a discrete time event history approach to informative drop out in mixed latent markov models with covariates summary mixed latent markov mlm models represent an important tool of analysis of longitudinal data when response variables are affected by time fixed and time varying unobserved heterogeneity in which the latter is accounted for by a hidden markov chain in order to avoid bias when using a model of this type in the presence of informative drop out we propose an event history eh extension of the latent markov approach that may be used with multivariate longitudinal data in which one or more outcomes of a different nature are observed at each time occasion the eh component of the resulting model is referred to the interval censored drop out and bias in mlm modeling is avoided by correlated random effects included in the different model components which follow common latent distributions in order to perform maximum likelihood estimation of the proposed model by the expectation maximization algorithm we extend the usual forward backward recursions of baum and welch the algorithm has the same complexity as the one adopted in cases of non informative drop out we illustrate the proposed approach through simulations and an application based on data coming from a medical study about primary biliary cirrhosis in which there are two outcomes of interest one continuous and the other binary

multi quadric quasi interpolation method coupled with fdm for the degasperis procesi equation in this paper the degasperis procesi dp equation which contains nonlinear high order derivatives and discontinuous solutions is recast to its equivalent form u p based on the equivalent formulation of dp equation a new numerical method is presented the multi quadric mq quasi interpolation method coupled with finite difference method is applied to approximate the spatial derivatives and the third order tvd method is used to approximate the time derivative several examples are presented to demonstrate the effectiveness of the proposed method

estimation in generalized mixed models regression models containing fixed and random effects may have a response variable which is not normally distributed the generalized mixed model includes both discrete and continuous response variables and is developed here for problems in which the regression variables enter linearly into the model best linear unbiased predictor methods are extended to maximum likelihood and residual maximum likelihood estimation procedures applications in modelling discrete response variables and in survival analysis are discussed

estimation of continuous time stochastic signals from sample covariances the problem of estimating the parameters in stochastic continuous time signals represented as continuous time autoregressive moving average arma processes from discrete time data is considered the proposed solution is to fit the covariance function of the process parameterized by the unknown parameters to sample covariances it is shown that the method is consistent and an expression for the approximate covariance matrix of the estimated parameter vector is derived the derived variances are compared with empirical variances from a monte carlo simulation and with the cramer rao bound it turns out that the variances are close to the cramer rao bound for certain choices of the sampling interval and the number of covariance elements used in the criterion function

numerical solution of the degasperis procesi equation by the cubic b spline quasi interpolation method abstract in this paper a numerical scheme is presented to solve the non dissipative degasperis procesi equation based on the u p formulation the cubic b spline quasi interpolation coupled with the finite difference method is applied to approximate the spatial derivatives and an optimal third order tvd runge kutta method to estimate the time derivative of the dependent variable the accuracy and effectiveness of the proposed method are validated by six classical problems numerical results indicate that the proposed scheme is simple easy to implement with high accuracy

convergence of a finite difference scheme for the camassa holm equation we prove that a certain finite difference scheme converges to the weak solution of the cauchy problem on a finite interval with periodic boundary conditions for the camassa holm equation u t u xxt 3uu x 2u xu xx uu xxx 0 with initial data u t 0 u 0 in h 1 0 1 here it is assumed that u 0 u 0 ge0 and in this case the solution is unique globally defined and energy preserving

mixed hidden markov models hidden markov models hmms are a useful tool for capturing the behavior of overdispersed autocorrelated data these models have been applied to many different problems including speech recognition precipitation modeling and gene finding and profiling typically hmms are applied to individual stochastic processes hmms for simultaneously modeling multiple processes as in the longitudinal data setting have not been widely studied in this article i present a new class of models mixed hmms mhmms where i use both covariates and random effects to capture differences among processes i define the models using the framework of generalized linear mixed models and discuss their interpretation i then provide algorithms for parameter estimation and illustrate the properties of the estimators via a simulation study finally to demonstrate the practical uses of mhmms i provide an application to data on lesion counts in multiple sclerosis patients i show that my model while parsimonious can describe the

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

b spline signal processing ii efficiency design and applications for pt i see ibid vol 41 no 2 p 821 33 1993 a class of recursive filtering algorithms for the efficient implementation of b spline interpolation and approximation techniques is described in terms of simplicity of realization and reduction of computational complexity these algorithms compare favorably with conventional matrix approaches a filtering interpretation low pass filter followed by an exact polynomial spline interpolator of smoothing spline and least squares approximation methods is proposed these techniques are applied to the design of digital filters for cubic spline signal processing an efficient implementation of a smoothing spline edge detector is proposed it is also shown how to construct a cubic spline image pyramid that minimizes the loss of information in passage from one resolution level to the next in terms of common measures of fidelity this data structure appears to be superior to the gaussian laplacian pyramid

a quaternion widely linear model for nonlinear gaussian estimation this paper deals with the nonlinear minimum mean squared error estimation problem by using a quaternion widely linear model on the basis of the information supplied by a gaussian signal and its square a quaternion observation process is defined and then by applying a widely linear processing an optimal estimator for the continuous time setting is provided the special structure of the estimator proves its superiority over the complex valued widely linear solution the continuous discrete version of the problem is also studied where the solution takes the form of a suboptimal estimator useful in practical applications in addition the particular case of signal plus noise is considered in which the suboptimal solution and its associated error can be implemented through an iterative algorithm two numerical simulation examples are presented showing the advantages of the proposed approach

