bayesian analysis of factorial experiments by mixture modelling a bayesian analysis for factorial experiments is presented using finite mixture distributions to model the main effects and interactions this allows both estimation and an analogue of hypothesis testing in a posterior analysis using a single prior specification a detailed formulation based on this approach is provided for the case of the two way model with replication allowing interactions issues in formulating a suitable prior are discussed in detail and in the context of two illustrative applications we discuss implementation presentation of posterior distributions sensitivity and performance of the markov chain monte carlo methods that are used

how porous is the graph of brownian motion we prove that the graph of brownian motion is almost surely porous and determine the hausdorff dimension of sets with a given porosity index in particular we show that the porosity index of the graph is yo 0 6948

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

generalized spatial dirichlet process models summary many models for the study of point referenced data explicitly introduce spatial random effects to capture residual spatial association these spatial effects are customarily modelled as a zeromean stationary gaussian process the spatial dirichlet process introduced by gelfand et al 2005 produces a random spatial process which is neither gaussian nor stationary rather it varies about a process that is assumed to be stationary and gaussian the spatial dirichlet process arises as a probability weighted collection of random surfaces this can be limiting for modelling and inferential purposes since it insists that a process realization must be one of these surfaces we introduce a random distribution for the spatial effects that allows different surface selection at different sites moreover we can specify the model so that the marginal distribution of the effect at each site still comes from a dirichlet process the development is offered constructively providing a multivariate extension of the stick breaking representation of the weights we then introduce mixing using this generalized spatial dirichlet process we illustrate with a simulated dataset of independent replications and note that we can embed the generalized process within a dynamic model specification to eliminate the independence assumption

identifiability of minimal stable rational causal systems using second order output cyclic spectra in this paper the blind identifiability of systems using the second order output cyclic spectra is considered it is shown that the class of minimal stable rational causal msrc systems is not identifiable and the identification is limited by a nontrivial ambiguity associated with the so called cyclic all pass factor the largest subclass of msrc systems that ensures the unique identification is shown to be the set of msrc systems that do not have special uniformly spaced maximum phase zeros

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

multilayered 3d lidar image construction using spatial models in a bayesian framework standard 3d imaging systems process only a single return at each pixel from an assumed single opaque surface however there are situations when the laser return consists of multiple peaks due to the footprint of the beam impinging on a target with surfaces distributed in depth or with semitransparent surfaces if all these returns are processed a more informative multilayered 3d image is created we propose a unified theory of pixel processing for lidar data using a bayesian approach that incorporates spatial constraints through a markov random field with a potts prior model this allows us to model uncertainty about the underlying spatial process to palliate some inherent deficiencies of this prior model we also introduce two proposal distributions one based on spatial mode jumping and the other on a spatial birth death process the different parameters of the several returns are estimated using reversible jump markov chain monte carlo rjmcmc techniques in combination with an adaptive strategy of delayed rejection to improve the estimates of the parameters

empirical bayes estimates of age standardized relative risks for use in disease mapping there have been many attempts in recent years to map incidence and mortality from diseases such as cancer such maps usually display either relative rates in each district as measured by a standardized mortality ratio smr or some similar index or the statistical significance level for a test of the difference between the rates in that district and elsewhere neither of these approaches is fully satisfactory and we propose a new approach using empirical bayes estimation the resulting estimators represent a weighted compromise between the smr the overall mean relative rate and a local mean of the relative rate in nearby areas the compromise solution depends on the reliability of each individual smr and on estimates of the overall amount of dispersion of relative rates over different districts

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

brownian motion at a slow point on rappelle des resultats de greenwood et perkins 1983 84 et on etudie les proprietes probabilistes et de trajectoire du processus x t b t t b t on montre en particulier que x est un processus de markov non homogene satisfaisant une certaine equation differentielle stochastique

a bayesian semiparametric model for case control studies with errors in variables summary we develop a model and a numerical estimation scheme for a bayesian approach to inference in case control studies with errors in covariables the model proposed in this paper is based on a nonparametric model for the unknown joint distribution for the missing data the observed covariates and the proxy this nonparametric distribution defines the measurement error component of the model which relates the missing covariates x with a proxy w the oxymoron nonparametric bayes refers to a class of flexible mixture distributions for the likelihood of disease given covariates we choose a logistic regression model by using a parametric disease model and nonparametric exposure model we obtain robust interpretable results quantifying the effect of exposure

approximating hidden gaussian markov random fields summary gaussian markov random field gmrf models are frequently used in a wide variety of applications in most cases parts of the gmrf are observed through mutually independent data hence the full conditional of the gmrf a hidden gmrf hgmrf is of interest we are concerned with the case where the likelihood is non gaussian leading to non gaussian hgmrf models several researchers have constructed block sampling markov chain monte carlo schemes based on approximations of the hgmrf by a gmrf using a second order expansion of the log density at or near the mode this is possible as the gmrf approximation can be sampled exactly with a known normalizing constant the markov property of the gmrf approximation yields computational efficiency the main contribution in the paper is to go beyond the gmrf approximation and to construct a class of non gaussian approximations which adapt automatically to the particular hgmrf that is under study the accuracy can be tuned by intuitive parameters to nearly any precision these non gaussian approximations share the same computational complexity as those which are based on gmrfs and can be sampled exactly with computable normalizing constants we apply our approximations in spatial disease mapping and model based geostatistical models with different likelihoods obtain procedures for block updating and construct metropolized independence samplers

on brownian slow points it is shown that for a wiener process x t both the quantities mathop inf limits t mathop overline lim limits h text to text 0 x t text text h x t sqrt h text and mathop text sup limits t mathop underline lim limits h text to text 0 text x t text text h x t sqrt h are almost surely equal to 1

