty and spatial variation in the underlying intensity measure for point process models inhomogeneous gamma process random fields and more generally markov random fields with infinitely divisible distributions are used to construct positively autocorrelated intensity measures for spatial poisson point processes these in turn are used to model the number and location of individual events a data augmentation scheme and markov chain monte carlo numerical methods are employed to generate samples from bayesian posterior and predictive distributions the methods are developed in both continuous and discrete settings and are applied to a problem in forest ecology

nonparametric bayesian dictionary learning for analysis of noisy and incomplete images nonparametric bayesian methods are considered for recovery of imagery based upon compressive incomplete and or noisy measurements a truncated beta bernoulli process is employed to infer an appropriate dictionary for the data under test and also for image recovery in the context of compressive sensing significant improvements in image recovery are manifested using learned dictionaries relative to using standard orthonormal image expansions the compressive measurement projections are also optimized for the learned dictionary additionally we consider simpler incomplete measurements defined by measuring a subset of image pixels uniformly selected at random spatial interrelationships within imagery are exploited through use of the dirichlet and probit stick breaking processes several example results are presented with comparisons to other methods in the literature

variance function estimation abstract heteroscedastic regression models are used in fields including economics engineering and the biological and physical sciences often the heteroscedasticity is modeled as a function of the covariates or the regression and other structural parameters standard asymptotic theory implies that how one estimates the variance function in particular the structural parameters has no effect on the first order properties of the regression parameter estimates there is evidence however both in practice and higher order theory to suggest that how one estimates the variance function does matter further in some settings estimation of the variance function is of independent interest or plays an important role in estimation of other quantities in this article we study variance function estimation in a unified way focusing on common methods proposed in the statistical and other literature to make both general observations and compare different estimation schemes we show that there are significant di

maximum likelihood estimation for the negative binomial dispersion parameter a 2 this yf y k for k 0 u 0 anscombe 1950 here u e y and k 1 a also var y u a2 k a aa2 this distribution has numerous applications in the biological sciences see e g breslow 1984 margolin kim and risko 1989 and the references in clark and perry 1989 anscombe 1950 observed that strictly speaking the maximum likelihood ml estimator of k k does not have a distribution since there exists a finite probability of observing a data set from which k may not be calculated this occurs when the sample mean exceeds the sample variance a more useful parameterization involves a 1 k giving

likelihood quasi likelihood and pseudolikelihood some comparisons summary there is considerable interest in the fitting of models jointly to the mean and dispersion of a response for the mean parameter the wedderburn estimating equations are widely accepted however there is some controversy about estimating the dispersion parameters finite sampling properties of several dispersion estimators are investigated for three models by simulation we compare the maximum extended quasi likelihood estimator the maximum pseudolikelihood estimator and the maximum likelihood estimator if it exists of these estimators the maximum extended quasi likelihood estimator is usually superior in minimizing the mean squared error

estimation of the shape parameter k of the negative binomial distribution using approximate bayesian methods an estimator of the shape parameter of the negative binomial distribution is introduced most of the available estimators of this parameter such as the method of moment and the maximum likelihood estimators mme and mle give inadmissible values when the mean of the observed sample is larger than its variance in this case the mme gives values while the mle is infinite such observed sample in not unlikely when the mean of the population is close to its variance the suggested estimator always has valid values and turned out to be more efficient for most values of the parameter space family size data is used for illustration of the procedure

negative binomial process count and mixture modeling the seemingly disjoint problems of count and mixture modeling are united under the negative binomial nb process a gamma process is employed to model the rate measure of a poisson process whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an nb process for count modeling a draw from the nb process consists of a poisson distributed finite number of distinct atoms each of which is associated with a logarithmic distributed number of data samples we reveal relationships between various count and mixture modeling distributions and construct a poisson logarithmic bivariate distribution that connects the nb and chinese restaurant table distributions fundamental properties of the models are developed and we derive efficient bayesian inference it is shown that with augmentation and normalization the nb process and gamma nb process can be reduced to the dirichlet process and hierarchical dirichlet process respectively these relationships highlight theoretical structural and computational advantages of the nb process a variety of nb processes including the beta geometric beta nb marked beta nb marked gamma nb and zero inflated nb processes with distinct sharing mechanisms are also constructed these models are applied to topic modeling with connections made to existing algorithms under poisson factor analysis example results show the importance of inferring both the nb dispersion and probability parameters

