analysis of pulsatile hormone concentration profiles with nonconstant basal concentration a bayesian approach many challenges arise in the analysis of pulsatile or episodic hormone concentration time series data among these challenges is the determination of the number and location of pulsatile events and the discrimination of events from noise analyses of these data are typically performed in two stages in the first stage the number and approximate location of the pulses are determined in the second stage a model typically a deconvolution model is fit to the data conditional on the number of pulses any error made in the first stage is carried over to the second stage furthermore current methods except two assume that the underlying basal concentration is constant we present a fully bayesian deconvolution model that simultaneously estimates the number of secretion episodes as well as their locations and a nonconstant basal concentration this model obviates the need to determine the number of events a priori furthermore we estimate probabilities for all candidate event locations we demonstrate our method on a real data set

bayesian analysis of mixture models with an unknown number of components an alternative to reversible jump methods richardson and green present a method of performing a bayesian analysis of data from a finite mixture distribution with an unknown number of components their method is a markov chain monte carlo mcmc approach which makes use of the reversible jump methodology described by green we describe an alternative mcmc method which views the parameters of the model as a marked point process extending methods suggested by ripley to create a markov birth death process with an appropriate stationary distribution our method is easy to implement even in the case of data in more than one dimension and we illustrate it on both univariate and bivariate data there appears to be considerable potential for applying these ideas to other contexts as an alternative to more general reversible jump methods and we conclude with a brief discussion of how this might be achieved

marginal likelihood estimation via power posteriors model choice plays an increasingly important role in statistics from a bayesian perspective a crucial goal is to compute the marginal likelihood of the data for a given model however this is typically a difficult task since it amounts to integrating over all model parameters the aim of the paper is to illustrate how this may be achieved by using ideas from thermodynamic integration or path sampling we show how the marginal likelihood can be computed via markov chain monte carlo methods on modified posterior distributions for each model this then allows bayes factors or posterior model probabilities to be calculated we show that this approach requires very little tuning and is straightforward to implement the new method is illustrated in a variety of challenging statistical settings

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

markov chain monte carlo 10 years and still running although markov chain monte carlo mcmc techniques can be traced back to the early 1950s and are almost contemporary with independent monte carlo methods the use of these techniques has only really taken off in the past 10 years at least in mainstream statistics with the work of gelfand and smith 1990 and the rediscovery of metropolis s and hastings s papers the impact on the discipline is deep and durable because these methods have opened new horizons in the scale of the problems that one can deal with thus enhancing the position of statistics in most applied fields the mcmc revolution has in particular boosted bayesian statistics to new heights by providing a virtually universal tool for dealing with integration and optimization problems this can be seen in for instance the explosion of papers dealing with complex models hierarchical modelings nonparametric bayesian estimation and spatial statistics this trend has also created new synergies with mathematicians and probabilists as well as econometricians engineers ecologists astronomers and others for theoretical requests and practical implications of mcmc techniques it is impossible to provide here a complete perspective on mcmc methods and applications for this as well as for other references we refer the reader to the books by gilks richardson and spiegelhalter 1995 and robert and casella 1999 here we focus on four particular aspects of mcmc algorithms theoretical foundations practical implementation bayesian inference and prospects the web provides many relevant sites including the mcmc preprint server http www statslab cam ac uk r mcmc which offers a most useful window to the current research on mcmc wilson s site on perfect simulation http dimacs rutgers edu dbwilson exact h which keeps track of papers and applets on this topic and a site on convergence control techniques http www ensae fr crest statistique robert mcdiag even more recent developments allow for on line computations through applets like breyer s http www maths lancs ac uk breyer java html which impressively illustrates the behavior of different samplers for simple problems note also that the bugs and coda software are freely available at http www mrc bsu cam ac uk bu

a constructive representation of univariate skewed distributions we introduce a general perspective on the introduction of skewness into symmetric distributions through inverse probability integral transformations we provide a constructive representation of skewed distributions where the skewing mechanism and the original symmetric distributions are specified separately we study the effects of the skewing mechanism on e g modality tail behavior and the amount of skewness generated the representation is used to introduce novel classes of skewed distributions where we induce certain prespecified characteristics through particular choices of the skewing mechanism finally we use a bayesian linear regression framework to compare the new classes with some existing distributions in the context of two empirical examples

