markov chain monte carlo methods for switching diffusion models reversible jump metropolis hastings updating schemes can be used to analyse continuous time latent models sometimes known as state space models or hidden markov models we consider models where the observed process x can be represented as a stochastic differential equation and where the latent process d is a continuous time markov chain we develop markov chain monte carlo methods for analysing both markov and non markov versions of these models as an illustration of how these methods can be used in practice we analyse data from the new york mercantile exchange oil market in addition we analyse data generated by a process that has linear and mean reverting states

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

modelling spatially correlated data via mixtures a bayesian approach the paper develops mixture models for spatially indexed data we confine attention to the case of finite typically irregular patterns of points or regions with prescribed spatial relationships and to problems where it is only the weights in the mixture that vary from one location to another our specific focus is on poisson distributed data and applications in disease mapping we work in a bayesian framework with the poisson parameters drawn from gamma priors and an unknown number of components we propose two alternative models for spatially dependent weights based on transformations of autoregressive gaussian processes in one the logistic normal model the mixture component labels are exchangeable in the other the grouped continuous model they are ordered reversible jump markov chain monte carlo algorithms for posterior inference are developed finally the performances of both of these formulations are examined on synthetic data and real data on mortality from a rare disease

hidden markov models and disease mapping we present new methodology to extend hidden markov models to the spatial domain and use this class of models to analyze spatial heterogeneity of count data on a rare phenomenon this situation occurs commonly in many domains of application particularly in disease mapping we assume that the counts follow a poisson model at the lowest level of the hierarchy and introduce a finite mixture model for the poisson rates at the next level the novelty lies in the model for allocation to the mixture components which follows a spatially correlated process the potts model and in treating the number of components of the spatial mixture as unknown inference is performed in a bayesian framework using reversible jump markov chain monte carlo the model introduced can be viewed as a bayesian semiparametric approach to specifying flexible spatial distribution in hierarchical models performance of the model and comparison with an alternative well known markov random field specification for the poisson rates are de

asymptotically regular problems i higher integrability abstract we consider weak solutions u of non linear systems of partial differential equations assuming that the system exhibits a certain kind of elliptic behavior near infinity we prove higher integrability results for the gradient du in particular we establish holder continuity of u in low dimensions moreover we obtain analogous results for vectorial minimizers of multi dimensional variational integrals finally we discuss an extension to minimizing sequences and applications to generalized minimizers

goal programming models and their duality relations for use in evaluating security portfolio and regression relations abstract the literature on multiple objective programming contains numerous examples in which goal programming is used to plan a selection of inputs to secure desired outputs that will conform as closely as possible to a collection of possibly conflicting objectives in this paper the orientation is changed from selection to evaluation and the dual variables associated with goal programming are brought into play for this purpose the body of the paper is devoted to an example in portfolio planning modelled along lines like those used by konno and yamazaki where closeness to risk and return objective is measured in sums of absolute deviations an appendix then shows how such a use of dual variables may be applied to evaluate least absolute value lav regressions relative to their sensitivity to data variations simple numerical examples are used to illustrate the potential uses of these dual variable values for evaluation in more complex situations that include determining whether an efficiency frontier has been attained

dealing with label switching in mixture models summary in a bayesian analysis of finite mixture models parameter estimation and clustering are sometimes less straightforward than might be expected in particular the common practice of estimating parameters by their posterior mean and summarizing joint posterior distributions by marginal distributions often leads to nonsensical answers this is due to the so called label switching problem which is caused by symmetry in the likelihood of the model parameters a frequent response to this problem is to remove the symmetry by using artificial identifiability constraints we demonstrate that this fails in general to solve the problem and we describe an alternative class of approaches relabelling algorithms which arise from attempting to minimize the posterior expected loss under a class of loss functions we describe in detail one particularly simple and general relabelling algorithm and illustrate its success in dealing with the label switching problem on two examples

a hierarchical ornstein uhlenbeck model for continuous repeated measurement data in this paper we present a diffusion model for the analysis of continuous time change in multivariate longitudinal data the central idea is to model the data from a single person with an ornstein uhlenbeck diffusion process we extend it hierarchically by allowing the parameters of the diffusion process to vary randomly over different persons with this approach both intra and interindividual differences are analyzed simultaneously furthermore the individual difference parameters can be regressed on covariates thereby providing an explanation of between person differences unstructured and unbalanced data pose no problem for the model to be applied we demonstrate the method on data from an experience sampling study to investigate changes in the core affect it can be concluded that different factors from the five factor model of personality are related to features of the trajectories in the core affect space such as the cross correlation and variability of the changes