a splitting approach for the fully nonlinear and weakly dispersive green naghdi model the fully nonlinear and weakly dispersive green naghdi model for shallow water waves of large amplitude is studied the original model is first recast under a new formulation more suitable for numerical resolution an hybrid finite volume and finite difference splitting approach is then proposed which could be adapted to many physical models that are dispersive corrections of hyperbolic systems the hyperbolic part of the equations is handled with a high order finite volume scheme allowing for breaking waves and dry areas the dispersive part is treated with a classical finite difference approach extensive numerical validations are then performed in one horizontal dimension relying both on analytical solutions and experimental data the results show that our approach gives a good account of all the processes of wave transformation in coastal areas shoaling wave breaking and run up

disease mapping via negative binomial regression m quantiles we introduce a semi parametric approach to ecological regression for disease mapping based on modelling the regression m quantiles of a negative binomial variable the proposed method is robust to outliers in the model covariates including those due to measurement error and can account for both spatial heterogeneity and spatial clustering a simulation experiment based on the well known scottish lip cancer data set is used to compare the m quantile modelling approach with a disease mapping approach based on a random effects model this suggests that the m quantile approach leads to predicted relative risks with smaller root mean square error the paper concludes with an illustrative application of the m quantile approach mapping low birth weight incidence data for english local authority districts for the years 2005 2010 copyright 2014 john wiley sons ltd

inverse problems for damped vibrating systems abstract linear damped vibrating systems are defined by three real definite matrices m 0 d 0 and k 0 the mass damping and stiffness matrices respectively it is assumed that all eigenvalues of the system are simple and nonreal so that the eigenvectors columns of a matrix x c c n n are also complex it is shown that when properly defined the eigenvectors have a special structure consistent with x c x r i i where x r r n n x r is nonsingular and is orthogonal by taking advantage of this structure solutions of the inverse problem are obtained i e given complete information on the eigenvalues and eigenvectors it is shown how m d and k can be found three points of view are developed and compared namely using spectral theory structure preserving similarities and factorisation theory

the two parameter poisson dirichlet distribution derived from a stable subordinator the two parameter poisson dirichlet distribution denoted mathsf pd alpha theta is a probability distribution on the set of decreasing positive sequences with sum 1 the usual poisson dirichlet distribution with a single parameter theta introduced by kingman is mathsf pd 0 theta known properties of mathsf pd 0 theta including the markov chain description due to vershik shmidt and ignatov are generalized to the two parameter case the size biased random permutation of mathsf pd alpha theta is a simple residual allocation model proposed by engen in the context of species diversity and rediscovered by perman and the authors in the study of excursions of brownian motion and bessel processes for 0 alpha 1 mathsf pd alpha 0 is the asymptotic distribution of ranked lengths of excursions of a markov chain away from a state whose recurrence time distribution is in the domain of attraction of a stable law of index alpha formulae in this case trace back to work of darling lamperti and wendel in the 1950s and 1960s the distribution of ranked lengths of excursions of a one dimensional brownian motion is mathsf pd 1 2 0 and the corresponding distribution for a brownian bredge is mathsf pd 1 2 1 2 the mathsf pd alpha 0 and mathsf pd alpha alpha distributions admit a similar interpretation in terms of the ranked lengths of excursions of a semistable markov process whose zero set is the range of a stable subordinator of index alpha

bayesian density estimation and inference using mixtures abstract we describe and illustrate bayesian inference in models for density estimation using mixtures of dirichlet processes these models provide natural settings for density estimation and are exemplified by special cases where data are modeled as a sample from mixtures of normal distributions efficient simulation methods are used to approximate various prior posterior and predictive distributions this allows for direct inference on a variety of practical issues including problems of local versus global smoothing uncertainty about density estimates assessment of modality and the inference on the numbers of components also convergence results are established for a general class of normal mixture models

