bayesian analysis of dichotomous quantal response models abstract qualitative response models qrm s are analyzed from the bayesian point of view using diffuse and informative prior distributions exact finite sample bayesian and large sample bayesian and non bayesian estimation results are compared in addition the paper provides 1 plots and discussion of the properties of likelihood functions for qrm s 2 posterior distributions for logit models derivatives and elasticities 3 bayesian prediction procedures for qrm s 4 new estimates for the median and other fractiles of the logistic distribution 5 posterior odds ratios for model selection problems and 6 comparisons of two alternative monte carlo numerical integration procedures it is concluded that asymptotic approximations are not accurate for small to moderate sized samples even when only a single input variable is used and that operational bayesian methods are available for providing both exact small sample and large sample approximate inferences for drm s

bayesian analysis of time evolution of earthquakes abstract we adopt a bayesian approach to analyze the occurrence times of seismic events and their magnitudes we choose an epidemic model for the process of occurrence times conditional on the observed magnitude values the locations of and dependencies between the model parameters are determined on the basis of historical and physical information the overall prior variability is deliberately made diffuse we generate samples from the joint posterior distribution of the model parameters by using a variant of the metropolis hastings algorithm we use the results in a variety of ways including the construction of pointwise posterior confidence bands for the conditional intensity of the point process as a function of time

bayesian isotonic regression and trend analysis in many applications the mean of a response variable can be assumed to be a nondecreasing function of a continuous predictor controlling for covariates in such cases interest often focuses on estimating the regression function while also assessing evidence of an association this article proposes a new framework for bayesian isotonic regression and order restricted inference approximating the regression function with a high dimensional piecewise linear model the nondecreasing constraint is incorporated through a prior distribution for the slopes consisting of a product mixture of point masses accounting for flat regions and truncated normal densities to borrow information across the intervals and smooth the curve the prior is formulated as a latent autoregressive normal process this structure facilitates efficient posterior computation since the full conditional distributions of the parameters have simple conjugate forms point and interval estimates of the regression function and posterior probabilities of an association for different regions of the predictor can be estimated from a single mcmc run generalizations to categorical outcomes and multiple predictors are described and the approach is applied to an epidemiology application

efficient implementation of markov chain monte carlo when using an unbiased likelihood estimator summary when an unbiased estimator of the likelihood is used within a metropolis hastings chain it is necessary to trade off the number of monte carlo samples used to construct this estimator against the asymptotic variances of the averages computed under this chain using many monte carlo samples will typically result in metropolis hastings averages with lower asymptotic variances than the corresponding averages that use fewer samples however the computing time required to construct the likelihood estimator increases with the number of samples under the assumption that the distribution of the additive noise introduced by the loglikelihood estimator is gaussian with variance inversely proportional to the number of samples and independent of the parameter value at which it is evaluated we provide guidelines on the number of samples to select we illustrate our results by considering a stochastic volatility model applied to stock index returns

bayesian semiparametric wiener system identification we present a novel method for wiener system identication the method relies on a semiparametric i e a mixed parametric nonparametric model of a wiener system we use a state space model for the linear dynamical system and a nonparametric gaussian process model for the static nonlinearity we avoid making strong assumptions such as monotonicity on the nonlinear mapping stochastic disturbances entering both as measurement noise and as process noise are handled in a systematic manner the nonparametric nature of the gaussian process allows us to handle a wide range of nonlinearities without making problem specic parameterizations we also consider sparsity promoting priors based on generalized hyperbolic distributions to automatically infer the order of the underlying dynamical system we derive an inference algorithm based on an ecient particle markov chain monte carlo method referred to as particle gibbs with ancestor sampling the method is proled on two challenging identication problems with good results blind wiener system identication is handled as a special case

global existence and asymptotic stability of smooth solutions to a fluid dynamics model of biofilms in one space dimension abstract in this paper we present an analytical study in the one space dimensional case of the fluid dynamics system proposed in 3 to model the formation of biofilms after showing the hyperbolicity of the system we show that in an open neighborhood of the physical parameters the system is totally dissipative near its unique non vanishing equilibrium point using this property we are able to prove existence and uniqueness of global smooth solutions to the cauchy problem on the whole line for small perturbations of this equilibrium point and the solutions are shown to converge exponentially in time at the equilibrium state

on the geometric convergence of the gibbs sampler summary the rate of convergence of the gibbs sampler is discussed the gibbs sampler is a monte carlo simulation method with extensive application to computational issues in the bayesian paradigm conditions for the geometric rate of convergence of the algorithm for discrete and continuous parameter spaces are derived and an illustrative exponential family example is given this paper investigates conditions under which the gibbs sampler gelfand and smith 1990 tanner and wong 1987 geman and geman 1984 converges at a geometric rate the main results appear in sections 2 and 3 where geometric convergence results are established with respect to total variation and supremum norms under fairly natural conditions on the underlying distribution for ease of exposition we shall concentrate on the two most commonly encountered situations where the state space is finite or continuous all our results will establish uniform convergence a strong form of geometric convergence under appropriate regularity conditions uniform convergence is a useful property in its own right but also happens to be a sufficient condition for certain ergodic central limit theorems such results are important for estimation in markov chain simulation but will not be considered in detail here our approach is to apply the theory of markov chains to the specific gibbs sampler case in the finite state space case uniform ergodicity is automatic however the situation is more complicated for continuous state spaces where even well behaved underlying distributions can give rise to markov chains which converge slowly or have unbounded kernels we give two results in this context corollary 2 and corollary 3 which establish uniform convergence under different sets of conditions on the underlying density finally we apply these results to an example of a bayesian hierarchical model where regularity conditions for geometric convergence are naturally satisfied here the hierarchical structure of the model is crucial in permitting application of corollary 3

