bayesian analysis of nonlinear autoregression models based on neural networks we show how bayesian neural networks can be used for time series analysis we consider a block based model building strategy to model linear and nonlinear features within the time series a linear combination of a linear autoregression term and a feedforward neural network ffnn with an unknown number of hidden nodes to allow for simpler models we also consider these terms separately as competing models to select from model identifiability problems arise when ffnn sigmoidal activation functions exhibit almost linear behavior or when there are almost duplicate or irrelevant neural network nodes new reversible jump moves are proposed to facilitate model selection mitigating model identifiability problems we illustrate this methodology analyzing several time series data examples

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

bayesian inversion of geoelectrical resistivity data summary enormous quantities of geoelectrical data are produced daily and often used for large scale reservoir modelling to interpret these data requires reliable and efficient inversion methods which adequately incorporate prior information and use realistically complex modelling structures we use models based on random coloured polygonal graphs as a powerful and flexible modelling framework for the layered composition of the earth and we contrast our approach with earlier methods based on smooth gaussian fields we demonstrate how the reconstruction algorithm may be efficiently implemented through the use of multigrid metropolis coupled markov chain monte carlo methods and illustrate the method on a set of field data

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

comparing non nested linear models abstract i consider the usual linear model situation except that there are two possible linear subspaces that may contain the true mean vector and neither of the two subspaces is nested within the other approximate confidence intervals are developed for the difference in mean squared error mse of prediction using the two models not assuming that either model is necessarily correct the confidence intervals are based on parametric bootstrap methods applied to mallows s cp estimate of the difference in mse this approach is shown to relate closely to hotelling s test comparing two simple linear regressions in the simplest case the problem is equivalent to finding a confidence interval for the product of the means of two independent normal observations each with variance one

a generalization of the vidav jorgens perturbation theorem for semigroups and its application to transport theory on considere des semigroupes t t engendres par l operateur de transport a k comme une perturbation du semi groupe s t engendre par a seul on montre que pour un n tous les produits de la forme ks td 1k ks tnd k t i 0 sont strictement singuliers alors s t et t t ont le meme rayon spectral essentiel

a bayesian approach to ordering gene markers a technique is presented whereby a marker map can be constructed using resource family data with an entire class of missing data the focus is on a half sib design where there is only information on a single parent and its progeny a bayesian approach is utilised with solutions obtained via a markov chain monte carlo algorithm features of the approach include the capacity to determine parameters for the ungenotyped dam population the ability to incorporate published information and its reliability and the production of posterior densities and the consequent deduction of a wide range of inferences these features are demonstrated through the analysis of simulated and experimental data

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

a flexible approach to parametric inference in nonlinear and time varying time series models many structural break and regime switching models have been used with macroeconomic and financial data in this paper we develop an extremely flexible modeling approach which can accommodate virtually any of these specifications we build on earlier work showing the relationship between flexible functional forms and random variation in parameters our contribution is based around the use of priors on the time variation that is developed from considering a hypothetical reordering of the data and distance between neighboring reordered observations the range of priors produced in this way can accommodate a wide variety of nonlinear time series models including those with regime switching and structural breaks by allowing the amount of random variation in parameters to depend on the distance between reordered observations the parameters can evolve in a wide variety of ways allowing for everything from models exhibiting abrupt change e g threshold autoregressive models or standard structural break models to those which allow for a gradual evolution of parameters e g smooth transition autoregressive models or time varying parameter models bayesian econometric methods for inference are developed for estimating the distance function and types of hypothetical reordering conditional on a hypothetical reordering and distance function a simple reordering of the actual data allows us to estimate our models with standard state space methods by a simple adjustment to the measurement equation we use artificial data to show the advantages of our approach before providing two empirical illustrations involving the modeling of real gdp growth

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

bayesian inference and state number determination for hidden markov models an application to the information content of the yield curve about inflation this paper is concerned with bayesian inference in hidden markov models focusing on switching regression models we propose a new methodology that delivers a joint estimation of the parameters and the number of regimes that have actually appeared in the studied sample the only prior information that is required on the latter quantity is an upper bound we implement a particle filter algorithm to compute the corresponding estimates applying this methodology to the information content of the yield curve regarding future inflation in four oecd countries we show that the predictive content for given country and combination of maturities is subject to regime switching