mixture models with a prior on the number of components abstracta natural bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with symmetric dirichlet weights and put a prior on the number of components that is to use a mixture of finite mixtures mfm the most commonly used method of inference for mfms is reversible jump markov chain monte carlo but it can be nontrivial to design good reversible jump moves especially in high dimensional spaces meanwhile there are samplers for dirichlet process mixture dpm models that are relatively simple and are easily adapted to new applications it turns out that in fact many of the essential properties of dpms are also exhibited by mfms an exchangeable partition distribution restaurant process random measure representation and stick breaking representation and crucially the mfm analogues are simple enough that they can be used much like the corresponding dpm properties consequently many of the powerful methods developed for inference in dpms

variable selection in clustering via dirichlet process mixture models summary the increased collection of high dimensional data in various fields has raised a strong interest in clustering algorithms and variable selection procedures in this paper we pro pose a model based method that addresses the two problems simultaneously we introduce a latent binary vector to identify discriminating variables and use dirichlet process mixture models to define the cluster structure we update the variable selection index using a metropolis algorithm and obtain inference on the cluster structure via a split merge markov chain monte carlo technique we explore the performance of the methodology on simulated data and illustrate an application with a dna microarray study

markov chain monte carlo convergence diagnostics a comparative review abstract a critical issue for users of markov chain monte carlo mcmc methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest research into methods of computing theoretical convergence bounds holds promise for the future but to date has yielded relatively little of practical use in applied work consequently most mcmc users address the convergence problem by applying diagnostic tools to the output produced by running their samplers after giving a brief overview of the area we provide an expository review of 13 convergence diagnostics describing the theoretical basis and practical implementation of each we then compare their performance in two simple models and conclude that all of the methods can fail to detect the sorts of convergence failure that they were designed to identify we thus recommend a combination of strategies aimed at evaluating and accelerating mcmc sampler convergence including ap

computing bayes factors by combining simulation and asymptotic approximations abstract the bayes factor is a ratio of two posterior normalizing constants which may be difficult to compute we compare several methods of estimating bayes factors when it is possible to simulate observations from the posterior distributions via markov chain monte carlo or other techniques the methods that we study are all easily applied without consideration of special features of the problem provided that each posterior distribution is well behaved in the sense of having a single dominant mode we consider a simulated version of laplace s method a simulated version of bartlett correction importance sampling and a reciprocal importance sampling technique we also introduce local volume corrections for each of these in addition we apply the bridge sampling method of meng and wong we find that a simulated version of laplace s method with local volume correction furnishes an accurate approximation that is especially useful when likelihood function evaluations are costly a simple bridge sampli

debye huckel theory for charge symmetric coulomb systems it is proven that the pressure density and correlation functions of a classical charge symmetric coulomb system are asymptotic as the plasma parameter e tends to zero to the approximations predicted by the debye huckel theory these approximations consist of the ideal gas term plus a term of one lower order in e the sine gordon transformation and some new correlation inequalities for the associated functional integrals are used

classical model selection via simulated annealing summary the classical approach to statistical analysis is usually based upon finding values for model parameters that maximize the likelihood function model choice in this context is often also based on the likelihood function but with the addition of a penalty term for the number of parameters though models may be compared pairwise by using likelihood ratio tests for example various criteria such as the akaike information criterion have been proposed as alternatives when multiple models need to be compared in practical terms the classical approach to model selection usually involves maximizing the likelihood function associated with each competing model and then calculating the corresponding criteria value s however when large numbers of models are possible this quickly becomes infeasible unless a method that simultaneously maximizes over both parameter and model space is available we propose an extension to the traditional simulated annealing algorithm that allows for moves that not only change parameter values but also move between competing models this transdimensional simulated annealing algorithm can therefore be used to locate models and parameters that minimize criteria such as the akaike information criterion but within a single algorithm removing the need for large numbers of simulations to be run we discuss the implementation of the transdimensional simulated annealing algorithm and use simulation studies to examine its performance in realistically complex modelling situations we illustrate our ideas with a pedagogic example based on the analysis of an autoregressive time series and two more detailed examples one on variable selection for logistic regression and the other on model selection for the analysis of integrated recapture recovery data

mean field theory for coulomb systems we study a classical charge symmetric system with an external charge distributionq in three dimensions in the limit that the plasma parameter zero we prove that ifq is scaled appropriately then the correlation functions converge pointwise to those of an ideal gas in the external mean field x where is given by 2z sinh q this is the mean field equation of debye and huckel the proof uses the sine gordon transformation the mayer expansion and a correlation inequality