a dispersively accurate compact finite difference method for the degasperis procesi equation in this paper we are aimed to solve the non dissipative degasperis procesi equation based on the u p formulation to resolve the computational difficulty at the wave crest where the first order derivative may diverge and the shockpeakon solution may form the first order spatial derivative term in the two step equations will be approximated in a conservative form the resulting equations will be approximated by the symplecticity preserving time stepping scheme and the spatial discretization scheme that can optimize the numerical wavenumber for the first order spatial derivative term this scheme will be developed in a three point grid stencil with the accuracy order of seventh within the combined compact finite difference framework besides the validation of numerical accuracy we will in particular address the discrete conservation of hamiltonians even when peakon collides with antipeakon and generates as a result a shockpeakon we will also demonstrate the capability of applying the proposed numerical method to sharply resolve some important features of the third order dispersive dp equation

an operator splitting method for the degasperis procesi equation an operator splitting method is proposed for the degasperis procesi dp equation by which the dp equation is decomposed into the burgers equation and the benjamin bona mahony bbm equation then a second order tvd scheme is applied for the burgers equation and a linearized implicit finite difference method is used for the bbm equation furthermore the strang splitting approach is used to construct the solution in one time step the numerical solutions of the dp equation agree with exact solutions e g the multipeakon solutions very well the proposed method also captures the formation and propagation of shockpeakon solutions and reveals wave breaking phenomena with good accuracy

some covariance models for longitudinal count data with overdispersion a family of covariance models for longitudinal counts with predictive covariates is presented these models account for overdispersion heteroscedasticity and dependence among repeated observations the approach is a quasi likelihood regression similar to the formulation given by liang and zeger 1986 biometrika 73 13 22 generalized estimating equations for both the covariate parameters and the variance covariance parameters are presented large sample properties of the parameter estimates are derived the proposed methods are illustrated by an analysis of epileptic seizure count data arising from a study of progabide as an adjuvant therapy for partial seizures

a convergent finite difference scheme for the camassa holm equation with general h 1 initial data we suggest a finite dfference scheme for the camassa holm equation that can handle general h 1 initial data the form of the difference scheme is judiciously chosen to ensure that it satisfies a total energy inequality we prove that the difference scheme converges strongly in h 1 towards a dissipative weak solution of the camassa holm equation

an integrable semi discretization of the camassa holm equation and its determinant solution an integrable semi discretization of the camassa holm ch equation is presented the keys of its construction are bilinear forms and determinant structure of solutions of the ch equation determinant formulas of n soliton solutions of the continuous and semi discrete camassa holm equations are presented based on determinant formulas we can generate multi soliton multi cuspon and multi soliton cuspon solutions numerical computations using the integrable semi discrete camassa holm equation are performed it is shown that the integrable semi discrete camassa holm equation gives very accurate numerical results even in the cases of cuspon cuspon and soliton cuspon interactions the numerical computation for an initial value condition which is not an exact solution is also presented

generalized linear models with random effects a gibbs sampling approach abstract generalized linear models have unified the approach to regression for a wide variety of discrete continuous and censored response variables that can be assumed to be independent across experimental units in applications such as longitudinal studies genetic studies of families and survey sampling observations may be obtained in clusters responses from the same cluster cannot be assumed to be independent with linear models correlation has been effectively modeled by assuming there are cluster specific random effects that derive from an underlying mixing distribution extensions of generalized linear models to include random effects has thus far been hampered by the need for numerical integration to evaluate likelihoods in this article we cast the generalized linear random effects model in a bayesian framework and use a monte carlo method the gibbs sampler to overcome the current computational limitations the resulting algorithm is flexible to easily accommodate changes in the number

maximum likelihood estimation for probit linear mixed models with correlated random effects the probit normal model for binary data mcculloch 1994 journal of the american statistical association 89 330 335 is extended to allow correlated random effects to obtain maximum likelihood estimates we use the em algorithm with its m step greatly simplified under the assumption of a probit link and its e step made feasible by gibbs sampling standard errors are calculated by inverting a monte carlo approximation of the information matrix rather than via the sem algorithm a method is also suggested that accounts for the monte carlo variation explicitly as an illustration we present a new analysis of the famous salamander mating data unlike previous analyses we find it necessary to introduce different variance components for different species of animals finally we consider models with correlated errors as well as correlated random effects

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

the analysis of binomial data by a generalized linear mixed model summary methods for generalized linear models are extended to provide estimates of location and variance parameters for mixed models fitted to binomial data formed by classifying samples from an underlying normal distribution the method estimates the parameters directly on the underlying scale for a balanced one way random effects model the variance estimator simplifies to the usual analysis of variance one the estimation of variances and the prediction of random effects for binomial traits is required by animal breeders the predictors given are analogous to best linear unbiased predictors henderson 1973 but differ from those presented by harville mee 1984