sharp regularity for the degenerate doubly nonlinear parabolic equation abstract the aim of this paper is to provide sharp regularity estimates for locally bounded solutions of the degenerate doubly nonlinear parabolic equation u t div m u m 1 d u p 2 d u f where m 1 p 2 and f l q r more precisely we show that solutions are locally of class c 0 where depends explicitly only on the optimal holder exponent for solutions of the homogeneous case the integrability of f in space and time and the nonlinearity parameters p and m

the influence curve approach in data envelopment analysis the behavior of efficiency in the stochastic dea model is examined here in terms of the influence curve approach which quantifies the influence of observed data on the empirical fit of the production frontier data influence is analyzed here through robustness two types of robustness and sensitivity issues are analyzed here in terms of a a new class of minimax measures and b a set nonlinear efficiency measures and it is shown through empirical applications that in suitable cases these measures outperform the conventional ones

asymptotic normality of the maximum likelihood estimator for general hidden markov models hidden markov models hmms have during the last decade become a widespread tool for modeling sequences of dependent random variables inference for such models is usually based on the maximum likelihood estimator mle and consistency of the mle for general hmms was recently proved by leroux in this paper we show that under mild conditions the mle is also asymptotically normal and prove that the observed information matrix is a consistent estimator of the fisher information

discrete and continuous time probabilistic models and algorithms for inferring neuronal up and down states up and down states the periodic fluctuations between increased and decreased spiking activity of a neuronal population are a fundamental feature of cortical circuits understanding up down state dynamics is important for understanding how these circuits represent and transmit information in the brain to date limited work has been done on characterizing the stochastic properties of up down state dynamics we present a set of markov and semi markov discrete and continuous time probability models for estimating up and down states from multiunit neural spiking activity we model multiunit neural spiking activity as a stochastic point process modulated by the hidden up and down states and the ensemble spiking history we estimate jointly the hidden states and the model parameters by maximum likelihood using an expectation maximization em algorithm and a monte carlo em algorithm that uses reversible jump markov chain monte carlo sampling in the e step we apply our models and algorithms in the analysis of both simulated multiunit spiking activity and actual multi unit spiking activity recorded from primary somatosensory cortex in a behaving rat during slow wave sleep our approach provides a statistical characterization of up down state dynamics that can serve as a basis for verifying and refining mechanistic descriptions of this process

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

markov chains for exploring posterior distributions several markov chain methods are available for sampling from a posterior distribution two important examples are the gibbs sampler and the metropolis algorithm in addition several strategies are available for constructing hybrid algorithms this paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues on the theoretical side results from the theory of general state space markov chains can be used to obtain convergence rates laws of large numbers and central limit theorems for estimates obtained from markov chain methods these theoretical results can be used to guide the construction of more efficient algorithms for the practical use of markov chain methods standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation

a stochastic model for the analysis of bivariate longitudinal aids data we present a model for multivariate repeated measures that incorporates random effects correlated stochastic processes and measurement errors the model is a multivariate generalization of the model for univariate longitudinal data given by taylor cumberland and sy 1994 journal of the american statistical association 89 727 736 the stochastic process used in this paper is the multivariate integrated ornstein uhlenbeck ou process which includes brownian motion and a random effects model as special limiting cases this process is an underlying continuous time autoregressive order ar 1 process for the derivatives of the multivariate observations the model allows unequally spaced observations and missing values for some of the variables we analyze cd4 t cell and beta 2 microglobulin measurements of the seroconverters at multiple time points from the los angeles section of the multicenter aids cohort study the model allows us to investigate the relationship between cd4 and beta 2 microglobulin through the correlations between their random effects and their serial correlation the data suggest that cd4 and beta 2 microglobulin follow a bivariate brownian motion process the fit of the model implies that an increase in beta 2 microglobulin is associated with a decrease in future cd4 but not vice versa agreeing with immunologic postulates about the relationship between these two variables

recursive computing and simulation free inference for general factorizable models summary we illustrate how the recursive algorithm of reeves pettitt 2004 for general factorizable models can be extended to allow exact sampling maximization of distributions and computation of marginal distributions all of the methods we describe apply to discrete valued markov random fields with nearest neighbour integrations defined on regular lattices in particular we illustrate that exact inference can be performed for hidden autologistic models defined on moderately sized lattices in this context we offer an extension of this methodology which allows approximate inference to be carried out for larger lattices without resorting to simulation techniques such as markov chain monte carlo in particular our work offers the basis for an automatic inference machine for such models