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

spillover phenomenon in quadratic model updating model updating concerns the modification of an existing but inaccurate model with measured data for models characterized by quadratic pencils the measured data usually involve incomplete knowledge of natural frequencies mode shapes or other spectral information in conducting the updating it is often desirable to match only the part of observed data without tampering with the other part of unmeasured or unknown eigenstructure inherent in the original model such an updating if possible is said to have no spillover this paper studies the spillover phenomenon in the updating of quadratic pencils in particular it is shown that an updating with no spillover is always possible for undamped quadratic pencils whereas spillover for damped quadratic pencils is generally unpreventable

positivity preserving dg and central dg methods for ideal mhd equations ideal mhd equations arise in many applications such as astrophysical plasmas and space physics and they consist of a system of nonlinear hyperbolic conservation laws the exact density r and pressure p should be non negative numerically such positivity property is not always satisfied by approximated solutions one can encounter this when simulating problems with low density high mach number or much large magnetic energy compared with internal energy when this occurs numerical instability may develop and the simulation can break down in this paper we propose positivity preserving discontinuous galerkin and central discontinuous galerkin methods for solving ideal mhd equations by following x zhang c w shu journal of computational physics 229 2010 8918 8934 in one dimension the positivity preserving property is established for both methods under a reasonable assumption the performance of the proposed methods in terms of accuracy stability and positivity preserving property is demonstrated through a set of one and two dimensional numerical experiments the proposed methods formally can be of any order of accuracy

efficiency lost by analyzing counts rather than event times in poisson and overdispersed poisson regression models abstract inference for point processes is most efficient if the event times for each individual are available sometimes the study design is such that only aggregated data are collected consisting of the number of events or recurrences for each individual over the observation period this article discusses the loss in efficiency of an analysis of the aggregated counts versus an analysis of the actual event times one particular case is exemplified that in which the purpose of the experiment or trial is to compare the effects of treatments and the loss in efficiency in the estimator of the treatment effect is computed the specific point process considered here is the nonhomogeneous poisson process with a proportional intensity model for the treatment effects random effects models are also considered with estimation via a quasi likelihood approach the quasi likelihood analysis proposed here is an extension of such techniques for the homogeneous poisson process the resulting estimating equations for

a new index of aggregation for animal counts a new index is described that is especially appropriate for measuring the aggregation of entomological data in the form of counts per sample unit and that can make use of spatial information when it is available calculation of the index is based on a comparison of the effort required of individuals in a sample to achieve complete crowding with that to achieve complete randomness the power of tests of randomness based on this index is found to be greater than those based on the index of dispersion especially when spatial information is available

robust estimation in heteroscedastic linear models we consider a heteroscedastic linear model in which the variances are given by a parametric function of the mean responses and a parameter theta we propose robust estimates for the regression parameter beta and show that as long as a reasonable starting estimate of theta is available our estimates of beta are asymptotically equivalent to the natural estimate obtained with known variances a particular method for estimating theta is proposed and shown by monte carlo to work quite well especially in power and exponential models for the variances we also briefly discuss a feedback estimate of beta

discontinuous galerkin methods for solving boussinesq green naghdi equations in resolving non linear and dispersive surface water waves a local discontinuous galerkin method for boussinesq green naghdi equations is presented and validated against experimental results for wave transformation over a submerged shoal currently green naghdi equations have many variants in this paper a numerical method in one dimension is presented for the green naghdi equations based on rotational characteristics in the velocity field stability criterion is also established for the linearized green naghdi equations for both the analytical problem and the numerical method verification is done against a linearized standing wave problem in flat bathymetry and h p denoted by k in this paper error rates are plotted validation plots show good agreement of the numerical results with the experimental ones

tests for detecting overdispersion in poisson regression models abstract poisson regression models are widely used in analyzing count data this article develops tests for detecting extra poisson variation in such situations the tests can be obtained as score tests against arbitrary mixed poisson alternatives and are generalizations of tests of fisher 1950 and collings and margolin 1985 accurate approximations for computing significance levels are given and the power of the tests against negative binomial alternatives is compared with those of the pearson and deviance statistics one way to test for extra poisson variation is to fit models that parametrically incorporate and then test for the absence of such variation within the models for example negative binomial models can be used in this way cameron and trivedi 1986 lawless 1987a the tests in this article require only the poisson model to be fitted two test statistics are developed that are motivated partly by a desire to have good distributional approximations for computing significance levels simu