two graphical displays for outlying and influential observations in regression summary the paper describes two procedures for detecting observations with outlying values either in the response variable or in the explanatory variables in multiple regression these procedures are presented as half normal plots with envelopes derived from simulation in order to avoid overinterpretation of the data analysis of a well known data set leads to the use of a data transformation a simple test for which is commended and to some comments on the relationship with robust regression the widespread availability of sophisticated computer software has made the fitting of multiple regression equations painless but the very ease of these procedures may cause insufficient care to be given to checking and scrutiny of the data transcription punching and data manipulation errors may lead to bad values both of the observations y and of the independent or explanatory variables x it is the purpose of the present paper to describe and exemplify two plots which provide checks against such bad values it is argued that these plots and a test for transformations should accompany any thorough regression analysis bad values of the response or outliers have long been detected by a variety of plots of residuals bad values of the explanatory variables are less easily detected even when they lead to an extreme point in the design space since the fitted equation will pass close to such an influential observation the residual may not be especially large even after allowance has been made for the small variance of the fitted value at such a point to detect such behaviour a quantity is needed which exhibits the dependence of the fitted model on each point or group of points discussions of such quantities are given by hoaglin welsch 1978 and more recently by belsley kuh welsch 1980 2 1 by cook weisberg 1980 and by pregibon 1981 the quantity used here is a modification of a statistic proposed by cook 1977 which is derived in 2 two half normal plots are presented in 3 as an aid to interpretation envelopes to the plots are generated by simulation examples of the plots are given in 4 both for simulated data and for the stack loss data given by brownlee 1965 p 454 transformations of this data set are discussed in 5 the paper concludes with some comments on the relationship with robust

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

semi widely simulation and estimation of continuous time bbc eta proper quaternion random signals the repercussions of quaternion bbc eta properness on the continuous time simulation and estimation problems are studied as a first step a semi widely linear quaternion karhunen loeve expansion is derived then this series representation is used in both problems to give the solutions the simulation technique proposed is useful for transformations of nonstationary gaussian quaternion signals the estimation problem is also analyzed in a continuous discrete setting and by considering two different formulations the cambanis formulation and the signal plus noise model initially the estimators are developed on the basis of a semi widely linear processing afterwards the solutions are improved by incorporating the information supplied by the square quaternion observations and by using a semi widely nonlinear processing in this last scenario we assume gaussian observations and unknown probability distributions of the signal of interest

partially ordered mixed hidden markov model for the disablement process of older adults at both the individual and societal levels the health and economic burden of disability in older adults is enormous in developed countries including the u s recent studies have revealed that the disablement process in older adults often comprises episodic periods of impaired functioning and periods that are relatively free of disability amid a secular and natural trend of decline in functioning rather than an irreversible progressive event that is analogous to a chronic disease disability is better conceptualized and mathematically modeled as states that do not necessarily follow a strict linear order of good to bad statistical tools including markov models which allow bidirectional transition between states and random effects models which allow individual specific rate of secular decline are pertinent in this article we propose a mixed effects multivariate hidden markov model to handle partially ordered disability states the model generalizes the continuation ratio model for ordinal dat

laplace s approximation for nonlinear mixed models summary an approximation to laplace s method for integrals is applied to marginal distributions of data arising from models in which both fixed and random effects enter nonlinearly the approach provides alternative derivations of some recent algorithms for fitting such models and it has direct ties with gaussian restricted maximum likelihood and the accompanying mixed model equations

colliding peakons and the formation of shocks in the degasperis procesi equation the degasperisprocesi equation dp is one of several equations known to model important nonlinear effects such as wave breaking and shock creation it is however a special property of the dp equ

on the uniqueness of discontinuous solutions to the degasperis procesi equation abstract we prove uniqueness within a class of discontinuous solutions to the nonlinear and third order dispersive degasperis procesi equation t u t x x 3 u 4 u x u 3 x u x x 2 u u x x x 3 u in a recent paper g m coclite k h karlsen on the well posedness of the degasperis procesi equation j funct anal 233 2006 60 91 we proved for this equation the existence and uniqueness of l 1 bv weak solutions satisfying an infinite family of kru kov type entropy inequalities the purpose of this paper is to replace the kru kov type entropy inequalities by an ole nik type estimate and to prove uniqueness via a nonlocal adjoint problem an implication is that a shock wave in an entropy weak solution to the degasperis procesi equation is admissible only if it jumps down in value like the inviscid burgers equation

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

on the camassa holm equation and a direct method of solution i bilinear form and solitary waves over the last decade a variety of techniques has been used to find exact solutions both analytic and other of the camassaholm equation the different approaches have met with varying measures of

a mixed non homogeneous hidden markov model for categorical data with application to alcohol consumption hidden markov models hmms are frequently used to analyse longitudinal data where the same set of subjects is repeatedly observed over time in this context several sources of heterogeneity may arise at individual and or time level which affect the hidden process that is the transition probabilities between the hidden states in this paper we propose the use of a finite mixture of non homogeneous hmms nh hmms to face the heterogeneity problem the non homogeneity of the model allows us to take into account observed sources of heterogeneity by means of a proper set of covariates time and or individual dependent explaining the variations in the transition probabilities moreover we handle the unobserved sources of heterogeneity at the individual level due to for example omitted covariates by introducing a random term with a discrete distribution the resulting model is a finite mixture of nh hmm that can be used to classify individuals according to their dynamic behaviour or to estimate a mixed nh hmm without any assumption regarding the distribution of the random term following the non parametric maximum likelihood approach we test the effectiveness of the proposal through a simulation study and an application to real data on alcohol abuse

b spline signal processing i theory the use of continuous b spline representations for signal processing applications such as interpolation differentiation filtering noise reduction and data compressions is considered the b spline coefficients are obtained through a linear transformation which unlike other commonly used transforms is space invariant and can be implemented efficiently by linear filtering the same property also applies for the indirect b spline transform as well as for the evaluation of approximating representations using smoothing or least squares splines the filters associated with these operations are fully characterized by explicitly evaluating their transfer functions for b splines of any order applications to differentiation filtering smoothing and least squares approximation are examined the extension of such operators for higher dimensional signals such as digital images is considered