infinite factorial unbounded state hidden markov model there are many scenarios in artificial intelligence signal processing or medicine in which a temporal sequence consists of several unknown overlapping independent causes and we are interested in accurately recovering those canonical causes factorial hidden markov models fhmms present the versatility to provide a good fit to these scenarios however in some scenarios the number of causes or the number of states of the fhmm cannot be known or limited a priori in this paper we propose an infinite factorial unbounded state hidden markov model ifuhmm in which the number of parallel hidden markovmodels hmms and states in each hmm are potentially unbounded we rely on a bayesian nonparametric bnp prior over integer valued matrices in which the columns represent the markov chains the rows the time indexes and the integers the state for each chain and time instant first we extend the existent infinite factorial binary state hmm to allow for any number of states then we modify this model to allow for an unbounded number of states and derive an mcmc based inference algorithm that properly deals with the trade off between the unbounded number of states and chains we illustrate the performance of our proposed models in the power disaggregation problem

properties of the maximum a posteriori path estimator in hidden markov models a hidden markov model hmm consists of a nonobservable markov chain x x0 x1 and a measured process y y 0 y1 whose distribution is determined by x to estimate the hidden path of x up to time n x0 x1 xn by the observations y 0 y1 yn usually the maximum a posteriori probability path estimator map path estimator is applied an effective means for calculating this estimator is the viterbi algorithm which is widely employed in the fields of coding theory correction of intersymbol interference and text recognition here properties of the map estimator are derived under a certain condition c it is shown that the limiting process u u0 u1 is a regenerative process particularly this means that u has an asymptotic distribution satisfies the central limit theorem and possesses a mean error furthermore condition c is satisfied for a broad class of hmms including the most important case for applications the hmm with additive white gaussian noise

a flexible prior distribution for markov switching autoregressions with student t errors this paper proposes an empirical bayes approach for markov switching autoregressions that can constrain some of the state dependent parameters regression coefficients and error variances to be approximately equal across regimes by flexibly reducing the dimension of the parameter space this can help to ensure regime separation and to detect the markov switching nature of the data the permutation sampler with a hierarchical prior is used for choosing the prior moments the identification constraint and the parameters governing prior state dependence the empirical relevance of the methodology is illustrated with an application to quarterly and monthly real interest rate data

bayesian inference in hidden markov models through the reversible jump markov chain monte carlo method hidden markov models form an extension of mixture models which provides a flexible class of models exhibiting dependence and a possibly large degree of variability we show how reversible jump markov chain monte carlo techniques can be used to estimate the parameters as well as the number of components of a hidden markov model in a bayesian framework we employ a mixture of zero mean normal distributions as our main example and apply this model to three sets of data from finance meteorology and geomagnetism

measuring efficiency by a fuzzy statistical approach methods of measuring economic efficiency of input output systems by employing a fuzzy statistical approach are explored here in the context of the recent technique of data envelopment analysis which utilizes a nonparametric approach to measure efficiency three applied fuzzy measures are illustrated here e g fuzzy linear programs fuzzy linear regressions and finally the fuzzy entropy measures in the context of a two person game theory model

a fuzzy systems approach in data envelopment analysis abstract the use of fuzzy set theoretic measures is explored here in the context of data envelopment analysis which utilizes a nonparametric approach to measure efficiency three types of fuzzy statics are employed here e g fuzzy mathematical programme fuzzy regression and fuzzy entropy to illustrate the types of decisions and solutions that are achievable when the data are vague and prior information is inexact and imprecise

a statistical test for detecting influential observations in dea this paper deals with the problem of detecting influential observations in deterministic nonparametric dea models the technique we present is intended to classify for a further analysis those sample observations considerably affecting the measured efficiency for the remaining units then the analyst will have to check whether these observations are contaminated by data errors or not this approach also allows to determine when efficiency changes due to the presence of a given unit in the sample are statistically significant thus ours is a statistical alternative to approach the problem of detecting influential observations in deterministic nonparametric dea models