fusion of hidden markov random field models and its bayesian estimation in this paper we present a hidden markov random field hmrf data fusion model the proposed model is applied to the segmentation of natural images based on the fusion of colors and textons into julesz ensembles the corresponding exploration selection estimation ese procedure for the estimation of the parameters is presented this method achieves the estimation of the parameters of the gaussian kernels the mixture proportions the region labels the number of regions and the markov hyper parameter meanwhile we present a new proof of the asymptotic convergence of the ese procedure based on original finite time bounds for the rate of convergence

bayesian model choice via markov chain monte carlo methods summary markov chain monte carlo mcmc integration methods enable the fitting of models of virtually unlimited complexity and as such have revolutionized the practice of bayesian data analysis however comparison across models may not proceed in a completely analogous fashion owing to violations of the conditions sufficient to ensure convergence of the markov chain in this paper we present a framework for bayesian model choice along with an mcmc algorithm that does not suffer from convergence difficulties our algorithm applies equally well to problems where only one model is contemplated but its proper size is not known at the outset such as problems involving integer valued parameters multiple changepoints or finite mixture distributions we illustrate our approach with two published examples

approximating posterior distributions by mixtures kernel density estimation techniques are used to smooth simulated samples from importance sampling function approximations to posterior distributions resulting in revised approximations that are mixtures of standard parametric forms usually multivariate normal or t distributions adaptive refinement of such mixture approximations involves repeating this process to home in successively on the posterior in fairly low dimensional problems this provides a general and automatic method of approximating posteriors by mixtures so that marginal densities and other summaries may be easily computed

a reliable data based bandwidth selection method for kernel density estimation we present a new method for data based selection of the bandwidth in kernel density estimation which has excellent properties it improves on a recent procedure of park and marron which itself is a good method in various ways first the new method has superior theoretical performance second it also has a computational advantage third the new method has reliably good performance for smooth densities in simulations performance that is second to none in the existing literature these methods are based on choosing the bandwidth to approximately minimize good quality estimates of the mean integrated squared error the key to the success of the current procedure is the reintroduction of a non stochastic term which was previously omitted together with use of the bandwidth to reduce bias in estimation without inflating variance

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

netons vibrations of complex networks we consider atoms interacting with each other through the topological structure of ac omplex network and investigate lattice vibrations of the system the quanta of which we call netons for convenience the density of neton levels obtained numerically reveals that unlike a local regular lattice the system develops a gap of finite width manifesting extreme rigidity of the network structure at low energies two different network models the small world network and the scale free network are compared the characteristic structure of the former is described by an additional peak in the level density whereas a power law tail is observed in the latter indicating excitability of netons at arbitrarily high energies the gap width is also found to vanish in the small world network when the connection range r 1

a model of text for experimentation in the social sciences abstractstatistical models of text have become increasingly popular in statistics and computer science as a method of exploring large document collections social scientists often want to move beyond exploration to measurement and experimentation and make inference about social and political processes that drive discourse and content in this article we develop a model of text data that supports this type of substantive research our approach is to posit a hierarchical mixed membership model for analyzing topical content of documents in which mixing weights are parameterized by observed covariates in this model topical prevalence and topical content are specified as a simple generalized linear model on an arbitrary number of document level covariates such as news source and time of release enabling researchers to introduce elements of the experimental design that informed document collection into the model within a generally applicable framework we demonstrate the proposed methodology by analyzi

bayesian analysis of quantitative trait locus data using reversible jump markov chain monte carlo the advent of molecular markers has created a great potential for the understanding of quantitative inheritance in plants as well as in animals taking the newly available data into account biometric models have been constructed for the mapping of quantitative trait loci qtls in current approaches the lack of knowledge on the number and location of the most important qtls contributing to a trait is a major problem in this paper we utilize reversible jump markov chain monte carlo methodology green 1995 biometrika 82 711 732 in order to compute the posterior quantities required for fully bayesian inference it yields posterior densities not only for the parameters given the number of qtl but also for the number of qtl itself as an example the algorithm is applied to simulated data according to a standard design in plant breeding

