an extended hazard model with longitudinal covariates summary in clinical trials and other medical studies it has become increasingly common to observe an event time of interest and longitudinal covariates simultaneously in the literature joint modelling approaches have been employed to analyze both survival and longitudinal processes and to investigate their association early attention has mostly been placed on developing adaptive and flexible longitudinal processes based on a prespecified survival model most commonly the cox proportional model in this paper we propose a general class of semi parametric hazard regres

a mixed mover stayer model for spatiotemporal two state processes studies of recurring infection or chronic disease often collect longitudinal data on the disease status of subjects two state transitional models are useful for analysis in such studies where at any point in time an individual may be said to occupy either a diseased or disease free state and interest centers on the transition process between states here two additional features are present the data are spatially arranged and it is important to account for spatial correlation in the transitional processes corresponding to different subjects in addition there are subgroups of individuals with different mechanisms of transitions these subgroups are not known a priori and hence group membership must be estimated covariates modulating transitions are included in a logistic additive framework inference for the resulting mixture spatial markov regression model is not straightforward we develop here a monte carlo expectation maximization algorithm for maximum likelihood estimation and a markov chain monte carlo sampling scheme for summarizing the posterior distribution in a bayesian analysis the methodology is applied to a study of recurrent weevil infestation in british columbia forests

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

semiparametric efficient estimation for shared frailty models with doubly censored clustered data in this paper we investigate frailty models for clustered survival data that are subject to both left and right censoring termed doubly censored data this model extends current survival literature by broadening the application of frailty models from right censoring to a more complicated situation with additional left censoring our approach is motivated by a recent hepatitis b study where the sample consists of families we adopt a likelihood approach that aims at the nonparametric maximum likelihood estimators npmle a new algorithm is proposed which not only works well for clustered data but also improve over existing algorithm for independent and doubly censored data a special case when the frailty variable is a constant equal to one this special case is well known to be a computational challenge due to the left censoring feature of the data the new algorithm not only resolves this challenge but also accommodate the additional frailty variable effectively asymptotic properties of the npmle are established along with semi parametric efficiency of the npmle for the finite dimensional parameters the consistency of bootstrap estimators for the standard errors of the npmle is also discussed we conducted some simulations to illustrate the numerical performance and robustness of the proposed algorithm which is also applied to the hepatitis b data

maximum likelihood variance components estimation for binary data abstract we consider a class of probit normal models for binary data and describe ml and reml estimation of variance components for that class as well as best prediction for the realized values of the random effects ml estimates are calculated using an em algorithm for complicated models em includes a gibbs step the computations are illustrated through two examples

on the applicability of regenerative simulation in markov chain monte carlo we consider the central limit theorem and the calculation of asymptotic standard errors for the ergodic averages constructed in markov chain monte carlo chan geyer 1994 established a central limit theorem for ergodic averages by assuming that the underlying markov chain is geometrically ergodic and that a simple moment condition is satisfied while it is relatively straightforward to check chan geyer s conditions their theorem does not lead to a consistent and easily computed estimate of the variance of the asymptotic normal distribution conversely mykland et al 1995 discuss the use of regeneration to establish an alternative central limit theorem with the advantage that a simple consistent estimator of the asymptotic variance is readily available however their result assumes a pair of unwieldy moment conditions whose verification is difficult in practice in this paper we show that the conditions of chan geyer s theorem are sufficient to establish the central limit theorem of mykland et al this result in conjunction with other recent developments should pave the way for more widespread use of the regenerative method in markov chain monte carlo our results are illustrated in the context of the slice sampler

a monte carlo implementation of the em algorithm and the poor man s data augmentation algorithms abstract the first part of this article presents the monte carlo implementation of the e step of the em algorithm given the current guess to the maximizer of the posterior distribution latent data patterns are generated from the conditional predictive distribution the expected value of the augmented log posterior is then updated as a mixture of augmented log posteriors mixed over the generated latent data patterns multiple imputations in the m step of the algorithm this mixture is maximized to obtain the update to the maximizer of the observed posterior the gradient and hessian of the observed log posterior are also expressed as mixtures mixed over the multiple imputations the relation between the monte carlo em mcem algorithm and the data augmentation algorithm is noted two modifications to the mcem algorithm the poor man s data augmentation algorithms which allow for the calculation of the entire posterior are then presented these approximations serve as diagnostics for the validity o

ascent based monte carlo expectation maximization summary the expectation maximization em algorithm is a popular tool for maximizing likelihood functions in the presence of missing data unfortunately em often requires the evaluation of analytically intractable and high dimensional integrals the monte carlo em mcem algorithm is the natural extension of em that employs monte carlo methods to estimate the relevant integrals typically a very large monte carlo sample size is required to estimate these integrals within an acceptable tolerance when the algorithm is near convergence even if this sample size were known at the onset of implementation of mcem its use throughout all iterations is wasteful especially when accurate starting values are not available we propose a data driven strategy for controlling monte carlo resources in mcem the algorithm proposed improves on similar existing methods by recovering em s ascent i e likelihood increasing property with high probability being more robust to the effect of user defined inputs and handling classical monte carlo and markov chain monte carlo methods within a common framework because of the first of these properties we refer to the algorithm as ascent based mcem we apply ascent based mcem to a variety of examples including one where it is used to accelerate the convergence of deterministic em dramatically