maximum likelihood algorithms for generalized linear mixed models abstract maximum likelihood algorithms are described for generalized linear mixed models i show how to construct a monte carlo version of the em algorithm propose a monte carlo newton raphson algorithm and evaluate and improve the use of importance sampling ideas calculation of the maximum likelihood estimates is feasible for a wide variety of problems where they were not previously i also use the newton raphson algorithm as a framework to compare maximum likelihood to the joint maximization or penalized quasi likelihood methods and explain why the latter can perform poorly

hidden markov models for zero inflated poisson counts with an application to substance use paradigms for substance abuse cue reactivity research involve short term pharmacological or stressful stimulation designed to elicit stress and craving responses in cocaine dependent subjects it is unclear as to whether stress induced from participation in such studies increases drug seeking behavior we propose a 2 state hidden markov model to model the number of cocaine abuses per week before and after participation in a stress and cue reactivity study the hypothesized latent state corresponds to high or low use to account for a preponderance of zeros we assume a zero inflated poisson model for the count data transition probabilities depend on the prior week s state fixed demographic variables and time varying covariates we adopt a bayesian approach to model fitting and use the conditional predictive ordinate statistic to demonstrate that the zero inflated poisson hidden markov model outperforms other models for longitudinal count data

symplectic structures their backlund transformations and hereditary symmetries abstract it is shown that compatible symplectic structures lead in a natural way to hereditary symmetries we recall that a hereditary symmetry is an operator valued function which immediately yields a hierarchy of evolution equations each having infinitely many commuting symmetries all generated by this hereditary symmetry furthermore this hereditary symmetry usually describes completely the soliton structure and the conservation laws of these equations this result then provide us with a method for constructing hereditary symmetries and hence exactly solvable evolution equations in addition we show how symplectic structures transform under backlund transformations this leads to a method for generating a whole class of symplectic structures from a given one several examples and applications are given illustrating the above results also the connection of our results with those of gelfand and dikii and of magri is briefly pointed out

a generalized linear model with nested strata of extra poisson variation on etend la definition de quasivraisemblance pour tenir compte de plusieurs strates de variation emboitees dans un modele lineaire generalise

heterogeneity in mantel haenszel type models summary the mantel haenszel problem involves inferences about a common odds ratio in a set of 2 x 2 tables although it is a fairly standard practice to test whether the odds ratios are indeed constant there is remarkably little methodology available for proceeding when there is evidence of some heterogeneity our interest is in models where the log odds ratios ok for tables k 1 2 k are thought of as a sample from a population with mean 0 and standard deviation a and inferences are desired regarding the parameters 0 a by mantel haenszel type models we mean to include the generalization involving pairs of poisson observations rather than 2 x 2 tables where the ok are logarithms of ratios of the poisson means within pairs direct computation of the likelihood function for 0 a in these settings involves numerical integration and the main point here is a simple approximation to this likelihood the approximation is based on laplace s method and is very accurate for practical applications inference regarding the parameter 0 of primary interest may be made from the profile likelihood function an alternative approach to likelihood methods based on approximations to the marginal means and variances is also considered the methods explored here can be readily generalized to settings where the parameters ok depend on covariables as well

quasi likelihood for multiplicative random effects summary a quasi likelihood approach similar to that described by morton 1987 is found to be particularly simple in the case of measurements subject to two or more sources of multiplicative error still further simplification occurs when the effects of interest also are multiplicative the multiplicative analogue of the balanced split plot model is considered in detail an analysis of gamma deviance replaces the familiar analysis of variance the efficiency of the quasi likelihood method relative to a more conventional analysis of logarithms of the data is explored briefly

maximum penalized likelihood estimation for independent and markov dependent mixture models summary this paper concerns the use and implementation of maximum penalized likelihood procedures for choosing the number of mixing components and estimating the parameters in independent and markov dependent mixture models computation of the estimates is achieved via algorithms for the automatic generation of starting values for the em algorithm computation of the information matrix is also discussed poisson mixture models are applied to a sequence of counts of movements by a fetal lamb in utero obtained by ultrasound the resulting estimates are seen to provide plausible mechanisms for the physiological process the analysis of count data that are overdispersed relative to the poisson distribution i e variance mean has received considerable recent attention such data might arise in a clinical study in which overdispersion is caused by unexplained or random subject effects alternatively we might observe a time series of counts in which temporal patterns in the data suggest that a poisson model and its implied randomness are inappropriate this paper is motivated by analysis of a time series of overdispersed count data generated in a study of central nervous system development in fetal lambs our data set consists of observed movement counts in 240 consecutive 5 second intervals obtained from a single animal in analysing these data we focus on the use of poisson mixture models assuming independent observations and also markov dependent mixture models or hidden markov models these models assume that the counts follow independent poisson distributions conditional on the rates which are generated from a mixing distribution either independently or with markov dependence we believe finite mixture models are particularly attractive because they provide plausible explanations for variation in the data this paper will emphasize the following issues concerning estimation inference and application of mixture models i choosing the number of model components ii applying the em algorithm to obtain parameter estimates iii generating sufficiently many starting values to identify a global maximum of the likelihood iv avoiding numerical instability

the simulation smoother for time series models summary recently suggested procedures for simulating from the posterior density of states given a gaussian state space time series are refined and extended we introduce and study the simulation smoother which draws from the multivariate posterior distribution of the disturbances of the model so avoiding the degeneracies inherent in state samplers the technique is important in gibbs sampling with non gaussian time series models and for performing bayesian analysis of gaussian time series