an application of the laplace method to finite mixture distributions abstract an exact bayesian analysis of finite mixture distributions is often computationally infeasible because the number of terms in the posterior density grows exponentially with the sample size a modification of the laplace method is presented and applied to estimation of posterior functions in a bayesian analysis of finite mixture distributions the procedure which involves computations similar to those required in maximum likelihood estimation is shown to have high asymptotic accuracy for finite mixtures of certain exponential family densities for these mixture densities the posterior density is also shown to be asymptotically normal an approximation of the posterior density of the number of components is presented the method is applied to duncan s barley data and to a distribution of lake chemistry data for north central wisconsin

the bayesian choice a decision theoretic motivation contents introduction decision theoretic foundations of statistical inference from prior information to prior distributions bayesian point estimation tests and confidence regions admissibility and complete classes invariance haar measures and equivariant estimators hierarchical and empirical bayes extensions bayesian calculations a defense of the bayesian choice

heteroscedastic normal exponential mixture models bayesian and classical approaches abstract in this paper we introduce a bayesian analysis for mixture of distributions belonging to the exponential family as a special case we consider a mixture of normal exponential distributions including joint modeling of the mean and variance we also consider joint modeling of the mean and variance heterogeneity markov chain monte carlo mcmc methods are used to obtain the posterior summaries of interest we also introduce and apply an em algorithm where the maximization is obtained applying the fisher scoring algorithm finally we also include analysis of real data sets to illustrate the proposed methodology

markov chain monte carlo methods for computing bayes factors a comparative review the problem of calculating posterior probabilities for a collection of competing models and associated bayes factors continues to be a formidable challenge for applied bayesian statisticians current approaches that take advantage of modern markov chain monte carlo computing methods include those that attempt to sample over some form of the joint space created by the model indicators and the parameters for each model others that sample over the model space alone and still others that attempt to estimate the marginal likelihood of each model directly because the collection of these is equivalent to the collection of model probabilities themselves we review several methods and compare them in the context of three examples a simple regression example a more challenging hierarchical longitudinal model and a binary data latent variable model we find that the joint model parameter space search methods perform adequately but can be difficult to program and tune whereas the marginal likelihood methods o

bayesian exploratory factor analysis this paper develops and applies a bayesian approach to exploratory factor analysis that improves on ad hoc classical approaches our framework relies on dedicated factor models and simultaneously determines the number of factors the allocation of each measurement to a unique factor and the corresponding factor loadings classical identification criteria are applied and integrated into our bayesian procedure to generate models that are stable and clearly interpretable a monte carlo study confirms the validity of the approach the method is used to produce interpretable low dimensional aggregates from a high dimensional set of psychological measurements

goodness of fit testing and quadratic functional estimation from indirect observations we consider the convolution model where i i d random variables x i having unknown density f are observed with additive i i d noise independent of the x s we assume that the density f belongs to either a sobolev class or a class of supersmooth functions the noise distribution is known and its characteristic function decays either polynomially or exponentially asymptotically we consider the problem of goodness of fit testing in the convolution model we prove upper bounds for the risk of a test statistic derived from a kernel estimator of the quadratic functional f f 2 based on indirect observations when the unknown density is smoother enough than the noise density we prove that this estimator is n 1 2 consistent asymptotically normal and efficient for the variance we compute otherwise we give nonparametric upper bounds for the risk of the same estimator we give an approach unifying the proof of nonparametric minimax lower bounds for both problems we establish them for sobolev densities and for supersmooth densities less smooth than exponential noise in the two setups we obtain exact testing constants associated with the asymptotic minimax rates

finite size corrections for coulomb systems in the debye huckel regime it has been argued that for a finite two dimensional classical coulomb system of characteristic size r in its conducting phase as r the total free energy times the inverse temperature admits an expansion of the form where is the euler characteristic of the manifold where the system exists the first two terms represent the bulk free energy and the surface free energy respectively the coefficients a and b are non universal but the coefficient of ln r is universal it does not depend on the detail of the microscopic constitution of the system particle densities temperature etc by doing the usual legendre transform this universal finite size correction is also present in the grand potential the explicit form of the expansion has been checked for some exactly solvable models for a special value of the coulombic coupling in this paper we present a method for obtaining these finite size corrections in the debye huckel regime it is based on the sine gordon field theory to find an expression for the grand canonical partition function in terms of the spectrum of the laplace operator as an example we find explicitly the grand potential expansion for a coulomb system confined in a disc and in an annulus with ideal conductor walls