high order well balanced cdg fe methods for shallow water waves by a green naghdi model in this paper we consider a one dimensional fully nonlinear weakly dispersive green naghdi model for shallow water waves over variable bottom topographies such model describes a large spectrum of shallow water waves and it is thus of great importance to design accurate and robust numerical methods for solving it the governing equations contain mixed spatial and temporal derivatives of the unknowns they also have still water stationary solutions which should be preserved in stable numerical simulations in our numerical approach we first reformulate the green naghdi equations into balance laws coupled with an elliptic equation we then propose a family of high order numerical methods which discretize the balance laws with well balanced central discontinuous galerkin methods and the elliptic part with continuous finite element methods linear dispersion analysis for both the reformulated green naghdi system and versions of the proposed numerical scheme is performed when the bottom topography is flat numerical tests are presented to illustrate the accuracy and stability of the proposed schemes as well as the capability of the green naghdi model to describe a wide range of shallow water wave phenomena

retrospective markov chain monte carlo methods for dirichlet process hierarchical models inference for dirichlet process hierarchical models is typically performed using markov chain monte carlo methods which can be roughly categorized into marginal and conditional methods the former integrate out analytically the infinite dimensional component of the hierarchical model and sample from the marginal distribution of the remaining variables using the gibbs sampler conditional methods impute the dirichlet process and update it as a component of the gibbs sampler since this requires imputation of an infinite dimensional process implementation of the conditional method has relied on finite approximations in this paper we show how to avoid such approximations by designing two novel markov chain monte carlo algorithms which sample from the exact posterior distribution of quantities of interest the approximations are avoided by the new technique of retrospective sampling we also show how the algorithms can obtain samples from functionals of the dirichlet process the marginal and the conditional methods are compared and a careful simulation study is included which involves a non conjugate model different datasets and prior specifications

solutions to a quadratic inverse eigenvalue problem abstract in this paper we consider the quadratic inverse eigenvalue problem qiep of constructing real symmetric matrices m c and k of size n n with m c k 0 so that the quadratic matrix polynomial q 2 m c k has m n m 2 n prescribed eigenpairs it is shown that for almost all prescribed eigenpairs the qiep has a solution with m nonsingular if m m and has only solutions with q 0 otherwise where m n 1 1 8 n 2 we also derive the expression of the general solution of the qiep for both cases furthermore we develop an algorithm for finding a particular solution to the qiep with m positive definite if it exists

the ames salmonella microsome mutagenicity assay issues of inference and validation abstract the importance of chemically induced mutation for human health is discussed briefly and the biological basis for the primary in vitro assay for mutagenicity the ames salmonella microsome assay is reviewed a previous analysis for ames test data based on two mathematical models of the competing risks of mutation and toxicity is shown to have inflated false positive rates a reason for this is the existence of local singularities in the fisher information matrix a new likelihood ratio test incorporating a pretest of a nuisance parameter is proposed and its size is validated with replicated experimental data through an analysis based on a finite mixture of binomials model

bias correction in generalized linear models summary in this paper we derive general formulae for first order biases of maximum likelihood estimates of the linear parameters linear predictors the dispersion parameter and fitted values in generalized linear models these formulae may be implemented in the glim program to compute bias corrected maximum likelihood estimates to order n 1 where n is the sample size with minimal effort by means of a supplementary weighted regression for linear logistic models it is shown that the asymptotic bias vector of j8 is almost collinear with f3 the approximate formula flp m for the bias of s in logistic models where p dim and m e mi is the sum of the binomial indices is derived and checked numerically

symmetry preserving eigenvalue embedding in finite element model updating of vibrating structures the eigenvalue embedding problem addressed in this paper is the one of reassigning a few troublesome eigenvalues of a symmetric finite element model to some suitable chosen ones in such a way that the updated model remains symmetric and the remaining large number of eigenvalues and eigenvectors of the original model is to remain unchanged the problem naturally arises in stabilizing a large scale system or combating dangerous vibrations which can be responsible for undesired phenomena such as resonance in large vibrating structures a new computationally efficient and symmetry preserving method and associated theories are presented in this paper the model is updated using low rank symmetric updates and other computational requirements of the method include only simple operations such as matrix multiplications and solutions of low order algebraic linear systems these features make the method practical for large scale applications the results of numerical experiments on the simulated data obtained from the boeing company and on some benchmark examples are presented to show the accuracy of the method computable error bounds for the updated matrices are also given by means of rigorous mathematical analysis