bayesian estimation of switching arma models abstract switching arma processes have recently appeared as an efficient modelling to nonlinear time series models because they can represent multiple or heterogeneous dynamics through simple components the levels of dependence between the observations are double at a first level the parameters of the model are selected by a markovian procedure at a second level the next observation is generated according to a standard time series model when the model involves a moving average structure the complexity of the resulting likelihood function is such that simulation techniques like those proposed by shephard 1994 biometrika 81 115 131 and billio and monfort 1998 journal of statistical planning and inference 68 65 103 are necessary to derive an inference on the parameters of the model we propose in this paper a bayesian approach with a non informative prior distribution developed in mengersen and robert 1996 bayesian statistics 5 oxford university press oxford pp 255 276 and robert and titterington 1998 statistics and computing 8 2 145 158 in the setup of mixtures of distributions and hidden markov models respectively the computation of the bayes estimates relies on mcmc techniques which iteratively simulate missing states innovations and parameters until convergence the performances of the method are illustrated on several simulated examples this work also extends the papers by chib and greenberg 1994 journal of econometrics 64 183 206 and chib 1996 journal of econometrics 75 1 79 97 which deal with arma and hidden markov models respectively

reversible jump birth and death and more general continuous time markov chain monte carlo samplers reversible jump methods are the most commonly used markov chain monte carlo tool for exploring variable dimension statistical models recently however an alternative approach based on birth and death processes has been proposed by stephens for mixtures of distributions we show that the birth and death setting can be generalized to include other types of continuous time jumps like split and combine moves in the spirit of richardson and green we illustrate these extensions both for mixtures of distributions and for hidden markov models we demonstrate the strong similarity of reversible jump and continuous time methodologies by showing that on appropriate rescaling of time the reversible jump chain converges to a limiting continuous time birth and death process a numerical comparison in the setting of mixtures of distributions highlights this similarity

holder estimates for nonlinear degenerate parabolic sytems on etablit des estimations de holder pour le gradient d espace u des solutions locales faibles des systemes paraboliques degeneres on etablit la continuite de holder des solutions non negatives d une equation parabolique degeneree

a holder estimate for nonlinear parabolic systems of p laplacian type abstract we extend the holder regularity results for weak solutions of the p laplacian systems originally obtained by dibenedetto to a larger class of right hand side terms by appropriately arranging two scale parameters on the sizes of a local parabolic cylinder and of the gradient of the solutions we get the same holder exponent as in the scalar case our method can also recover the classical parabolic case p 2

a neighbour model for field experiments summary a neighbour type model is proposed as an alternative to that of wilkinson et al 1983 for the analysis of field variety trials the model assumes that the varieties are grouped into complete replicates and that the plots within a replicate are side by side a method for the estimation of the variance parameters is developed as an extension of the procedure commonly used in incomplete block designs the model is investigated using data from the 166 cereal variety trials studied by patterson hunter 1983 results show worthwhile gains in efficiency over conventional incomplete block analysis

boundary estimates for solutions of nonlinear degenerate parabolic systems on etablit la regularite partout jusqu a la frontiere pour des solutions faibles de systemes paraboliques du type u l t div du p 2 du l f l x t u du dans t l 1 2 m u t r m m n p max 1 2n n 2 est un ouvert borne de r n n 2 0 t t 0 t

the uncertainty of storm season changes quantifying the uncertainty of autocovariance changepoints in oceanography there is interest in determining storm season changes for logistical reasons such as equipment maintenance scheduling in particular there is interest in capturing the uncertainty associated with these changes in terms of the number and location of them such changes are associated with autocovariance changes this article proposes a framework to quantify the uncertainty of autocovariance changepoints in time series motivated by this oceanographic application more specifically the framework considers time series under the locally stationary wavelet lsw framework deriving a joint density for scale processes in the raw wavelet periodogram by embedding this density within a hidden markov model hmm framework we consider changepoint characteristics under this multiscale setting such a methodology allows us to model changepoints and their uncertainty for a wide range of models including piecewise second order stationary processes for example piecewise moving average processes

estimation of infection and recovery rates for highly polymorphic parasites when detectability is imperfect using hidden markov models a bayesian hierarchical model is proposed for estimating parasitic infection dynamics for highly polymorphic parasites when detectability of the parasite using standard tests is imperfect the parasite dynamics are modelled as a non homogeneous hidden two state markov process where the observed process is the detection or failure to detect a parasitic genotype this is assumed to be conditionally independent given the hidden process that is the underlying true presence of the parasite which evolves according to a first order markov chain the model allows the transition probabilities of the hidden states as well as the detectability parameter of the test to depend on a number of covariates full bayesian inference is implemented using markov chain monte carlo simulation the model is applied to a panel data set of malaria genotype data from a randomized controlled trial of bed nets in tanzanian children aged 6 30 months with the age of the host and bed net use as covariates this analysis confirmed that the duration of infections with parasites belonging to the msp 2 fc27 allelic family increased with age

