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

sur la presentation des representations supersingulieres de mathrm gl _2 f soit f une extension quadratique de mathbb q p nous prouvons que les representations lisses irreductibles supersingulieres a caractere central de mathrm gl 2 f ne sont pas de presentation finie

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

explicit description of irreducible gl2 qp representations over f p let p be an odd prime number the classi cation of irreducible representations of gl2 qp over fp is known thanks to the works of barthel livne and breuil in the present paper we illustrate an exhaustive description of such irreducible representations through the study of certain functions on the bruhat tits tree of gl2 qp in particular we are able to detect the socle ltration for the kz restriction of supersingular representations principal series and special series

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

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

complete analysis of phase transitions and ensemble equivalence for the curie weiss potts model using the theory of large deviations we analyze the phase transition structure of the curie weiss potts spin model which is a mean field approximation to the nearest neighbor potts model it is equivalent to the potts model on the complete graph on n vertices the analysis is carried out both for the canonical ensemble and the microcanonical ensemble besides giving explicit formulas for the microcanonical entropy and for the equilibrium macrostates with respect to the two ensembles we analyze ensemble equivalence and nonequivalence at the level of equilibrium macrostates relating these to concavity and support properties of the microcanonical entropy the curie weiss potts model is the first statistical mechanical model for which such a detailed and rigorous analysis has been carried out

chaos butterflies also generate phase transitions we exhibit examples of mixing subshifts of finite type and of continuous potentials such that there are phase transitions but the pressure is always strictly convex more surprisingly we show that the pressure can be analytic on some interval although there exist several equilibrium states

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

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

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

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

iwahori hecke model for supersingular representations of gl2 qp abstract in this paper we realize a regular supersingular representation of gl 2 q p as a quotient of a representation induced from the iwahori subgroup of gl 2 q p we also show that this realization provides a uniform way of looking at all the self extensions of which have a four dimensional space of i 1 invariants

on the breuil mezard conjecture we give a new local proof of the breuil mezard conjecture for 2 dimensional representations of the absolute galois group of qp when p 5 and the representation has scalar endomorphisms

local product structure for equilibrium states the usual way to study the local structure of equilibrium state of an axioma diffeomorphism or flow is to use the symbolic dynamic and to push results on the manifold a new geometrical method is given it consists in proving that equilibrium states for holder continuous functions are related to other equilibrium states of some special sub systems satisfying a sort of expansiveness using different kinds of extensions the local product structure of gibbs measure is proven

a canonical torsion theory for pro p iwahori hecke modules abstract let f be a locally compact nonarchimedean field with residue characteristic p and g the group of f rational points of a connected split reductive group over f we define a torsion pair in the category mod h of modules over the pro p iwahori hecke k algebra h of g where k is an arbitrary field we prove that under a certain hypothesis the torsionfree class embeds fully faithfully into the category mod i g of smooth k representations of g generated by their pro p iwahori fixed vectors if the characteristic of k is different from p then this hypothesis is always satisfied and the torsionfree class is the whole category mod h if k contains the residue field of f then we study the case g s l 2 f we show that our hypothesis is satisfied and we describe explicitly the torsionfree and the torsion classes if f q p and p 2 then an h module is in the torsion class if and only if it is a union of supersingular finite length submodules it lies in the torsionfree class if and only if it does not contain any nonzero supersingular finite length module if f q p the torsionfree class is the whole category mod h and we give a new proof of the fact that mod h is equivalent to mod i g these results are based on the computation of the h module structure of certain natural cohomology spaces for the pro p iwahori subgroup i of g

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

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 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

low temperature phase transitions in the quadratic family abstract we give the first example of a quadratic map having a phase transition after the first zero of the geometric pressure function this implies that several dimension spectra and large deviation rate functions associated to this map are not expected to be real analytic in contrast to the uniformly hyperbolic case the quadratic map we study has a non recurrent critical point so it is non uniformly hyperbolic in a strong sense

renormalisation induced phase transitions for unimodal maps the thermodynamical formalism is studied for renormalisable maps of the interval and the natural potential t log df multiple and indeed infinitely many phase transitions at positive t can occur for some quadratic maps all unimodal quadratic maps with positive topological entropy exhibit a phase transition in the negative spectrum

a satake isomorphism for representations modulo p of reductive groups over local fields let f be a local field with finite residue field of characteristic p let g be a connected reductive group over f and b a minimal parabolic subgroup of g with levi decomposition b zu let k be a special parabolic subgroup of g in good position relative to z u fix an absolutely irreducible smooth representation of k on a vector space v over some field c of characteristic p writing h g k v for the intertwining hecke algebra of v in g we define a natural algebra homomorphism from h g k v to h z z k v u k we show it is injective and identify its image we thus generalize work of f herzig who assumed f of characteristic 0 g unramified and k hyperspecial and took for c an algebraic closure of the prime field fp we show that in the general case h g k v need not be commutative that is in contrast with the cases herzig considers and with the more classical situation where v is trivial and the field of coefficients is the field of complex numbers

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

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

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

regularity properties and pathologies of position space renormalization group transformations scope and limitations of gibbsian theory we reconsider the conceptual foundations of the renormalization group rg formalism and prove some rigorous theorems on the regularity properties and possible pathologies of the rg map our main results apply to local in position space rg maps acting on systems of bounded spins compact single spin space regarding regularity we show that the rg map defined on a suitable space of interactions formal hamiltonians is always single valued and lipschitz continuous on its domain of definition this rules out a recently proposed scenario for the rg description of first order phase transitions on the pathological side we make rigorous some arguments of griffiths pearce and israel and prove in several cases that the renormalized measure is not a gibbs measure for any reasonable interaction this means that the rg map is ill defined and that the conventional rg description of first order phase transitions is not universally valid for decimation or kadanoff transformations applied to the ising model in dimension d 3 these pathologies occur in a full neighborhood 0 h e of the low temperature part of the first order phase transition surface for block averaging transformations applied to the ising model in dimension d 2 the pathologies occur at low temperatures for arbitrary magnetic field strength pathologies may also occur in the critical region for ising models in dimension d 4 we discuss the heuristic and numerical evidence on rg pathologies in the light of our rigorous theorems in addition we discuss critically the concept of gibbs measure which is at the heart of present day classical statistical mechanics we provide a careful and we hope pedagogical overview of the theory of gibbsian measures as well as the less familiar non gibbsian measures emphasizing the distinction between these two objects and the possible occurrence of the latter in different physical situations we give a rather complete catalogue of the known examples of such occurrences the main message of this paper is that despite a well established tradition gibbsiannessshould not be taken for granted

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

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

generic frechet differentiability of the pressure in certain lattice systems this note has two goals the first is to give an explicit description theorem 1 of the duals of certain weighted products h of a countable family of banach spaces these products include the usual spaces of interactions which arise in statistical mechanics the second goal is to use this description to prove that if the factor spaces are finite dimensional and the weight functionh satisfies a certain growth condition then the pressure is frechet differentiable wherever it is gateaux differentiable hence is frechet differentiable in a denseg subset

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

on the universal mod p supersingular quotients for gl2 f over f p for a general f qp abstract let f q p be a finite extension we explore the universal supersingular mod p representations of gl 2 f by computing a basis for their spaces of invariants under the pro p iwahori subgroup this generalizes works of breuil and schein from q p and the totally ramified cases to an arbitrary extension f q p using these results we then construct for an unramified f q p quotients of the universal supersingular modules which have as quotients all the supersingular representations of gl 2 f with a gl 2 o f socle that is expected to appear in the mod p local langlands correspondence a construction in the case of an extension of q p with inertia degree 2 and suitable ramification index is also presented