dynamic linear model diagnostics summary in time series analysis using dynamic linear models retrospective analysis involves the calculation of filtered or smoothed distributions for state parameters in the past we develop and illustrate novel results that are useful in retrospective assessment of the influence of individual observations on such distributions in particular new and computationally simple filtering equations are derived for past state parameters based on leaving out one observation at a time providing dynamic model based versions of methods currently used in standard static regression diagnostics

some aspects of polya tree distributions for statistical modelling the definition and elementary properties of polya tree distributions are reviewed two theorems are presented showing that polya trees can be constructed to concentrate arbitrarily closely about any desired pdf and that polya tree priors can put positive mass in every relative entropy neighborhood of every positive density with finite entropy thereby satisfying a consistency condition such theorems are false for dirichlet processes models are constructed combining partially specified polya trees with other information such as monotonicity or unimodality it is shown how to compute bounds on posterior expectations over the class of all priors with the given specifications a numerical example is given a theorem of diaconis and freedman about dirichlet processes is generalized to polya trees allowing polya trees to be the models for errors in regression problems finally empirical bayes models using dirichlet processes are generalized to polya trees an example from berry and christensen is reanalyzed with a polya tree model

a sampling theory approach for continuous arma identification the problem of estimating continuous domain autoregressive moving average processes from sampled data is considered the proposed approach incorporates the sampling process into the problem formulation while introducing exponential models for both the continuous and the sampled processes we derive an exact evaluation of the discrete domain power spectrum using exponential b splines and further suggest an estimation approach that is based on digitally filtering the available data the proposed functional which is related to whittle s likelihood function exhibits several local minima that originate from aliasing the global minimum however corresponds to a maximum likelihood estimator regardless of the sampling step experimental results indicate that the proposed approach closely follows the cramer rao bound for various aliasing configurations

markov and semi markov switching linear mixed models used to identify forest tree growth components tree growth is assumed to be mainly the result of three components i an endogenous component assumed to be structured as a succession of roughly stationary phases separated by marked change points that are asynchronous among individuals ii a time varying environmental component assumed to take the form of synchronous fluctuations among individuals and iii an individual component corresponding mainly to the local environment of each tree to identify and characterize these three components we propose to use semi markov switching linear mixed models i e models that combine linear mixed models in a semi markovian manner the underlying semi markov chain represents the succession of growth phases and their lengths endogenous component whereas the linear mixed models attached to each state of the underlying semi markov chain represent in the corresponding growth phase both the influence of time varying climatic covariates environmental component as fixed effects and interindividual heterogeneity individual component as random effects in this article we address the estimation of markov and semi markov switching linear mixed models in a general framework we propose a monte carlo expectation maximization like algorithm whose iterations decompose into three steps i sampling of state sequences given random effects ii prediction of random effects given state sequences and iii maximization the proposed statistical modeling approach is illustrated by the analysis of successive annual shoots along corsican pine trunks influenced by climatic covariates resume d auteur

integral and integrable algorithms for a nonlinear shallow water wave equation an asymptotic higher order model of wave dynamics in shallow water is examined in a combined analytical and numerical study with the aim of establishing robust and efficient numerical solution methods based on the hamiltonian structure of the nonlinear equation an algorithm corresponding to a completely integrable particle lattice is implemented first each particle in the particle method travels along a characteristic curve the resulting system of nonlinear ordinary differential equations can have solutions that blow up in finite time we isolate the conditions for global existence and prove l1 norm convergence of the method in the limit of zero spatial step size and infinite particles the numerical results show that this method captures the essence of the solution without using an overly large number of particles a fast summation algorithm is introduced to evaluate the integrals of the particle method so that the computational cost is reduced from o n2 to o n where n is the number of particles the method possesses some analogies with point vortex methods for 2d euler equations in particular near singular solutions exist and singularities are prevented from occurring in finite time by mechanisms akin to those in the evolution of vortex patches the second method is based on integro differential formulations of the equation two different algorithms are proposed based on different ways of extracting the time derivative of the dependent variable by an appropriately defined inverse operator the integro differential formulations reduce the order of spatial derivatives thereby relaxing the stability constraint and allowing large time steps in an explicit numerical scheme in addition to the cauchy problem on the infinite line we include results on the study of the nonlinear equation posed in the quarter space time plane we discuss the minimum number of boundary conditions required for solution uniqueness and illustrate this with numerical examples

multipeakons and the classical moment problem abstract classical results of stieltjes are used to obtain explicit formulas for the peakon antipeakon solutions of the camassa holm equation the closed form solution is expressed in terms of the orthogonal polynomials of the related classical moment problem it is shown that collisions occur only in peakon antipeakon pairs and the details of the collisions are analyzed using results from the moment problem a sharp result on the steepening of the slope at the time of collision is given asymptotic formulas are given and the scattering shifts are calculated explicitly