transformations in stochastic dea models abstract a set of transformations based on the lp norm are used to generate alternative parametric and nonparametric formulations of production frontiers particular attention is paid to the cases p 1 least absolute value estimation and p chebyshev estimation a class of generalized transformations of inputs and outputs by using the box cox transformations is also explored and illustrated

on the estimation of technical inefficiency in the stochastic frontier production function model abstract the error term in the stochastic frontier model is of the form v u where v is a normal error term representing pure randomness and u is a non negative error term representing technical inefficiency the entire v u is easily estimated for each observation but a previously unsolved problem is how to separate it into its two components v and u this paper suggests a solution to this problem by considering the expected value of u conditional on v u an explicit formula is given for the half normal and exponential cases

joint bayesian model selection and parameter estimation of the generalized extreme value model with covariates using birth death markov chain monte carlo 1 this paper describes bayesian estimation of the parameters of the generalized extreme value gev model with covariates for this model the parameters of the gev distribution are functions of covariates allowing for dependent parameters and or trends a markov chain monte carlo mcmc algorithm is generally used to estimate the posterior distributions of the parameters in a bayesian framework in this paper the birth death mcmc bdmcmc procedure is developed in order to carry out both parameter estimation and bayesian model selection the bdmcmc methods allow the jump between models of different dimensions the general algorithm consists of two types of sampling steps the first one involves dimension changing moves and the second is conditional on a fixed model parameters are estimated in a fully bayesian framework and the model is selected by the length of time that the mcmc chain remains in that model real and simulated data sets illustrate the usefulness of the proposed methodology

holder estimates for parabolic p x t laplacian systems in this paper we establish the local holder continuity of the spatial gradient of weak solutions to the parabolic p x t laplacian system begin array lll partial t u rm div left a x t du p x t 2 du right 0 end array more precisely we prove that begin array lll du in c rm loc 0 alpha alpha 2 quad rm for some alpha in 0 1 end array provided p and a are holder continuous

bayesian inference for markov processes with diffusion and discrete components summary data arising in certain radio tracking experiments consist of both a continuous spatial component and a discrete component related to behaviour this leads naturally to stochastic models with a state space which is a product of continuous and discrete components we consider a class of such models in continuous time which can be thought of as diffusions in random environments they are related to switching diffusion or hidden markov models but observations are made on both components at discrete time points so that neither component is completely hidden we describe and illustrate an approach to fully bayesian inference for these general models the algorithm used is a hybrid markov chain monte carlo method the diffusion parameters the environment parameters and the sample path of the environment process itself are updated separately in sequence and the individual steps are a mixture of gibbs and random walk metropolishastings types some implementation and model checking issues are discussed and an example using data arising from a radio tracking experiment is described

computational and inferential difficulties with mixture posterior distributions abstract this article deals with both exploration and interpretation problems related to posterior distributions for mixture models the specification of mixture posterior distributions means that the presence of k modes is known immediately standard markov chain monte carlo mcmc techniques usually have difficulties with well separated modes such as occur here the mcmc sampler stays within a neighborhood of a local mode and fails to visit other equally important modes we show that exploration of these modes can be imposed using tempered transitions however if the prior distribution does not distinguish between the different components then the posterior mixture distribution is symmetric and standard estimators such as posterior means cannot be used we propose alternatives for bayesian inference for permutation invariant posteriors including a clustering device and alternative appropriate loss functions

hidden markov models with applications in cell adhesion experiments estimation of the number of hidden states is challenging in hidden markov models motivated by the analysis of a specific type of cell adhesion experiments a new framework based on a hidden markov model and double penalized order selection is proposed the order selection procedure is shown to be consistent in estimating the number of states a modified expectation maximization algorithm is introduced to efficiently estimate parameters in the model simulations show that the proposed framework outperforms existing methods applications of the proposed methodology to real data demonstrate the accuracy of estimating receptor ligand bond lifetimes and waiting times which are essential in kinetic parameter estimation supplementary materials for this article are available online