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

convergence of adaptive mixtures of importance sampling schemes in the design of ecient simulation algorithms one is often beset with a poor choice of proposal distributions although the performances of a given kernel can clarify how adequate it is for the problem at hand a permanent on line modification of kernels causes concerns about the validity of the resulting algorithm while the issue is quite complex and most often intractable for mcmc algorithms the equivalent version for importance sampling algorithms can be validated quite precisely we derive sucient convergence conditions for a wide class of population monte carlo algorithms and show that rao blackwellized versions asymptotically achieve an optimum in terms of a kullback divergence criterion while more rudimentary versions simply do not benefit from repeated updating

a coupling regeneration scheme for diagnosing convergence in markov chain monte carlo algorithms abstract here i propose a convergence diagnostic for markov chain monte carlo mcmc algorithms based on couplings of a markov chain with an auxiliary chain that is periodically restarted from a fixed parameter value the diagnostic provides a mechanism for estimating the specific constants governing the rate of convergence of geometrically and uniformly ergodic chains and provides a lower bound on the effective sample size of a mcmc run it also provides a simple procedure for obtaining what is with high probability an independent sample from the stationary distribution

robust full bayesian learning for radial basis networks we propose a hierarchical full bayesian model for radial basis networks this model treats the model dimension number of neurons model parameters regularization parameters and noise parameters as unknown random variables we develop a reversible jump markov chain monte carlo mcmc method to perform the bayesian computation we find that the results obtained using this method are not only better than the ones reported previously but also appear to be robust with respect to the prior specification in addition we propose a novel and computationally efficient reversible jump mcmc simulated annealing algorithm to optimize neural networks this algorithm enables us to maximize the joint posterior distribution of the network parameters and the number of basis function it performs a global search in the joint space of the parameters and number of parameters thereby surmounting the problem of local minima to a large extent we show that by calibrating the full hierarchical bayesian prior we can obtain the classical akaike information criterion bayesian information criterion and minimum description length model selection criteria within a penalized likelihood framework finally we present a geometric convergence theorem for the algorithm with homogeneous transition kernel and a convergence theorem for the reversible jump mcmc simulated annealing method

asymptotic efficiency of the sample mean in markov chain monte carlo schemes in many cases a univariate time series derived from a time reversible stationary markov chain has the property that there is a distribution function on 1 1 0 1 such that for all non negative integers l its lth moment is the ith lag autocorrelation of the time series we discuss some consequences of this property effects of the asymptotic efficiency of the sample mean on the efficiency of subsampling a stationary markov chain are discussed the stationarity assumption is then relaxed we show that under certain regularity conditions the sample mean of a strongly asymptotically stationary process is asymptotically efficient in that it has the smallest mean square error asymptotically in a broad class of linear estimators

monte carlo inference in econometric models with symmetric stable disturbances the paper develops markov chain monte carlo methods to perform exact posterior analysis in models with symmetric stable paretian disturbances it is shown how posterior moments and marginal densities of functions of parameters can be computed methodically by combining a gibbs sampler with metropolis independence chains the new method is shown to perform satisfactorily in constructed examples the method is also applied to a set of monthly real exchange rates and the question of difference versus trend stationarity is taken up jointly with the problem of inference about the parameter of the stable distribution

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

generalized linear models with random effects a gibbs sampling approach abstract generalized linear models have unified the approach to regression for a wide variety of discrete continuous and censored response variables that can be assumed to be independent across experimental units in applications such as longitudinal studies genetic studies of families and survey sampling observations may be obtained in clusters responses from the same cluster cannot be assumed to be independent with linear models correlation has been effectively modeled by assuming there are cluster specific random effects that derive from an underlying mixing distribution extensions of generalized linear models to include random effects has thus far been hampered by the need for numerical integration to evaluate likelihoods in this article we cast the generalized linear random effects model in a bayesian framework and use a monte carlo method the gibbs sampler to overcome the current computational limitations the resulting algorithm is flexible to easily accommodate changes in the number

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 inference in econometric models using monte carlo integration methods for the systematic application of monte carlo integration with importance sampling to bayesian inference in econometric models are developed conditions under which the numerical approximation of a posterior moment converges almost surely to the true value as the number of monte carlo replications increases and the numerical accuracy of this approximation may be assessed reliably are set forth methods for the analytical verification of these conditions are discussed

bayesian modeling of measurement error in predictor variables using item response theory it is shown that measurement error in predictor variables can be modeled using item response theory irt the predictor variables that may be defined at any level of an hierarchical regression model are treated as latent variables the normal ogive model is used to describe the relation between the latent variables and dichotomous observed variables which may be responses to tests or questionnaires it will be shown that the multilevel model with measurement error in the observed predictor variables can be estimated in a bayesian framework using gibbs sampling in this article handling measurement error via the normal ogive model is compared with alternative approaches using the classical true score model examples using real data are given