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

least squares parameter estimation of continuous time arx models from discrete time data when modeling a system from discrete time data a continuous time parameterization is desirable in some situations in a direct estimation approach the derivatives are approximated by appropriate differences for an arx model this lead to a linear regression the well known least squares method would then be very desirable since it can have good numerical properties and low computational burden in particular for fast or nonuniform sampling it is examined under what conditions a least squares fit for this linear regression will give adequate results for an arx model the choice of derivative approximation is crucial for this approach to be useful standard approximations like euler backward or euler forward cannot be used directly the precise conditions on the derivative approximation are derived and analyzed it is shown that if the highest order derivative is selected with care a least squares estimate will be accurate the theoretical analysis is complemented by some numerical examples which provide further insight into the choice of derivative approximation

on the unique identification of continuous time autoregressive models from sampled data in this work we investigate the relationship between continuous time autoregressive ar models and their sampled version we consider uniform sampling and derive criteria for uniquely determining the continuous time parameters from sampled data the model order is assumed to be known we achieve this by removing a set of measure zero from the collection of all ar models and by investigating the asymptotic behavior of the remaining set of autocorrelation functions we provide necessary and sufficient conditions for uniqueness of general ar models and we demonstrate the usefulness of this result by considering particular examples we further exploit our theory and introduce an estimation algorithm that recovers continuous time ar parameters from sampled data regardless of the sampling interval we demonstrate the usefulness of our algorithm for various gaussian and non gaussian ar processes

diagnostics for mixed model analysis of variance we describe a new method for assessment of model inadequacy in maximum likelihood mixed model analysis of variance in particular we discuss its use in diagnosing perturbations from the usual assumption of constant error variance and from the assumption that each realization of a given random factor has been drawn from the same normal population computer implementation of the procedure is described and an example is presented involving the analysis of filter cartridges used with commercial respirators

a local discontinuous galerkin method for the camassa holm equation in this paper we develop analyze and test a local discontinuous galerkin ldg method for solving the camassa holm equation which contains nonlinear high order derivatives the ldg method has the flexibility for arbitrary h and p adaptivity we prove the l 2 stability for general solutions and give a detailed error estimate for smooth solutions and provide numerical simulation results for different types of solutions of the nonlinear camassa holm equation to illustrate the accuracy and capability of the ldg method

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

a delta least squares lattice algorithm for fast sampling most shift operator based adaptive algorithms exhibit poor numerical behavior when the input discrete time process is obtained from a continuous time process by fast sampling this includes the shift operator based least squares lattice algorithm we develop a delta least squares lattice algorithm this algorithm has a low computational complexity compared with the delta levinson rls algorithm and shows better numerical properties compared with the shift least squares lattice algorithm under fast sampling computer simulations show that the new algorithm also outperforms an existing delta least squares lattice algorithm

bias correction in generalised linear mixed models with a single component of dispersion summary general expressions are derived for the asymptotic biases in three approximate estimators of regression coefficients and variance component for small values of the variance component in generalised linear mixed models with canonical link function and a single source of extraneous variation the estimators involve first and second order laplace expansions of the integrated likelihood and a related procedure known as penalised quasilikelihood numerical studies of a series of matched pairs of binary outcomes show that the first order estimators of the variance component are seriously biased easily computed correction factors produce satisfactory estimators of small variance components comparable to those obtained with a second order laplace expansion and markedly improve the asymptotic performance for larger values for a series of matched pairs of binomial observations the variance correction factors rapidly approach one as the binomial denominators increase these results greatly extend the range of parameter values for which the approximate estimation procedures have satisfactory asymptotic properties

the beta geometric distribution applied to comparative fecundability studies a convenient measure of fecundability is time number of menstrual cycles required to achieve pregnancy couples attempting pregnancy are heterogeneous in their per cycle probability of success if success probabilities vary among couples according to a beta distribution then cycles to pregnancy will have a beta geometric distribution the likelihood ratio test can thus be employed in studies of exposures that may impair fecundability covariates are incorporated in a natural way the model is illustrated by applying it to data on cycles to pregnancy in smokers and nonsmokers with adjustment for covariates summary in fre excerpt

posterior mode estimation by extended kalman filtering for multivariate dynamic generalized linear models abstract a family of multivariate dynamic generalized linear models is introduced as a general framework for the analysis of time series with observations from the exponential family besides common conditionally gaussian models this article deals with univariate models for counted and binary data and as the most interesting multivariate case models for nonstationary multicategorical time series for univariate responses a related yet different class of models has been introduced in a bayesian setting by west harrison and migon assuming conjugate prior posterior distributions for the natural parameter of the exponential family they derive an approximate filter for estimation of time varying states or parameters however their method raises some problems in particular in extending it to the multivariate case a different approach to filtering and smoothing is chosen in this article to avoid a full bayesian analysis based on numerical integration which becomes computationally critical for higher

nonparametric inference in hidden markov models using p splines summary hidden markov models hmms are flexible time series models in which the distribution of the observations depends on unobserved serially correlated states the state dependent distributions in hmms are usually taken from some class of parametrically specified distributions the choice of this class can be difficult and an unfortunate choice can have serious consequences for example on state estimates and more generally on the resulting model complexity and interpretation we demonstrate these practical issues in a real data application concerned with vertical speeds of a diving beaked whale where we demonstrate that parametric approaches can easily lead to overly complex state processes impeding meaningful biological inference in contrast for the dive data hmms with nonparametrically estimated state dependent distributions are much more parsimonious in terms of the number of states and easier to interpret while fitting the data equally well our nonparametric estimation approach is based on the idea of representing the densities of the state dependent distributions as linear combinations of a large number of standardized b spline basis functions imposing a penalty term on non smoothness in order to maintain a good balance between goodness of fit and smoothness