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

marginal likelihood from the gibbs output abstract in the context of bayes estimation via gibbs sampling with or without data augmentation a simple approach is developed for computing the marginal density of the sample data marginal likelihood given parameter draws from the posterior distribution consequently bayes factors for model comparisons can be routinely computed as a by product of the simulation hitherto this calculation has proved extremely challenging our approach exploits the fact that the marginal density can be expressed as the prior times the likelihood function over the posterior density this simple identity holds for any parameter value an estimate of the posterior density is shown to be available if all complete conditional densities used in the gibbs sampler have closed form expressions to improve accuracy the posterior density is estimated at a high density point and the numerical standard error of resulting estimate is derived the ideas are applied to probit regression and finite mixture models

a trickiness of the high temperature limit for number density correlation functions in classical coulomb fluids the debye huckel theory describes rigorously the thermal equilibrium of classical coulomb fluids in the high temperature 0 regime denotes the inverse temperature it is generally believed that the debye huckel theory and the systematic high temperature expansion provide an adequate description also in the region of small strictly positive values of 0 this hypothesis is tested in the present paper on a two dimensional coulomb gas of pointlike unit charges interacting via a logarithmic potential which is equivalent to an integrable sine gordon field model in particular we apply a form factor method to obtain the exact asymptotic large distance behavior of particle correlation functions considered in the charge and number density combinations we first determine the general forms of the leading and subleading asymptotic terms at strictly positive 0 and then evaluate their high temperature 0 forms in the case of the charge correlation function the leading asymptotic term at a strictly positive 0 is also the leading one in the high temperature 0 regime on the contrary the 0 behavior of the number density correlation function is accompanied by an interference between the first two asymptotic terms consequently the large distance behavior of this function exhibits a discontinuity when going from strictly positive values of 0 to the debye huckel limit 0 this is the crucial conclusion of the paper the large distance asymptotics and the high temperature limit do not commute for the density correlation function of the two dimensional coulomb gas

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

population based reversible jump markov chain monte carlo we present an extension of population based markov chain monte carlo to the transdimensional case a major challenge is that of simulating from high and transdimensional target measures in such cases markov chain monte carlo methods may not adequately traverse the support of the target the simulation results will be unreliable we develop population methods to deal with such problems and give a result proving the uniform ergodicity of these population algorithms under mild assumptions this result is used to demonstrate the superiority in terms of convergence rate of a population transition kernel over a reversible jump sampler for a bayesian variable selection problem we also give an example of a population algorithm for a bayesian multivariate mixture model with an unknown number of components this is applied to gene expression data of 1000 data points in six dimensions and it is demonstrated that our algorithm outperforms some competing markov chain samplers in this example we show how to combine the methods of parallel chains geyer 1991 tempering geyer thompson 1995 snooker algorithms gilks et al 1994 constrained sampling and delayed rejection green mira 2001

bayesian nonparametric modeling of higher order markov chains we consider the problem of flexible modeling of higher order markov chains when an upper bound on the order of the chain is known but the true order and nature of the serial dependence are unknown we propose bayesian nonparametric methodology based on conditional tensor factorizations which can characterize any transition probability with a specified maximal order the methodology selects the important lags and captures higher order interactions among the lags while also facilitating calculation of bayes factors for a variety of hypotheses of interest we design efficient markov chain monte carlo algorithms for posterior computation allowing for uncertainty in the set of important lags to be included and in the nature and order of the serial dependence the methods are illustrated using simulation experiments and real world applications supplementary materials for this article are available online

generalized smooth finite mixtures we propose a general class of models and a unified bayesian inference methodology for flexibly estimating the density of a response variable conditional on a possibly high dimensional set of covari

bayesian estimation and model selection in ordered latent class models for polytomous items in a latent class irt model in which the latent classes are ordered on one dimension the class specific response probabilities are subject to inequality constraints the number of these inequality constraints increase dramatically with the number of response categories per item if assumptions like monotonicity or double monotonicity of the cumulative category response functions are postulated a markov chain monte carlo method the gibbs sampler can sample from the multivariate posterior distribution of the parameters under the constraints bayesian model selection can be done by posterior predictive checks and bayes factors a simulation study is done to evaluate results of the application of these methods to ordered latent class models in three realistic situations also an example of the presented methods is given for existing data with polytomous items it can be concluded that the bayesian estimation procedure can handle the inequality constraints on the parameters very well however the application of bayesian model selection methods requires more research