automatic bayesian curve fitting summary a method of estimating a variety of curves by a sequence of piecewise polynomials is proposed motivated by a bayesian model and an appropriate summary of the resulting posterior distribution a joint distribution is set up over both the number and the position of the knots defining the piecewise polynomials throughout we use reversible jump markov chain monte carlo methods to compute the posteriors the methodology has been successful in giving good estimates for smooth functions i e continuous and differentiable as well as functions which are not differentiable and perhaps not even continuous at a finite number of points the methodology is extended to deal with generalized additive models

bayesian analysis of two overdispersed poisson models in this paper we consider the bayesian analysis of two overdispersed poisson models the first is an overdispersed generalized poisson model the second is an ordinary poisson and overdispersed generalized poisson mixture model shoukri and consul 1989 comimintiicationis inz statistics simnllationi anzd comiiptutationi 18 1465 1480 have previously considered a limited form of approximate bayesian analysis for the first of these two models requiring the use of pearson curves and the assumption that a certain model parameter has support on a finite number of values by way of comparison this paper demonstrates how a full bayesian analysis of either model may proceed by making use of the gibbs sampler and adaptive rejection sampling methods for log concave densities the methodology is illustrated with an application to a biological data set

group testing with blockers and synergism discovery and development of a new drug can cost hundreds of millions of dollars pharmaceutical companies have used group testing methodology routinely as one of the efficient high throughput screening techniques to search for lead compounds among collections of hundreds of thousands of chemical compounds the lead compounds can be modified to produce new and effective molecules which eventually may lead to new drugs this article develops models and estimation procedures to obtain quantitative information from data in such applications it investigates group testing procedures and studies cost efficiency when the standard assumption adopted by dorfman that tested items act independently of one another is violated the investigation is focused on but not limited to the square array pooling method and the methodologies developed are illustrated through simulations and a drug discovery dataset from glaxo wellcome inc

bayesian latent variable models for clustered mixed outcomes a general framework is proposed for modelling clustered mixed outcomes a mixture of generalized linear models is used to describe the joint distribution of a set of underlying variables and an arbitrary function relates the underlying variables to be observed outcomes the model accommodates multilevel data structures general covariate effects and distinct link functions and error distributions for each underlying variable within the framework proposed novel models are developed for clustered multiple binary unordered categorical and joint discrete and continuous outcomes a markov chain monte carlo sampling algorithm is described for estimating the posterior distributions of the parameters and latent variables because of the flexibility of the modelling framework and estimation procedure extensions to ordered categorical outcomes and more complex data structures are straightforward the methods are illustrated by using data from a reproductive toxicity study

likelihood analysis of non gaussian measurement time series summary in this paper we provide methods for estimating non gaussian time series models these techniques rely on markov chain monte carlo to carry out simulation smoothing and bayesian posterior analysis of parameters and on importance sampling to estimate the likelihood function for classical inference the time series structure of the models is used to ensure that our simulation algorithms are efficient

bayesian deconvolution of noisy filtered point processes the detection and estimation of filtered point processes using noisy data is an essential requirement in many seismic ultrasonic and nuclear applications we address this joint detection estimation problem using a bayesian approach which allows us to easily include any relevant prior information performing bayesian inference for such a complex model is a challenging computational problem as it requires the evaluation of intricate high dimensional integrals we develop here an efficient stochastic procedure based on a reversible jump markov chain monte carlo method to solve this problem and prove the geometric convergence of the algorithm the proposed model and algorithm are demonstrated on an application arising in nuclear science

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

likelihood estimation and inference in a class of nonregular econometric models we study inference in structural models with a jump in the conditional density where location and size of the jump are described by regression curves two prominent examples are auction models where the bid density jumps from zero to a positive value at the lowest cost and equilibrium job search models where the wage density jumps from one positive level to another at the reservation wage general inference in such models remained a long standing unresolved problem primarily due to nonregularities and computational difficulties caused by discontinuous likelihood functions this paper develops likelihood based estimation and inference methods for these models focusing on optimal bayes and maximum likelihood procedures we derive convergence rates and distribution theory and develop bayes and wald inference we show that bayes estimators and confidence intervals are attractive both theoretically and computationally and that bayes confidence intervals based on posterior quantiles provide a valid large sample inference method

bayesian forecasting of multinomial time series through conditionally gaussian dynamic models abstract we consider inference in the class of conditionally gaussian dynamic models for nonnormal multivariate time series in such models data are represented as drawn from nonnormal sampling distributions whose parameters are related both through time and hierarchically across several multivariate series a key example the main focus here is time series of multinomial observations a common occurrence in sociological and demographic studies involving categorical count data however we present this development in a more general setting as the resulting methods apply beyond the multinomial context we discuss inference in the proposed model class via a posterior simulation scheme based on appropriate modifications of existing markov chain monte carlo algorithms for normal dynamic linear models and including metropolis hastings components we develop an analysis of time series of flows of students in the italian secondary education system as an illustration of the models and methods