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

on bayesian analysis of mixtures with an unknown number of components with discussion new methodology for fully bayesian mixture analysis is developed making use of reversible jump markov chain monte carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture a sample from the full joint distribution of all unknown variables is thereby generated and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution the methodology is applied here to the analysis of univariate normal mixtures using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context

regularity of solutions of nonlinear degenerate parabolic systems soit le systeme parabolique u i t div u p 2 u i 0 i m avec p 1 ou u i u i x t grad x et x r n ouvert pour toute solution de ce systeme avec max 1 2n n 2 p u est continu dans t

inference and model choice for sequentially ordered hidden markov models summary the system equation of a hidden markov model is rewritten to label the components by order of appearance and to make explicit the random behaviour of the number of components mt we argue that this reformulation is often a good way to achieve identifiability as it facilitates the interpretation of the posterior density and the estimation of the number of components that have appeared in a given sample we develop a sequential monte carlo algorithm for estimating the reformulated model which relies on particle filtering and gibbs sampling our algorithm has a computational cost that is similar to that of a markov chain monte carlo sampler and is much less likely to be affected by label switching i e the possibility of becoming trapped in a local mode of the posterior density the extension to transdimensional priors is also considered the approach is illustrated by two real data examples

bayesian methods for hidden markov models markov chain monte carlo mcmc sampling strategies can be used to simulate hidden markov model hmm parameters from their posterior distribution given observed data some mcmc methods used in practice for computing likelihood conditional probabilities of hidden states and the most likely sequence of states can be improved by incorporating established recursive algorithms the most important of these is a set of forward backward recursions calculating conditional distributions of the hidden states given observed data and model parameters i show how to use the recursive algorithms in an mcmc context and demonstrate mathematical and empirical results showing a gibbs sampler using the forward backward recursions mixes more rapidly than another sampler often used for hmms iintroduce an augmented variables technique for obtaining unique state labels in hmms and finite mixture models i show how recursive computing allows the statistically efficient use of mcmc output when estimating the hidden states i

corrigendum on bayesian analysis of mixtures with an unknown number of components we regret to report that there is an error in equation 12 on p 740 concerning the birth death move for empty components the correct expression is a p k 1 p k 1 b k w y1 j 1y wj yk k 1 dk 1 k0 1 bk 1 g1 k wj 1y wj in the paper as printed the power of 1y wj in the nal factor the jacobian term was given as k instead of ky 1 the source of the error was neglect of the condition j wj 1 in computing the partial derivatives of wj with respect to wj note that expression 11 for the split combine move acceptance ratio is correct as printed having made the correction we repeated the calculations leading to all the numerical results reported in the paper as might be expected the e ects of the error are noticeable but small the maximum changes to any of the posterior probabilities p kjy presented in tables 1 and 2 and fig 6 are 0 015 0 011 and 0 020 respectively in each case the maximum discrepancy occurs near the mode of the distributions and so has little impact the error in fig 2 is within plotting accuracy in none of the gures is the visual impression altered and none of our qualitative conclusions are a ected we are grateful to tobias ryden of lund university for discovering this error and we apologize for any confusion that it has caused

an exact gibbs sampler for the markov modulated poisson process a markov modulated poisson process mmpp is a poisson process whose intensity varies according to a markov process we present a novel technique for simulating from the exact distribution of a continuous time markov chain over an interval given the start and end states and the infinitesimal generator and use this to create a gibbs sampler which samples from the exact distribution of the hidden markov chain in an mmpp we apply the gibbs sampler to modelling the occurrence of a rare dna motif the chi site and to inferring regions of the genome with evidence of high or low intensities for occurrences of this site

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

calculating posterior distributions and modal estimates in markov mixture models abstract this paper is concerned with finite mixture models in which the populations from one observation to the next are selected according to an unobserved markov process a new full bayesian approach based on the method of gibbs sampling is developed calculations are simplified by data augmentation achieved by introducing a population index variable into the list of unknown parameters it is shown that the latent variables one for each observation can be simulated from their joint distribution given the data and the remaining parameters this result serves to accelerate the convergence of the gibbs sample modal estimates are also computed by stochastic versions of the em algorithm these provide an alternative to a full bayesian approach and to existing methods of locating the maximum likelihood estimate the ideas are applied in detail to poisson data mixtures of multivariate normal distributions and autoregressive time series

a recursive algorithm for markov random fields summary we propose a recursive algorithm as a more useful alternative to the brook expansion for the joint distribution of a vector of random variables when the original formulation is in terms of the corresponding full conditional distributions as occurs for markov random fields usually in practical applications the computational load will still be excessive but then the algorithm can be used to obtain the componentwise full conditionals of a system after marginalising over some variables or the joint distribution of subsets of the variables conditioned on values of the remainder which is required for block gibbs sampling as an illustrative example we apply the algorithm in the simplest nontrivial setting of hidden markov chains more important we demonstrate how it applies to markov random fields on regular lattices and to perfect block gibbs sampling for binary systems