on quasilinear non uniformly parabolic equations in general form abstract the present paper is concerned with the first boundary value problem for a certain class of quasilinear non uniformly parabolic equations new a priori estimates of the solution and of its gradient are obtained these are independent of the smoothness of the coefficients existence and uniqueness theorems are proved

on the convergence of monte carlo maximum likelihood calculations summary monte carlo maximum likelihood for normalized families of distributions can be used for an extremely broad class of models given any family he 0 e 0 of non negative integrable functions maximum likelihood estimates in the family obtained by normalizing the functions to integrate to 1 can be approximated by monte carlo simulation the only regularity conditions being a compactification of the parameter space such that the evaluation maps 0 h0 x remain continuous then with probability 1 the monte carlo approximant to the log likelihood hypoconverges to the exact log likelihood its maximizer converges to the exact maximum likelihood estimate approximations to profile likelihoods hypoconverge to the exact profile and level sets of the approximate likelihood support regions converge to the exact sets in painleve kuratowski set convergence the same results hold when there are missing data if a wald type integrability condition is satisfied asymptotic normality of the monte carlo error and convergence of the monte carlo approximation to the observed fisher information are also shown

a correlated probit model for joint modeling of clustered binary and continuous responses a difficulty in joint modeling of continuous and discrete response variables is the lack of a natural multivariate distribution for joint modeling of clustered observations on binary and continuous responses we study a correlated probit model that has an underlying normal latent variable for the binary responses catalano and ryan have factored the model into a marginal and a conditional component and used generalized estimating equations methodology to estimate the effects we propose a monte carlo expectation conditional maximization algorithm for finding maximum likelihood estimates of the mixed model itself extending and accelerating an algorithm for models with binary responses we demonstrate the methodology with a developmental toxicity study measuring fetal weight and a binary malformation status for several litters of mice a simulation study suggests that efficiency gains of joint fittings over separate fittings of the response variables occur mainly for small datasets with strong correlation

publication bias and meta analysis for 2x2 tables an average markov chain monte carlo em algorithm summary a major difficulty in meta analysis is publication bias studies with positive outcomes are more likely to be published than studies reporting negative or inconclusive results correcting for this bias is not possible without making untestable assumptions in this paper a sensitivity analysis is discussed for the meta analysis of 2 2 tables using exact conditional distributions a markov chain monte carlo em algorithm is used to calculate maximum likelihood estimates a rule for increasing the accuracy of estimation and automating the choice of the number of iterations is suggested

variable selection in a log linear birnbaum saunders regression model for high dimensional survival data via the elastic net and stochastic em the birnbaum saunders bs distribution is broadly used to model failure times in reliability and survival analysis in this article we propose a simultaneous parameter estimation and variable selection procedure in a log linear bs regression model for high dimensional survival data to deal with censored survival data we iteratively run a combination of the stochastic em algorithm sem and variable selection procedure to generate pseudo complete data and select variables until convergence treating pseudo complete data as uncensored data via sem makes it possible to incorporate iterative penalized least squares and simplify computation we demonstrate the efficacy of our method using simulated and real datasets

empirical supremum rejection sampling reference stat article 2002 003doi 10 1093 biomet 89 4 745view record in web of science record created on 2006 04 21 modified on 2017 05 12

maximizing generalized linear mixed model likelihoods with an automated monte carlo em algorithm summary two new implementations of the em algorithm are proposed for maximum likelihood fitting of generalized linear mixed models both methods use random independent and identically distributed sampling to construct monte carlo approximations at the e step one approach involves generating random samples from the exact conditional distribution of the random effects given the data by rejection sampling using the marginal distribution as a candidate the second method uses a multivariate t importance sampling approximation in many applications the two methods are complementary rejection sampling is more efficient when sample sizes are small whereas importance sampling is better with larger sample sizes monte carlo approximation using random samples allows the monte carlo error at each iteration to be assessed by using standard central limit theory combined with taylor series methods specifically we construct a sandwich variance estimate for the maximizer at each approximate e step this suggests a rule for automatically increasing the monte carlo sample size after iterations in which the true em step is swamped by monte carlo error in contrast techniques for assessing monte carlo error have not been developed for use with alternative implementations of monte carlo em algorithms utilizing markov chain monte carlo e step approximations three different data sets including the infamous salamander data of mccullagh and nelder are used to illustrate the techniques and to compare them with the alternatives the results show that the methods proposed can be considerably more efficient than those based on markov chain monte carlo algorithms however the methods proposed may break down when the intractable integrals in the likelihood function are of high dimension