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

nonparametric bayesian estimation of positive false discovery rates we propose a dirichlet process mixture model dpmm for the p value distribution in a multiple testing problem the dpmm allows us to obtain posterior estimates of quantities such as the proportion of true null hypothesis and the probability of rejection of a single hypothesis we describe a markov chain monte carlo algorithm for computing the posterior and the posterior estimates we propose an estimator of the positive false discovery rate based on these posterior estimates and investigate the performance of the proposed estimator via simulation we also apply our methodology to analyze a leukemia data set

bayesian semiparametric analysis of developmental toxicology data modeling of developmental toxicity studies often requires simple parametric analyses of the dose response relationship between exposure and probability of a birth defect but poses challenges because of nonstandard distributions of birth defects for a fixed level of exposure this article is motivated by two such experiments in which the distribution of the outcome variable is challenging to both the standard logistic model with binomial response and its parametric multistage elaborations we approach our analysis using a bayesian semiparametric model that we tailored specifically to developmental toxicology studies it combines parametric dose response relationships with a flexible nonparametric specification of the distribution of the response obtained via a product of dirichlet process mixtures approach pdpm our formulation achieves three goals 1 the distribution of the response is modeled in a general way 2 the degree to which the distribution of the response adapts nonparametrically to the observations is driven by the data and 3 the marginal posterior distribution of the parameters of interest is available in closed form the logistic regression model as well as many of its extensions such as the beta binomial model and finite mixture models are special cases in the context of the two motivating examples and a simulated example we provide model comparisons illustrate overdispersion diagnostics that can assist model specification show how to derive posterior distributions of the effective dose parameters and predictive distributions of response and discuss the sensitivity of the results to the choice of the prior distribution

convergence of slice sampler markov chains we analyse theoretical properties of the slice sampler we find that the algorithm has extremely robust geometric ergodicity properties for the case of just one auxiliary variable we demonstrate that the algorithm is stochastically monotone and we deduce analytic bounds on the total variation distance from stationarity of the method by using foster lyapunov drift condition methodology

striated metropolis hastings sampler for high dimensional models having efficient and accurate samplers for simulating the posterior distribution is crucial for bayesian analysis we develop a generic posterior simulator called the dynamic striated metropolis hastings dsmh sampler grounded in the metropolis hastings algorithm it pools the strengths from the equi energy and sequential monte carlo samplers while avoiding the weaknesses of the standard metropolis hastings algorithm and those of importance sampling in particular the dsmh sampler possesses the capacity to cope with extremely irregular distributions that contain winding ridges and multiple peaks and it is robust to how the sampling procedure progresses across stages the high dimensional application studied in this paper provides a natural platform for testing any generic sampler

importance weighted marginal bayesian posterior density estimation abstract markov chain sampling schemes generate dependent observations i 0 i n from a full joint posterior distribution data frequently only certain marginals of this full posterior density are of interest thus an interesting problem is how to estimate the marginal posterior densities based on the dependent observations i 0 i n from data we propose a new importance weighted marginal density estimation iwmde method an iwmde is obtained by averaging many dependent observations of the ratio of the full joint posterior densities multiplied by a weighting conditional density w the asymptotic properties for the iwmde and the guidelines for choosing a weighting conditional density w are also considered a bivariate normal model and a constrained linear multiple regression model are used to illustrate how to derive the iwmde s for the marginal posterior densities

asymptotic behavior of solutions for finite difference equations of reaction diffusion abstract the method of upper lower solutions and the associated existence comparison theorem for continuous reaction diffusion equations are extended to a finite difference system which is a discrete version of the continuous problem of either parabolic type or elliptic type under appropriate boundary condition it is shown by using the existence comparison theorem for the discrete system that for a certain class of initial functions the corresponding time dependent solution converges monotonically to a steady state solution this monotone convergence leads to the stability property of the steady state solution as well as an estimate of the stability region in the framework of the finite difference system numerical results are given for an enzyme substrate reaction model where multiple steady state solutions exist for a certain range of physical parameters in this situation the time dependent solution converges either to the maximal solution or to the minimal solution depending on the corresponding initial function

on monte carlo methods for estimating ratios of normalizing constants recently estimating ratios of normalizing constants has played an important role in bayesian computations applications of estimating ratios of normalizing constants arise in many aspects of bayesian statistical inference in this article we present an overview and discuss the current monte carlo methods for estimating ratios of normalizing constants then we propose a new ratio importance sampling method and establish its theoretical framework we find that the ratio importance sampling method can be better than the current methods for example the bridge sampling method meng and wong and the path sampling method gelman and meng in the sense of minimizing asymptotic relative mean square errors of estimators an example is given for illustrative purposes finally we present two special applications and the general implementation issues for estimating ratios of normalizing constants

bayesian inference in a sample selection model this paper develops methods of bayesian inference in a sample selection model the main feature of this model is that the outcome variable is only partially observed we first present a gibbs sampling algorithm for a model in which the selection and outcome errors are normally distributed the algorithm is then extended to analyze models that are characterized by nonnormality specifically we use a dirichlet process prior and model the distribution of the unobservables as a mixture of normal distributions with a random number of components the posterior distribution in this model can simultaneously detect the presence of selection effects and departures from normality our methods are illustrated using some simulated data and an abstract from the rand health insurance experiment

on the convergence of finite difference schemes for parabolic equations with variable coefficients we study the convergence of the finite difference schemes for the first initial boundary value problem for linear second order parabolic equations with variable coefficients using the bilinear version of the bramble hilbert lemma we obtain estimate of convergence in discretew 2 1 1 2 norm compatible with the smoothness of generalized solutionu w 2 2 q 1 3 and coefficients of equation

on prequential model assessment in life history analysis summary we extend the prequential approach introduced by a p dawid to continuous time marked point processes a prequential forecasting system is expressed by means of the stochastic intensities of the point process the exact independence and 1 exponentiality of the derived compensators are used to assess the predictive performance of the model and the inferential procedure