a continuous time linear system identification method for slowly sampled data both direct and indirect methods exist for identifying continuous time linear systems a direct method estimates continuous time input and output signals from their samples and then use them to obtain a continuous time model whereas an indirect method estimates a discrete time model first both methods rely on fast sampling to ensure good accuracy in this paper we propose a more direct method where a continuous time linear model is directly fitted to the available samples this method produces an exact model asymptotically modulo some possible aliasing ambiguity even when the sampling rate is relatively slow we also state conditions under which the aliasing ambiguity can be resolved and we provide experiments showing that the proposed method is a valid option when a slow sampling frequency must be used but a large number of samples is available

global existence and blow up phenomena for the degasperis procesi equation this paper is concerned with several aspects of the existence of global solutions and the formation of singularities for the degasperis procesi equation on the line global strong solutions to the equation are determined for a class of initial profiles on the other hand it is shown that the first blow up can occur only in the form of wave breaking a new wave breaking mechanism for solutions is described in detail and two results of blow up solutions with certain initial profiles are established

global weak solutions and blow up structure for the degasperis procesi equation in this paper we study several qualitative properties of the degasperis procesi equation we first established the precise blow up rate and then determine the blow up set of blow up strong solutions to this equation for a large class of initial data we finally prove the existence and uniqueness of global weak solutions to the equation provided the initial data satisfies appropriate conditions

an energy conserving galerkin scheme for a class of nonlinear dispersive equations a galerkin scheme is presented for a class of conservative nonlinear dispersive equations such as the camassa holm equation and the regularized long wave equation the scheme has two advantageous features first it is conservative in that it keeps the discrete analogue of the continuous energy conservation property in the original equations second it can be formulated only with cheap h 1 elements even if the original equations include third derivative u x x x numerical experiments confirm the stability and effectiveness of the proposed scheme

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

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

bias correction in generalized linear mixed models with multiple components of dispersion abstract general formulas are derived for the asymptotic bias in regression coefficients and variance components estimated by penalized quasi likelihood pql in generalized linear mixed models with canonical link function and multiple sets of independent random effects easily computed correction matrices result in variance component estimates that have satisfactory asymptotic behavior for small values of the variance components and significantly reduce bias for larger values both first order and second order correction procedures are developed for regression coefficients estimated by pql the methods are illustrated through an analysis of an experiment on salamander matings involving crossed male and female random effects and their properties are evaluated in a simulation study

stability of peakons the peakons are peaked solitary wave solutions of a certain nonlinear dispersive equation that is a model in shallow water theory and the theory of hyperelastic rods we give a very simple proof of the orbital stability of the peakons in the h1 norm 2000 john wiley sons inc

multi symplectic integration of the camassa holm equation the camassa holm equation is rich in geometric structures it is completely integrable bi hamiltonian and it represents geodesics for a certain metric in the group of diffeomorphism here two new multi symplectic formulations for the camassa holm equation are presented and the associated local conservation laws are shown to correspond to certain well known hamiltonian functionals the multi symplectic discretisation of each formulation is exemplified by means of the euler box scheme numerical experiments show that the schemes have good conservative properties and one of them is designed to handle the conservative continuation of peakon antipeakon collisions

conjugate priors for exponential families having quadratic variance functions abstract consider a natural exponential family parameterized by it is well known that the standard conjugate prior on is characterized by a condition of posterior linearity for the expectation of the model mean parameter often however this family is not parameterized in terms of but rather in terms of a more usual parameter such at the mean the main question we address is under what conditions does a standard conjugate prior on induce a linear posterior expectation on itself we prove that essentially this happens iff the exponential family has quadratic variance function a consequence of this result is that the standard conjugate on coincides with the prior on induced by the standard conjugate on iff the variance function is quadratic the rest of the article covers more specific issues related to conjugate priors for exponential families in particular we analyze the monotonicity of the expected posterior variance for with respect to the sample size and the hyperparameter

identification of linear continuous time systems under irregular and random output sampling this paper considers the problem of identifiability and parameter estimation of single input single output linear time invariant stable continuous time systems under irregular and random sampling schemes conditions for system identifiability are established under inputs of exponential polynomial types and a tight bound on sampling density identification algorithms of gauss newton iterative types are developed to generate convergent estimates when the sampled output is corrupted by observation noises input design sampling times and convergent algorithms are intertwined persistent excitation pe conditions for strongly convergent algorithms are derived unlike the traditional identification the pe conditions under irregular and random sampling involve both sampling times and input values under the given pe conditions iterative and recursive algorithms are developed to estimate the original continuous time system parameters the corresponding convergence results are obtained several simulation examples are provided to verify the theoretical results

multilevel time series models with applications to repeated measures data the analysis of repeated measures data can be conducted efficiently using a two level random coefficients model a standard assumption is that the within individual level 1 residuals are uncorrelated in some cases especially where measurements are made close together in time this may not be reasonable and this additional correlation structure should also be modelled a time series model for such data is proposed which consists of a standard multilevel model for repeated measures data augmented by an autocorrelation model for the level 1 residuals first and second order autoregressive models are considered in detail together with a seasonal component both discrete and continuous time are considered and it is shown how the autocorrelation parameters can themselves be structured in terms of further explanatory variables the models are fitted to a data set consisting of repeated height measurements on children

multivariate longitudinal data analysis with mixed effects hidden markov models summary multiple longitudinal responses are often collected as a means to capture relevant features of the true outcome of interest which is often hidden and not directly measurable we outline an approach which models these multivariate longitudinal responses as generated from a hidden disease process we propose a class of models which uses a hidden markov model with separate but correlated random effects between multiple longitudinal responses this approach was motivated by a smoking cessation clinical trial where a bivariate longitudinal response involving both a continuous and a binomial response was collected for each participant to monitor smoking behavior a bayesian method using markov chain monte carlo is used comparison of separate univariate response models to the bivariate response models was undertaken our methods are demonstrated on the smoking cessation clinical trial dataset and properties of our approach are examined through extensive simulation studies