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

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

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

weak spectral mapping theorems for c0 groups associated to transport equations in slab geometry abstract we show in this paper that the c 0 groups governing neutron transport equations with reflecting boundary conditions in slab geometry satisfy a weak spectral mapping theorem in any l p spaces 1 p the main part of this paper is dealing with collisionless transport c 0 group while the full transport c 0 group is dealt with by stability arguments

fast bayesian approach for parameter estimation this paper presents two techniques i e the proper orthogonal decomposition pod and the stochastic collocation method scm for constructing surrogate models to accelerate the bayesian inference approach for parameter estimation problems associated with partial differential equations pod is a model reduction technique that derives reduced order models using an optimal problem adapted basis to effect significant reduction of the problem size and hence computational cost scm is an uncertainty propagation technique that approximates the parameterized solution and reduces further forward solves to function evaluations the utility of the techniques is assessed on the non linear inverse problem of probabilistically calibrating scalar robin coefficients from boundary measurements arising in the quenching process and non destructive evaluation a hierarchical bayesian model that handles flexibly the regularization parameter and the noise level is employed and the posterior state space is explored by the markov chain monte carlo the numerical results indicate that significant computational gains can be realized without sacrificing the accuracy

three dimensional edge waves in plates this paper describes the propagation of three dimensional symmetric waves localized near the traction free edge of a semi infinite elastic plate with either traction free or fixed faces for both t

estimating bayes factors via posterior simulation with the laplace metropolis estimator abstract the key quantity needed for bayesian hypothesis testing and model selection is the integrated or marginal likelihood of a model we describe a way to use posterior simulation output to estimate integrated likelihoods we describe the basic laplace metropolis estimator for models without random effects for models with random effects we introduce the compound laplace metropolis estimator we apply this estimator to data from the world fertility survey and show it to give accurate results batching of simulation output is used to assess the uncertainty involved in using the compound laplace metropolis estimator the method allows us to test for the effects of independent variables in a random effects model and also to test for the presence of the random effects

optimal spectral theory of the linear boltzmann equation we give optimal compactness results in lp spaces 1 p related to spectral theory of general neutron transport equations on spatial domains with finite lebesgue measure

singular one dimensional transport equations on lp spaces we prove the well posedness of the cauchy problem governed by a linear mono energetic singular transport equation i e transport equation with unbounded collision frequency and unbounded collision operator with specular reflecting and periodic boundary conditions on lp spaces the large time behaviour of its solution is also considered we discuss the compactness properties of the second order remainder term of the dyson phillips expansion for a large class of singular collision operators this allows us to evaluate the essential type of the transport semigroup from which the asymptotic behaviour of the solution is derived

the critical spectrum of a strongly continuous semigroup for a strongly continuous semigroup t t t 0 with generator a we introduce its critical spectrum crit t t this yields in an optimal way the spectral mapping theorem t t et a crit t t and improves classical stability results

on l1 exponential trend to equilibrium for conservative linear kinetic equations on the torus we compute the growth bound of weighted advection semigroups on the n dimensional flat torus with general not necessarily bounded measurable nonnegative collision frequencies and give a compactness theorem in l1 spaces of interest for the stability of essential type of kinetic semigroups under perturbation by scattering operators this provides us with a characterisation of the existence of a spectral gap for general conservative neutron transport like equations various related questions are also dealt with

orthogonality relations for fluid structural waves in a three dimensional rectangular duct with flexible walls an exact expression for the fluid coupled structural waves that propagate in a three dimensional rectangular waveguide with elastic walls is presented in terms of the non separable eigenfunctions n y z it is proved that these eigenfunctions are linearly dependent and that an eigenfunction expansion representation of a suitably smooth function f y z converges point wise to that function orthogonality results for the derivatives n y a z are derived which together with a partial orthogonality relation for n y z enable the solution of a wide range of acoustic scattering problems two prototype problems of the type typically encountered in two part scattering problems are solved and numerical results showing the displacement of the elastic walls are presented