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

central limit theorem for additive functionals of reversible markov processes and applications to simple exclusions we prove a functional central limit theorem for additive functionals of stationary reversible ergodic markov chains under virtually no assumptions other than the necessary ones we use these results to study the asymptotic behavior of a tagged particle in an infinite particle system performing simple excluded random walk

the joint measurement of technical and allocative inefficiencies an application of bayesian inference in nonlinear random effects models this article estimates technical and allocative inefficiencies and increase in costs therefrom of individual firms using a translog cost system consisting of the cost function and the cost share equations we call it a nonlinear random effects system because technical and allocative inefficiencies are random hence the term random effects and are separated from the random noise terms appearing in each equation of the system and because the inefficiency terms appear in the system in a highly nonlinear fashion which helps in separating them from random errors we use bayesian inference procedures based on markov chain monte carlo mcmc techniques to estimate the proposed system inferences on firm specific technical inefficiency and both input specific and firm specific allocative inefficiencies are developed using mcmc techniques we apply the new methods to a sample of 500 u s commercial banks we focus on input allocation problem based on the assumption that banks minimize cost empirical results sh

an analytical evaluation of alternative strategies in steady state simulation we consider the simple technique of making independent and probabilistically identical simulation replications to estimate the steady state mean of a stochastic process for a fixed total sample size using a first order autoregressive model with high autocorrelation and time dependent distributions we analytically quantify and investigate the effects of the number of replications and of initial deletions of output on several different measures of point estimator and confidence interval quality this analysis leads to general recommendations on the choice of replications and deletion in particular we conclude that deletion of some amount of the initial output in a replication can be an effective and efficient method of dealing with initialization bias this conclusion differs from several previous studies on the efficacy of deletion

semiparametric bayesian inference in autoregressive panel data models this paper develops bayesian methods for inference in dynamic panel data models with individual effects and applies them to study longitudinal data on earnings from the panel study of income dynamics psid we study semiparametric versions of commonly used random effects autoregressive models in which the distribution of the disturbances is not restricted to fall in a parametric class to model the unknown distributions without resorting to strong parametric assumptions we draw upon recent advances in the theory and computation of nonparametric bayesian models using dirichlet process priors the overall approach can be viewed as an application of the general semiparametric bayesian approach of west muller and escobar 1994 which in turn makes use of results on bayesian density estimation by escobar 1994 and escobar and west 1995 most conventional panel data methods e g anderson and hsiao 1981 macurdy

inference for mixtures of finite polya tree models mixtures of polya tree models provide a flexible alternative when a parametric model may only hold approximately i provide computational strategies for obtaining full semiparametric inference for mixtures of finite polya tree models given a standard parameterization including models that would be troublesome to fit using dirichlet process mixtures recommendations are put forth on choosing the level of a finite polya tree and model comparison is discussed several examples demonstrate the utility of finite polya tree modeling including data fit to generalized linear mixed models and several survival models

a nonparametric multidimensional latent class irt model in a bayesian framework we propose a nonparametric item response theory model for dichotomously scored items in a bayesian framework the model is based on a latent class lc formulation and it is multidimensional with dimensions corresponding to a partition of the items in homogenous groups that are specified on the basis of inequality constraints among the conditional success probabilities given the latent class moreover an innovative system of prior distributions is proposed following the encompassing approach in which the largest model is the unconstrained lc model a reversible jump type algorithm is described for sampling from the joint posterior distribution of the model parameters of the encompassing model by suitably post processing its output we then make inference on the number of dimensions i e number of groups of items measuring the same latent trait and we cluster items according to the dimensions when unidimensionality is violated the approach is illustrated by two examples on simulated data and two applications based on educational and quality of life data

persistent random walks in random environment weak convergence of a class of functionals of prwre is proved as a consequence clt is obtained for the normed trajectory

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

marginal bayesian semiparametric modeling of mismeasured multivariate interval censored data motivated by data gathered in an oral health study we propose a bayesian nonparametric approach for population averaged modeling of correlated time to event data when the responses can only be de

the efficiency of one long run versus independent replication in steady state simulation we evaluate the efficiency of one long run versus independent replications in steady state discrete event simulation assuming that an initial portion of each replication will be deleted to allow the process to approach steady state we provide supporting evidence in favor of one long run but we also show that multiple replications can be more efficient the advantage of one long run increases if the amount deleted increases or if the covariance function decreases more quickly assuming it is nonnegative and decreasing thus assuming that the amount deleted depends on the way the process approaches steady state one long run tends to be efficient when the covariance function decays rapidly compared to the rate the process approaches steady state we also discuss ways to determine the initial portion to delete we consider the case of an exponential covariance function in detail and use it as a basis for approximations we also consider the m g queueing model and reflected brownian motion the latter