spatial moving average risk smoothing this paper introduces spatial moving average risk smoothing smars as a new way of carrying out disease mapping this proposal applies the moving average ideas of time series theory to the spatial domain making use of a spatial moving average process of unknown order to define dependence on the risk of a disease occurring correlation of the risks for different locations will be a function of m values m being unknown providing a rich class of correlation functions that may be reproduced by smars moreover the distance in terms of neighborhoods that should be covered for two units to be found to make the correlation of their risks 0 is a quantity to be fitted by the model this way we reproduce patterns that range from spatially independent to long range spatially dependent we will also show a theoretical study of the correlation structure induced by smars illustrating the wide variety of correlation functions that this proposal is able to reproduce we will also present three applications of smars to both simulated and real datasets these applications will show smars to be a competitive disease mapping model when compared with alternative proposals that have already appeared in the literature finally the application of smars to the study of mortality for 21 causes of death in the comunitat valenciana will allow us to identify some qualitative differences in the patterns of those diseases copyright 2012 john wiley sons ltd

a least squares approach to blind channel identification conventional blind channel identification algorithms are based on channel outputs and knowledge of the probabilistic model of channel input in some practical applications however the input statistical model may not be known or there may not be sufficient data to obtain accurate enough estimates of certain statistics in this paper we consider the system input to be an unknown deterministic signal and study the problem of blind identification of multichannel fir systems without requiring the knowledge of the input statistical model a new blind identification algorithm based solely on the system outputs is proposed necessary and sufficient identifiability conditions in terms of the multichannel systems and the deterministic input signal are also presented

fast sampling of gaussian markov random fields this paper demonstrates how gaussian markov random fields conditional autoregressions can be sampled quickly by using numerical techniques for sparse matrices the algorithm is general and efficient and expands easily to various forms for conditional simulation and evaluation of normalization constants we demonstrate its use by constructing efficient block updates in markov chain monte carlo algorithms for disease mapping

markov chain monte carlo estimation of classical and dynamic switching and mixture models bayesian estimation of a very general model class where the distribution of the observations depends on a latent process taking values in a discrete state space is discussed in this article this model class covers finite mixture modeling markov switching autoregressive modeling and dynamic linear models with switching the consequences the unidentifiability of this type of model has on markov chain monte carlo mcmc estimation are explicitly dealt with joint bayesian estimation of all latent variables model parameters and parameters that determine the probability law of the latent process is carried out by a new mcmc method called permutation sampling the permutation sampler first samples from the unconstrained posterior which often can be done in a convenient multimove manner and then applies a permutation of the current labeling of the states of the latent process in a first run the random permutation sampler used selected the permutation randomly the mcmc output of the random permutation s

bayesian non parametric models for spatially indexed data of mixed type we develop bayesian nonparametric models for spatially indexed data of mixed type our work is motivated by challenges that occur in environmental epidemiology where the usual presence of several confounding variables that exhibit complex interactions and high correlations makes it difficult to estimate and under stand the effects of risk factors on health outcomes of interest the modeling approach we adopt assumes that responses and confounding variables are manifestations of continuous latent variables and uses mul tivariate gaussians to jointly model these responses and confounding variables are not treated equally as relevant parameters of the distributions of the responses only are modeled in terms of explanatory variables or risk factors spatial dependence is introduced by allowing the weights of the nonparametric process priors to be location specific obtained as probit transformations of gaussian markov random fields con founding variables and spatial configuration have a similar role in the model in that they only in uence along with the responses the allocation probabilities of the areas into the mixture components thereby allowing for exible adjustment of the effects of observed confounders while allowing for the possibility of residual spatial structure possibly occurring due to unmeasured or undiscovered spatially varying factors aspects of the model are illustrated in simulation studies and an application to a real data set

a critical case for brownian slow points letxt be a brownian motion and lets c be the set of realsr 0 such that uxr t xru c t 0 t h for someh h r 0 it is known thats c is empty ifc 1 a s in this paper we prove thats 1 is empty a s

a conditioned limit theorem for random walk and brownian local time on square root boundaries we count the number of times a random walk exits from a square root boundary and show that the normalized counting process and the normalized random walk converge jointly in law to a local time whose inverse is a stable subordinator of a known index and a brownian motion the study of this limit process leads to some precise sample path properties of brownian motion these properties improve earlier results of dvoretsky and kahane on the existence of small oscillations in the brownian path

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 hausdorff dimension of the brownian slow points for each c1 c2 consider the set of one sided slow points of the brownian path b defined by s c 1 c 2 omega t exists delta 0 text b t h b t in c 1 h 1 2 c 2 h 1 2 forall 0 underset raise0 3em hbox smash scriptscriptstyle leqslant h underset raise0 3em hbox smash scriptscriptstyle leqslant delta we find the hausdorff dimension of s c1 c2 as well as s c1 c2 a where a a progressively measurable set satisfying certain hypotheses in particular the hausdorff dimension of the two sided slow points s c1 c2 and the one sided and two sided slow points in the zero set of b are obtained by making an appropriate choice of a these results show for example that s c c o or o according as c is greater than or less than the smallest positive zero of m 1 2 1 2 x2 2 1 3069 where m is the confluent hypergeometric function this confirms a conjecture of burgess davis whose methods play a major role in the proofs the results are also extended to higher dimensions

blind identification of arma channels with periodically modulated inputs previous results have pointed out the importance of inducing cyclostationarity at the transmitter for blind identification of fir communication channels the present paper considers the blind identification problem of an arma p q channel by exploiting the cyclostationarity induced at the transmitter through periodic encoding of the input it is shown that causal and stable arma p q channels can be uniquely identified from the output second order cyclic statistics irrespective of the location of channel poles and zeros and color of additive stationary noise provided that the cyclostationary input has at least q 1 nonzero cycles

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