estimation in generalized linear models with random effects summary a conceptually very simple but general algorithm for the estimation of the fixed effects random effects and components of dispersion in generalized linear models with random effects is proposed conditions are described under which the algorithm yields approximate maximum likelihood or quasi maximum likelihood estimates of the fixed effects and dispersion components and approximate empirical bayes estimates of the random effects the algorithm is applied to two data sets to illustrate the estimation of components of dispersion and the modelling of overdispersion

stability of peakons for the degasperis procesi equation the degasperis procesi equation can be derived as a member of a oneparameter family of asymptotic shallow water approximations to the euler equations with the same asymptotic accuracy as that of the camassaholm equation in this paper we study the orbital stability problem of the peaked solitons to the degasperis procesi equation on the line by constructing a liapunov function we prove that the shapes of these peakon solitons are stable under small perturbations

random effects models for serial observations with binary response this paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants each subject s serial responses are assumed to arise from a logistic model but with regression coefficients that vary between subjects the logistic regression parameters are assumed to be normally distributed in the population inference is based upon maximum likelihood estimation of fixed effects and variance components and empirical bayes estimation of random effects exact solutions are analytically and computationally infeasible but an approximation based on the mode of the posterior distribution of the random parameters is proposed and is implemented by means of the em algorithm this approximate method is compared with a simpler two step method proposed by korn and whittemore using data from a panel study of asthmatics originally described in that paper one advantage of the estimation strategy described here is the ability to use all of the data including that from subjects with insufficient data to permit fitting of a separate logistic regression model as required by the korn and whittemore method however the new method is computationally intensive

conservative finite difference schemes for the degasperis procesi equation we consider the numerical integration of the degasperis procesi equation which was recently introduced as a completely integrable shallow water equation for the equation we propose nonlinear and linear finite difference schemes that preserve two invariants associated with the bi hamiltonian form of the equation at the same time we also prove the unique solvability of the schemes and show some numerical examples

hierarchical generalized linear models and frailty models with bayesian nonparametric mixing summary this paper proposes bayesian nonparametric mixing for some well known and popular models the distribution of the observations is assumed to contain an unknown mixed effects term which includes a fixed effects term a function of the observed covariates and an additive or multiplicative random effects term typically these random effects are assumed to be independent of the observed covariates and independent and identically distributed from a distribution from some known parametric family this assumption may be suspect if either there is interaction between observed covariates and unobserved covariates or the fixed effects predictor of observed covariates is misspecified another cause for concern might be simply that the covariates affect more than just the location of the mixed effects distribution as a consequence the distribution of the random effects could be highly irregular in modality and skewness leaving parametric families unable to model the distribution adequately this paper therefore proposes a bayesian nonparametric prior for the random effects to capture possible deviances in modality and skewness and to explore the observed covariates effect on the distribution of the mixed effects

a finite difference method for the korteweg de vries and the kadomtsev petviashvili equations a linearized implicit finite difference method for the korteweg de vries equation is proposed and straightforwardly extended to the kadomtsev petviashvili equation we investigate the order of accuracy of the method and prove the method to be unconditionally linearly stable the numerical experiments for the korteweg de vries and the kadomtsev petviashvili equations are carried out with various conditions numerical results for the collision of two lump type solitary wave solutions to the kadomtsev petviashvili equation are also reported

pairwise likelihood inference for nested hidden markov chain models for multilevel longitudinal data in the context of multilevel longitudinal data where sample units are collected in clusters an important aspect that should be accounted for is the unobserved heterogeneity between sample units and between clusters for this aim we propose an approach based on nested hidden latent markov chains which are associated with every sample unit and with every cluster the approach allows us to account for the previously mentioned forms of unobserved heterogeneity in a dynamic fashion it also allows us to account for the correlation that may arise between the responses provided by the units belonging to the same cluster under the assumed model computing the manifest distribution of these response variables is infeasible even with a few units per cluster therefore we make inference on this model through a composite likelihood function based on all the possible pairs of subjects within each cluster properties of the composite likelihood estimator are assessed by simulation the proposed approach is illu

estimation of continuous time autoregressive model from finely sampled data we extend our two earlier continuous time estimation methods for continuous time autoregressive car model to derive estimators using only finely sampled discrete time data the approach is based on the approximation of derivatives by divided differences coupled with some bias correction two types of estimators are provided having bias of the order o h or of o h sup 2 respectively for small sampling interval h the procedures are computationally efficient and always yield a stable autoregressive polynomial simulations show that their bias are quite low

robust empirical bayes analyses of event rates a collection of i similar items generates point event histories for example machines experience failures or operators make mistakes suppose the intervals between events are modeled as iid exponential i or the counts as poisson i t i for the ith item furthermore so as to represent between item variability each individual rate parameter i is presumed drawn from a fixed super population with density g being a vector parameter a parametric empirical bayes peb setup for g specified alternatively as log student t n or gamma we exhibit the results of numerical procedures for estimating superpopulation parameters ll and for describing pooled estimates of the individual rates i obtained via bayes s formula three data sets are analyzed and convenient explicit approximate formulas are furnished for i estimates in the student t case the individual estimates are seen to have a robust quality