regions of stability equivalence theorems and courant friedichs lewy condition the celebrated cfl condition for discretizations of hyperbolic pdes is shown to be equivalent to some results of jeltsch and nevanlinna concerning regions of stability ofk step m stage linear methods for the integration of odes we characterize the methods for the numerical integration of the model equation ut ux which are weakly stable when the mesh ratio takes the maximum value allowed by the cfl condition we provide new equivalence theorems between stability and convergence which improve on the classical results

global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy we consider the cauchy problem for a general one dimensional n n hyperbolic symmetrizable system of balance laws it is well known that in many physical examples for instance for the isentropic euler system with damping the dissipation due to the source term may prevent the shock formation at least for smooth and small initial data our main goal is to find a set of general and realistic sufficient conditions to guarantee the global existence of smooth solutions and possibly to investigate their asymptotic behavior for systems which are entropy dissipative a quite natural generalization of the kawashima condition for hyperbolic parabolic systems can be given in this paper we first propose a general framework for this kind of problem by using the so called entropy variables then we go on to prove some general statements about the global existence of smooth solutions under different sets of conditions in particular the present approach is suitable for dealing with most of the physical examples of systems with a relaxation extension our main tools will be some refined energy estimates and the use of a suitable version of the kawashima condition

bayesian hierarchical analysis of within units variances in repeated measures experiments we develop hierarchical bayesian models for biomedical data that consist of multiple measurements on each individual under each of several conditions the focus is on investigating differences in within subject variation between conditions we present both population level and individual level comparisons we extend the partial likelihood models of chinchilli et al with a unique bayesian hierarchical framework for variance components and associated degrees of freedom we use the gibbs sampler to estimate posterior marginal distributions for the parameters of the bayesian hierarchical models the application involves a comparison of two cholesterol analysers each applied repeatedly to a sample of subjects both the partial likelihood and bayesian approaches yield similar results although confidence limits tend to be wider under the bayesian models

efficient monte carlo procedures for generating points uniformly distributed over bounded regions we consider the monte carlo problem of generating points uniformly distributed within an arbitrary bounded measurable region the class of markovian methods considered generate points asymptotically uniformly distributed within the region computational experience suggests the methods are potentially superior to conventional rejection techniques for large dimensional regions

practical bayesian density estimation using mixtures of normals abstract mixtures of normals provide a flexible model for estimating densities in a bayesian framework there are some difficulties with this model however first standard reference priors yield improper posteriors second the posterior for the number of components in the mixture is not well defined if the reference prior is used third posterior simulation does not provide a direct estimate of the posterior for the number of components we present some practical methods for coping with these problems finally we give some results on the consistency of the method when the maximum number of components is allowed to grow with the sample size

nonparametric seemingly unrelated regression abstract a method is presented for simultaneously estimating a system of nonparametric regressions which may seem unrelated but where the errors are potentially correlated between equations we show that the advantage of estimating such a seemingly unrelated system of nonparametric regressions is that less observations can be required to obtain reliable function estimates than if each of the regression equations is estimated separately and the correlation ignored this increase in efficiency is investigated empirically using both simulated and real data the method uses a bayesian hierarchical framework where each regression function is represented as a linear combination of a large number of basis terms all the regression coefficients and the variance matrix of the errors are estimated simultaneously by their posterior means the computation is carried out using a markov chain monte carlo sampling scheme that employs a focused sampling step to combat the high dimensional representation of the unknown regression functions the methodology extends easily to other nonparametric multivariate regression models

simulated annealing for maximum a posteriori parameter estimation of hidden markov models hidden markov models are mixture models in which the populations from one observation to the next are selected according to an unobserved finite state space markov chain given a realization of the observation process our aim is to estimate both the parameters of the markov chain and of the mixture model in a bayesian framework we present an original simulated annealing algorithm which in the same way as the em expectation maximization algorithm relies on data augmentation and is based on stochastic simulation of the hidden markov chain this algorithm is shown to converge toward the set of maximum a posteriori map parameters under suitable regularity conditions

bayesian analysis of cross section and clustered data treatment models this paper is concerned with the problem of determining the effect of a categorical treatment variable on a response given that the treatment is non randomly assigned and the response on any given subject is observed for one setting of the treatment we consider classes of models that are designed for such problems these models are subjected to a fully bayesian analysis based on markov chain monte carlo methods the analysis of the treatment effect is then based on amongst other things the posterior distribution of the potential outcomes counter factuals at the subject level which is obtained as a by product of the mcmc simulation procedure the analysis is extended to models with categorical treatments and binary and clustered outcomes the problem of model comparisons is also considered different aspects of the methodology are illustrated through two data examples

bayesian analysis of order statistics models for ranking data in this paper a class of probability models for ranking data the order statistics models is investigated we extend the usual normal order statistics model into one where the underlying random variables follow a multivariate normal distribution bayesian approach and the gibbs sampling technique are used for parameter estimation in addition methods to assess the adequacy of model fit are introduced robustness of the model is studied by considering a multivariate t distribution the proposed method is applied to analyze the presidential election data of the american psychological association apa

variable transformation to obtain geometric ergodicity in the random walk metropolis algorithm a random walk metropolis sampler is geometrically ergodic if its equilibrium density is super exponentially light and satisfies a curvature condition stochastic process appl 85 2000 341 361 many applications including bayesian analysis with conjugate priors of logistic and poisson regression and of log linear models for categorical data result in posterior distributions that are not super exponentially light we show how to apply the change of variable formula for diffeomorphisms to obtain new densities that do satisfy the conditions for geometric ergodicity sampling the new variable and mapping the results back to the old gives a geometrically ergodic sampler for the original variable this method of obtaining geometric ergodicity has very wide applicability