bayesian inferences of latent class models with an unknown number of classes this paper focuses on analyzing data collected in situations where investigators use multiple discrete indicators as surrogates for example a set of questionnaires a very flexible latent class model is used for analysis we propose a bayesian framework to perform the joint estimation of the number of latent classes and model parameters the proposed approach applies the reversible jump markov chain monte carlo to analyze finite mixtures of multivariate multinomial distributions in the paper we also develop a procedure for the unique labeling of the classes we have carried out a detailed sensitivity analysis for various hyperparameter specifications which leads us to make standard default recommendations for the choice of priors the usefulness of the proposed method is demonstrated through computer simulations and a study on subtypes of schizophrenia using the positive and negative syndrome scale panss

eigenvalue of a semi infinite elastic strip a semi infinite elastic strip subjected to traction free boundary conditions is studied in the context of in plane stationary vibrations by using normal rayleigh lamb mode expansion the problem of existence of the strip eigenmode is reformulated in terms of the linear dependence within infinite system of normal modes the concept of gram s determinant is used to introduce a generalized criterion of linear dependence which is valid for infinite systems of modes and complex frequencies using this criterion it is demonstrated numerically that in addition to the edge resonance for the poisson ratio nz0 there exists another value of nz0 22475 associated with an undamped resonance this resonance is best explained physically by the orthogonality between the edge mode

revisiting the edge resonance for lamb waves in a semi infinite plate the resonance for the elastic plate with a free edge is studied from the point of view of complex resonance the variations of the real part and of the imaginary part of the complex resonance frequency as a function of the poisson ratio are determined numerically the results confirm the real resonance frequency theoretically predicted in i roitberg et al q j mech appl math 51 1 13 1998 for a zero poisson ratio 1 0 and a real resonance frequency that corresponds to a lame mode is discovered for a poisson ratio 2 0 2248 it is shown that both real resonance frequencies may exist at these two particular values of because of the decoupling between the propagating lamb mode and the set of evanescent lamb modes

balanced exponential growth of operator semigroups abstract ac0 semigroups t t 0 on a banach spacex weakly strongly uniformly approachesbalanced or asynchronous exponential growthif there exists somes r such that formula exists in the weak strong uniform operator topology andpis not the 0 operator in this paper the strong and uniform approach to balanced exponential growth is characterized and applicable sufficient conditions are derived the results will be applied to models for age size structured population dynamics in a forthcoming publication

flexural edge waves in semi infinite elastic plates abstract this paper presents a detailed analysis of the dispersion for flexural edge waves in semi infinite isotropic elastic plates a solution to the dynamic equations of motion is constructed by the superposition of two partial solutions each providing zero shear stresses at the plate faces a dispersion equation is expressed via the determinant of an infinite system of linear algebraic equations the system is reduced to a finite one by taking into account the asymptotic behaviour of unknown coefficients the accuracy of the solution is confirmed by a good agreement with the available experimental data and by a proper satisfaction of the prescribed boundary conditions a detailed analysis of dispersion properties for the edge wave and corresponding displacements at various frequencies is carried out in addition to the well known results it is shown that the plate height does not influence the existence of the edge wave at high frequencies and as the frequency increases the phase velocity of the edge wave in a semi infinite plate asymptotically approaches the velocity of an edge wave in a right angled wedge the performed analysis allows evaluating the plate theories such as the kirchhoff theory or other refined plate theories developed for modeling edge waves in semi infinite elastic plates at low frequencies

on three dimensional edge waves in semi infinite isotropic plates subject to mixed face boundary conditions this paper is concerned with the propagation of three dimensional waves localized near the edge of a semi infinite elastic plate subject to mixed face boundary conditions in the linear isotropic case it is shown that the problem is closely related to that of rayleigh surface wave propagation along the free surface of the corresponding half space the cut off frequencies of the analyzed edge waves coincide with the natural frequencies of the associated cross sectional semi infinite strip it is also demonstrated that the eigenspectrum of a rectangular rod can be expressed in terms of the considered three dimensional waves the results are then generalized to a prestressed isotropic incompressible material it is noted that the density of the edge wave spectrum is strongly influenced by the prestress it is illustrated that the areas of negative group velocity may exist for large primary deformation long wave asymptotic expansions in the vicinity of the cut off frequencies are presented