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

modeling the random effects covariance matrix for longitudinal data with covariates measurement error longitudinal data occur frequently in practice such as medical studies and life sciences generalized linear mixed models glmms are commonly used to analyze such data it is typically assumed that the random effects covariance matrix is constant among subjects in these models in many situations however the correlation structure may differ among subjects and ignoring this heterogeneity can lead to biases in model parameters estimate recently lee et al developed a heterogeneous random effects covariance matrix for glmms for error free covariates covariates measured with error also happen frequently in the longitudinal data set up eg blood pressure and cholesterol level ignoring this issue in the data may produce bias in model parameters estimate and lead to wrong conclusions in this paper we propose an approach to properly model the random effects covariance matrix based on covariates in the class of glmms where we also have covariates measured with error the resulting parameters from the decomposition of random effects covariance matrix have a sensible interpretation and can be easily modeled without the concern of positive definiteness of the resulting estimator the performance of the proposed approach is evaluated through simulation studies which show that the proposed method performs very well in terms of bias mean squared error and coverage rate an application of the proposed method is also provided using a longitudinal data from manitoba follow up study

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

network inference from co occurrences the discovery of networks is a fundamental problem arising in numerous fields of science and technology including communication systems biology sociology and neuroscience unfortunately it is often difficult or impossible to obtain data that directly reveal network structure and so one must infer a network from incomplete data this paper considers inferring network structure from co occurrence data observations that identify which network components e g switches routers genes carry each transmission but do not indicate the order in which they handle the transmission without order information the number of networks that are consistent with the data grows exponentially with the size of the network i e the number of nodes yet the basic engineering evolutionary principles underlying most networks strongly suggest that not all data consistent networks are equally likely in particular nodes that co occur in many observations are probably closely connected with this in mind we model the co occurrence observations as independent realizations of a random walk on the network subjected to a random permutation to account for the lack of order information treating permutations as missing data we derive an expectation maximization em algorithm for estimating the random walk parameters the model and em algorithm significantly simplify the problem but the computational complexity of the reconstruction process does grow exponentially in the length of each transmission path for networks with long paths the exact e step may be computationally intractable we propose a polynomial time monte carlo em algorithm based on importance sampling and derive conditions that ensure convergence of the algorithm with high probability simulations and experiments with internet measurements demonstrate the promise of this approach

improving estimates of genetic maps a maximum likelihood approach as a result of previous large multipoint linkage studies there is a substantial amount of existing marker data due to the increased sample size genetic maps estimated from these data could be more accurate than publicly available maps however current methods for map estimation are restricted to data sets containing pedigrees with a small number of individuals or cannot make full use of marker data that are observed at several loci on members of large extended pedigrees in this article a maximum likelihood ml method for map estimation that can make full use of the marker data in a large multipoint linkage study is described the method is applied to replicate sets of simulated marker data involving seven linked loci and pedigree structures based on the real multipoint linkage study of abkevich et al 2003 american journal of human genetics 73 1271 1281 the variance of the ml estimate is accurately estimated and tests of both simple and composite null hypotheses are performed an efficient procedure for combining map estimates over data sets is also suggested

consistent results on life abstract the findings presented by bennett and bourzutschky that the cellular automaton game of life is not self organized critical which was earlier suggested by bak et al have been questioned most recently by alstrom and leao the reason for this is that the two groups used systems with different boundary conditions and measured different properties we measure the same properties as bak et al and find that the power law seen for smaller lattices disappears for larger lattices the conclusion is that the game of life is subcritical but with a rather long length scale

acceleration of stochastic approximation by averaging a new recursive algorithm of stochastic approximation type with the averaging of trajectories is investigated convergence with probability one is proved for a variety of classical optimization and identification problems it is also demonstrated for these problems that the proposed algorithm achieves the highest possible rate of convergence

learning bayesian network parameters under equivalence constraints we propose a principled approach for learning parameters in bayesian networks from incomplete datasets where the examples of a dataset are subject to equivalence constraints these equivalence constraints arise from datasets where examples are tied together in that we may not know the value of a particular variable but whatever that value is we know it must be the same across different examples we formalize the problem by defining the notion of a constrained dataset and a corresponding constrained likelihood that we seek to optimize we further propose a new learning algorithm that can effectively learn more accurate bayesian networks using equivalence constraints which we demonstrate empirically moreover we highlight how our general approach can be brought to bear on more specialized learning tasks such as those in semi supervised clustering and topic modeling where more domain specific approaches were previously developed

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

regeneration in markov chain samplers abstract markov chain sampling has recently received considerable attention in particular in the context of bayesian computation and maximum likelihood estimation this article discusses the use of markov chain splitting originally developed for the theoretical analysis of general state space markov chains to introduce regeneration into markov chain samplers this allows the use of regenerative methods for analyzing the output of these samplers and can provide a useful diagnostic of sampler performance the approach is applied to several samplers including certain metropolis samplers that can be used on their own or in hybrid samplers and is illustrated in several examples