bayesian computation via the gibbs sampler and related markov chain monte carlo methods the use of the gibbs sampler for bayesian computation is reviewed and illustrated in the context of some canonical examples other markov chain monte carlo simulation methods are also briefly described and comments are made on the advantages of sample based approaches for bayesian inference summaries

optimal monte carlo updating based on peskun s theorem it is shown that optimal transition matrices in markov chain monte carlo should have zero diagonal elements except for the diagonal element corresponding to the largest weight we will compare the statistical efficiency of this sampler to existing algorithms such as heat bath updating and the metropolis algorithm we provide numerical results for the potts model as an application in classical physics as an application in quantum physics we consider the spin 3 2xy model and the bose hubbard model which have been simulated by the directed loop algorithm in the stochastic series expansion framework

a bayesian hierarchical model for categorical data with nonignorable nonresponse les modeles log lineaires ont montre leur utilite pour lisser des tableaux de contingence lorsque les variables categorielles sont sujettes a des non reponses qu on ne peut ignorer un modele log lineaire peut etre ajuste a un tableau de donnees augmente qui inclut une variable indicatrice indiquant si les individus sont repondants ou non les estimateurs calcules par maximum de vraisemblance a partir de tableaux de donnees augmentes sont connus pour leur instabilite en raison de solutions frontieres park et brown 1994 et park 1998 ont developpe des modeles bayesiens empiriques qui tendent a lisser les estimateurs a distance de la frontiere avec ces approches les estimateurs pour les non repondants ont ete calcules en maximisant une distribution a posteriori par l algorithme em pour etendre leur precedent travail nous avons developpe un modele hierarchique bayesien qui incorpore un modele log lineaire pour specifier la distribution a priori de plus du fait de l incertitude dans le processus de selection des variables associe a un seul modele log lineaire un nombre fini des modeles en nombre fini ont ete consideres simultanement en utilisant la procedure stochastique de selection de variables ssvs de mcculloch 1997 l integration de la procedure ssvs dans un echantillonneur de monte carlo par chaines de markov mcmc est direct et conduit a des estimations des frequences dans les cellules pour les non repondants qui sont les moyennes resultantes de plusieurs modeles log lineaires les methodes sont demontrees avec un exemple de donnees de niveaux de creatinine chez des patients ayant survecus a des transplantations renales une etude de simulation a ete conduite afin de rechercher les proprietes du modele

asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy we study the asymptotic time behavior of global smooth solutions to general entropy dissipative hyperbolic systems of balance law in m space dimensions under the shizuta kawashima condition we show that these solutions approach constant equilibrium state in the lp norm at a rate o t m 2 1 1 p as t tends to infty for p in min m 2 infty moreover we can show that we can approximate with a faster order of convergence theconservative part of the solution in terms of the linearized hyperbolic operator for m 2 and by a parabolic equation in the spirit of chapman enskog expansion the main tool is given by a detailed analysis of the green function for the linearized problem

fixed width output analysis for markov chain monte carlo markov chain monte carlo is a method of producing a correlated sample to estimate features of a target distribution through ergodic averages a fundamental question is when sampling should stop that is at what point the ergodic averages are good estimates of the desired quantities we consider a method that stops the simulation when the width of a confidence interval based on an ergodic average is less than a user specified value hence calculating a monte carlo standard error is a critical step in assessing the simulation output we consider the regenerative simulation and batch means methods of estimating the variance of the asymptotic normal distribution we give sufficient conditions for the strong consistency of both methods and investigate their finite sample properties in various examples

bayesian wavelet networks for nonparametric regression radial wavelet networks have been proposed previously as a method for nonparametric regression we analyze their performance within a bayesian framework we derive probability distributions over both the dimension of the networks and the network coefficients by placing a prior on the degrees of freedom of the model this process bypasses the need to test or select a finite number of networks during the modeling process predictions are formed by mixing over many models of varying dimension and parameterization we show that the complexity of the models adapts to the complexity of the data and produces good results on a number of benchmark test series

on numerical asymptotic behavior of finite element solutions for parabolic equations in this paper we investigate the numerical asymptotic behavior of the finite element solutions for linear parabolic equations under some appropriate conditions we also give some results of numerical experiments in the two dimensional problems to indicate the effectiveness of our results

sequentially interacting markov chain monte carlo methods we introduce a novel methodology for sampling from a sequence of probability distributions of increasing dimension and estimating their normalizing constants these problems are usually addressed using sequential monte carlo smc methods the alternative sequentially interacting markov chain monte carlo simcmc scheme proposed here works by generating interacting non markovian sequences which behave asymptotically like independent metropolis hastings mh markov chains with the desired limiting distributions contrary to smc methods this scheme allows us to iteratively improve our estimates in an mcmc like fashion we establish convergence of the algorithm under realistic verifiable assumptions and demonstrate its performance on several examples arising in bayesian time series analysis