preconditioning markov chain monte carlo simulations using coarse scale models we study the preconditioning of markov chain monte carlo mcmc methods using coarse scale models with applications to subsurface characterization the purpose of preconditioning is to reduce the fine scale computational cost and increase the acceptance rate in the mcmc sampling this goal is achieved by generating markov chains based on two stage computations in the first stage a new proposal is first tested by the coarse scale model based on multiscale finite volume methods the full fine scale computation will be conducted only if the proposal passes the coarse scale screening for more efficient simulations an approximation of the full fine scale computation using precomputed multiscale basis functions can also be used comparing with the regular mcmc method the preconditioned mcmc method generates a modified markov chain by incorporating the coarse scale information of the problem the conditions under which the modified markov chain will converge to the correct posterior distribution are stated in the paper the validity of these assumptions for our application and the conditions which would guarantee a high acceptance rate are also discussed we would like to note that coarse scale models used in the simulations need to be inexpensive but not necessarily very accurate as our analysis and numerical simulations demonstrate we present numerical examples for sampling permeability fields using two point geostatistics the karhunen loeve expansion is used to represent the realizations of the permeability field conditioned to the dynamic data such as production data as well as some static data our numerical examples show that the acceptance rate can be increased by more than 10 times if mcmc simulations are preconditioned using coarse scale models

probabilistic inversion of expert judgments in the quantification of model uncertainty expert judgment is frequently used to assess parameter values of quantitative management science models particularly in decision making contexts experts can however only be expected to assess observable quantities not abstract model parameters this means that we need a method for translating expert assessed uncertainties on model outputs into uncertainties on model parameter values this process is calledprobabilistic inversion the probability distribution on model parameters obtained in this way can be used in a variety of ways but in particular in an uncertainty analysis or as a bayes prior this paper discusses computational algorithms that have proven successful in various projects and gives examples from environmental modelling and banking those algorithms are given a theoretical basis by adopting a minimum information approach to modelling partial information the role of minimum information is two fold it enables us to resolve the problem of nonuniqueness of distributions given the information we have and it provides numerical stability to the algorithm by guaranteeing convergence properties

bayesian inference with optimal maps we present a new approach to bayesian inference that entirely avoids markov chain simulation by constructing a map that pushes forward the prior measure to the posterior measure existence and uniqueness of a suitable measure preserving map is established by formulating the problem in the context of optimal transport theory we discuss various means of explicitly parameterizing the map and computing it efficiently through solution of an optimization problem exploiting gradient information from the forward model when possible the resulting algorithm overcomes many of the computational bottlenecks associated with markov chain monte carlo advantages of a map based representation of the posterior include analytical expressions for posterior moments and the ability to generate arbitrary numbers of independent posterior samples without additional likelihood evaluations or forward solves the optimization approach also provides clear convergence criteria for posterior approximation and facilitates model selection through automatic evaluation of the marginal likelihood we demonstrate the accuracy and efficiency of the approach on nonlinear inverse problems of varying dimension involving the inference of parameters appearing in ordinary and partial differential equations

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

fully bayesian reconstructions from single photon emission computed tomography data abstract with suitably chosen priors bayesian models are useful in image reconstruction i consider reconstructions from single photon emission computerized tomography data using a gibbs pairwise difference prior a fully bayesian approach is presented where the prior parameters are considered drawn from hyperpriors the approach is problematical because the normalization constant in the prior is an intractable function of its parameters here the constant is estimated off line by reverse logistic regression markov chain monte carlo methods are used on simulated and real data to gain estimates of the posterior mean and pixelwise credibility bounds the resulting reconstructions are compared to those obtained by filtered back projection maximum likelihood em and the one step late solution to the fixed parameter posterior mode