a hierarchical finite mixture model that accommodates zero inflated counts non independence and heterogeneity a number of mixture modeling approaches assume both normality and independent observations however these two assumptions are at odds with the reality of many data sets which are often characterized by an abundance of zero valued or highly skewed observations as well as observations from biologically related i e non independent subjects we present here a finite mixture model with a zero inflated poisson regression component that may be applied to both types of data this flexible approach allows the use of covariates to model both the poisson mean and rate of zero inflation and can incorporate random effects to accommodate non independent observations we demonstrate the utility of this approach by applying these models to a candidate endophenotype for schizophrenia but the same methods are applicable to other types of data characterized by zero inflation and non independence

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

on the bayes optimality of f measure maximizers the f measure which has originally been introduced in information retrieval is nowadays routinely used as a performance metric for problems such as binary classification multi label classification and structured output prediction optimizing this measure is a statistically and computationally challenging problem since no closed form solution exists adopting a decision theoretic perspective this article provides a formal and experimental analysis of different approaches for maximizing the f measure we start with a bayes risk analysis of related loss functions such as hamming loss and subset zero one loss showing that optimizing such losses as a surrogate of the f measure leads to a high worst case regret subsequently we perform a similar type of analysis for f measure maximizing algorithms showing that such algorithms are approximate while relying on additional assumptions regarding the statistical distribution of the binary response variables furthermore we present a new algorithm which is not only computationally efficient but also bayes optimal regardless of the underlying distribution to this end the algorithm requires only a quadratic with respect to the number of binary responses number of parameters of the joint distribution we illustrate the practical performance of all analyzed methods by means of experiments with multi label classification problems

density estimation with confidence sets exemplified by superclusters and voids in the galaxies abstract a method is presented for forming both a point estimate and a confidence set of semiparametric densities the final product is a three dimensional figure that displays a selection of density estimates for a plausible range of smoothing parameters the boundaries of the smoothing parameter are determined by a nonparametric goodness of fit test that is based on the sample spacings for each value of the smoothing parameter our estimator is selected by choosing the normal mixture that maximizes a function of the sample spacings a point estimate is selected from this confidence set by using the method of cross validation an algorithm to find the mixing distribution that maximizes the spacings functional is presented these methods are illustrated with a data set from the astronomy literature the measurements are velocities at which galaxies in the corona borealis region are moving away from our galaxy if the galaxies are clustered the velocity density will be multimodal with clusters correspond

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

robust estimation in the normal mixture model based on robust clustering summary we introduce a robust estimation procedure that is based on the choice of a representative trimmed subsample through an initial robust clustering procedure and subsequent improvements based on maximum likelihood to obtain the initial trimming we resort to the trimmed k means a simple procedure designed for finding the core of the clusters under appropriate configurations by handling the trimmed data as censored maximum likelihood estimation provides in each step the location and shape of the next trimming data driven restrictions on the parameters requiring that every distribution in the mixture must be sufficiently represented in the initial clustered region allow singularities to be avoided and guarantee the existence of the estimator our analysis includes robustness properties and asymptotic results as well as worked examples

estimation of finite mixture distributions through bayesian sampling summary a formal bayesian analysis of a mixture model usually leads to intractable calculations since the posterior distribution takes into account all the partitions of the sample we present approximation methods which evaluate the posterior distribution and bayes estimators by gibbs sampling relying on the missing data structure of the mixture model the data augmentation method is shown to converge geometrically since a duality principle transfers properties from the discrete missing data chain to the parameters the fully conditional gibbs alternative is shown to be ergodic and geometric convergence is established in the normal case we also consider non informative approximations associated with improper priors assuming that the sample corresponds exactly to a k component mixture

on fast supervised learning for normal mixture models with missing information it is an important research issue to deal with mixture models when missing values occur in the data in this paper computational strategies using auxiliary indicator matrices are introduced for efficiently handling mixtures of multivariate normal distributions when the data are missing at random and have an arbitrary missing data pattern meaning that missing data can occur anywhere we develop a novel em algorithm that can dramatically save computation time and be exploited in many applications such as density estimation supervised clustering and prediction of missing values in the aspect of multiple imputations for missing data we also offer a data augmentation scheme using the gibbs sampler our proposed methodologies are illustrated through some real data sets with varying proportions of missing values