simulation based optimal bayesian experimental design for nonlinear systems the optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction particularly in situations where experiments are time consuming and expensive to conduct we propose a general mathematical framework and an algorithmic approach for optimal experimental design with nonlinear simulation based models in particular we focus on finding sets of experiments that provide the most information about targeted sets of parameters our framework employs a bayesian statistical setting which provides a foundation for inference from noisy indirect and incomplete data and a natural mechanism for incorporating heterogeneous sources of information an objective function is constructed from information theoretic measures reflecting expected information gain from proposed combinations of experiments polynomial chaos approximations and a two stage monte carlo sampling method are used to evaluate the expected information gain stochastic approximation algorithms are then used to make optimization feasible in computationally intensive and high dimensional settings these algorithms are demonstrated on model problems and on nonlinear parameter inference problems arising in detailed combustion kinetics

a general framework for random effects survival analysis in the cox proportional hazards setting summary the use of random effects modeling in statistics has increased greatly in recent years the introduction of such modeling into event time analysis has proceeded more slowly however previously random effects models for survival data have either required assumptions regarding the form of the baseline hazard function or restrictions on the classes of models that can be fit in this paper we develop a method of random effect analysis of survival data the hierarchical cox model that is an extension of cox s original formulation in that the baseline hazard function remains unspecified this method also allows an arbitrary distribution for the random effects we accomplish this using markov chain monte carlo methods in a bayesian setting the method is illustrated with three models for a dataset with times to multiple occurrences of mammory tumors for 48 rats treated with a carcinogen and then randomized to either treatment or control this analysis is more satisfying than standard approaches such as studying the first event for each subject which does not fully use the data or assuming independence which in this case would overestimate the precision

asymptotic behavior of the gibbs sampler mild sufficient conditions for the ergodicity of the gibbs sampler are obtained the geometric ergodicity of the gibbs sampler is then discussed where the main tool is the drift criterion this criterion requires the construction of a generalized energy function so that the chain is dissipating energy at a suitable rate whenever it lies outside the center of the state space for the two variable case a useful recipe is provided for constructing appropriate energy functions these results are illustrated with four examples

fully exponential laplace approximations to expectations and variances of nonpositive functions abstract tierney and kadane 1986 presented a simple second order approximation for posterior expectations of positive functions they used laplace s method for asymptotic evaluation of integrals in which the integrand is written as f exp nh and the function h is approximated by a quadratic the form in which they applied laplace s method however was fully exponential the integrand was written instead as exp nh log f this allowed first order approximations to be used in the numerator and denominator of a ratio of integrals to produce a second order expansion for the ratio other second order expansions hartigan 1965 johnson 1970 lindley 1961 1980 mosteller and wallace 1964 require computation of more derivatives of the log likelihood function in this article we extend the fully exponential method to apply to expectations and variances of nonpositive functions to obtain a second order approximation to an expectation e g we use the fully exponential method to approximate

semiparametric bayesian inference for time series with mixed spectra summary a bayesian analysis is presented of a time series which is the sum of a stationary component with a smooth spectral density and a deterministic component consisting of a linear combination of a trend and periodic terms the periodic terms may have known or unknown frequencies the advantage of our approach is that different features of the data such as the regression parameters the spectral density unknown frequencies and missing observations are combined in a hierarchical bayesian framework and estimated simultaneously a bayesian test to detect deterministic components in the data is also constructed by using an asymptotic approximation to the likelihood the computation is carried out efficiently using the markov chain monte carlo method in o mn operations where n is the sample size and m is the number of iterations we show empirically that our approach works well on real and simulated samples

on linear intensity models for mixed doubly stochastic poisson and self exciting point processes a flexible family of parametric models for intensity processes is introduced to represent a causal relationship between a point process and another stochastic process algorithms for the maximum likelihood computation and the procedure of model selection are discussed

pathwise accuracy and ergodicity of metropolized integrators for sdes metropolized integrators for ergodic stochastic differential equations sdes are proposed that 1 are ergodic with respect to the known equilibrium distribution of the sdes and 2 approximate pathwise the solutions of the sdes on finitetime intervals both these properties are demonstrated in the paper and precise strong error estimates are obtained it is also shown that the metropolized integrator retains these properties even in situations where the drift in the sde is nonglobally lipschitz and vanilla explicit integrators for sdes typically become unstable and fail to be ergodic 2009 wiley periodicals inc

decision analysis by augmented probability simulation we provide a generic monte carlo method to find the alternative of maximum expected utility in a decision analysis we define an artificial distribution on the product space of alternatives and states and show that the optimal alternative is the mode of the implied marginal distribution on the alternatives after drawing a sample from the artificial distribution we may use exploratory data analysis tools to approximately identify the optimal alternative we illustrate our method for some important types of influence diagrams

robust empirical bayes analyses of event rates a collection of i similar items generates point event histories for example machines experience failures or operators make mistakes suppose the intervals between events are modeled as iid exponential i or the counts as poisson i t i for the ith item furthermore so as to represent between item variability each individual rate parameter i is presumed drawn from a fixed super population with density g being a vector parameter a parametric empirical bayes peb setup for g specified alternatively as log student t n or gamma we exhibit the results of numerical procedures for estimating superpopulation parameters ll and for describing pooled estimates of the individual rates i obtained via bayes s formula three data sets are analyzed and convenient explicit approximate formulas are furnished for i estimates in the student t case the individual estimates are seen to have a robust quality