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

models for estimating bayes factors with applications to phylogeny and tests of monophyly summary bayes factors comparing two or more competing hypotheses are often estimated by constructing a markov chain monte carlo mcmc sampler to explore the joint space of the hypotheses to obtain ecien t bayes factor estimates carlin and chib 1995 suggest adjusting the prior odds of the competing hypotheses so that the posterior odds are approximately one then estimating the bayes factor by simple division a byproduct is that one often produces several independent mcmc chains only one of which is actually used for estimation we extend this approach to incorporate output from multiple chains by proposing three statistical models the rst assumes independent sampler draws and models the hypothesis indicator function using logistic regression for various choices of the prior odds the two more complex models relax the independence assumption by allowing for higherlag dependence within the mcmc output these models allow us to estimate the uncertainty in our bayes factor calculation and to fully use several dieren t mcmc chains even when the prior odds of the hypotheses vary from chain to chain we apply these methods to calculate bayes factors for tests of monophyly in two phylogenetic

fully bayesian estimation of gibbs hyperparameters for emission computed tomography data in recent years many investigators have proposed gibbs prior models to regularize images reconstructed from emission computed tomography data unfortunately hyperparameters used to specify gibbs priors can greatly influence the degree of regularity imposed by such priors and as a result numerous procedures have been proposed to estimate hyperparameter values from observed image data many of these procedures attempt to maximize the joint posterior distribution on the image scene to implement these methods approximations to the joint posterior densities are required because the dependence of the gibbs partition function on the hyperparameter values is unknown here the authors use recent results in markov chain monte carlo mcmc sampling to estimate the relative values of gibbs partition functions and using these values sample from joint posterior distributions on image scenes this allows for a fully bayesian procedure which does not fix the hyperparameters at some estimated or specified value but enables uncertainty about these values to be propagated through to the estimated intensities the authors utilize realizations from the posterior distribution for determining credible regions for the intensity of the emission source the authors consider two different markov random field mrf models the power model and a line site model as applications they estimate the posterior distribution of source intensities from computer simulated data as well as data collected from a physical single photon emission computed tomography spect phantom

a two stage bayesian model selection strategy for supersaturated designs in early stages of experimentation one often has many candidate factors of which only few have significant influence on the response supersaturated designs can offer important advantages however standard regression techniques of fitting a prediction line using all candidate variables fail to analyze data from such designs stepwise regression may be used but has drawbacks as reported in the literature a two stage bayesian model selection strategy able to keep all possible models under consideration while providing a level of robustness akin to bayesian analyses incorporating noninformative priors is proposed the strategy is demonstrated on a well known dataset and compared to competing methods via simulation

a compactness result for perturbed semigroups and application to a transport model abstract in this paper we are concerned with the compactness properties of remainder terms of the dyson phillips expansion of perturbed semigroups on general banach spaces more specifically we derive conditions which ensure the compactness of the remainder term r n t for some integer n our result applies directly to discuss the time asymptotic behaviour for large times of the solution of a one dimensional transport equation with reentry boundary conditions on l 1 spaces without regularity conditions on the initial data

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

markov random field models for high dimensional parameters in simulations of fluid flow in porous media we give an approach for using flow information from a system of wells to characterize hydrologic properties of an aquifer in particular we consider experiments where an impulse of tracer fluid is injected along with the water at the input wells and its concentration is recorded over time at the uptake wells we focus on characterizing the spatially varying permeability field which is a key attribute of the aquifer for determining flow paths and rates for a given flow experiment as is standard for estimation from such flow data we use complicated subsurface flow code that simulates the fluid flow through the aquifer for a particular well configuration and aquifer specification in particular the permeability field over a grid the solution to this ill posed problem requires that some regularity conditions be imposed on the permeability field typically this regularity is accomplished by specifying a stationary gaussian process model for the permeability field here we use an intrinsically stationary

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

expectation propagation for nonlinear inverse problems with an application to electrical impedance tomography in this paper we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the bayesian formulation of nonlinear inverse problems it is capable of efficiently delivering reliable estimates of the posterior mean and covariance thereby providing an inverse solution together with quantified uncertainties some theoretical properties of the iterative algorithm are discussed and the efficient implementation for an important class of problems of projection type is described the method is illustrated with one typical nonlinear inverse problem electrical impedance tomography with complete electrode model under sparsity constraints numerical results for real experimental data are presented and compared with that by markov chain monte carlo the results indicate that the method is accurate and computationally very efficient

a multi resolution non parametric bayesian framework for identification of spatially varying model parameters this paper proposes a hierarchical multi resolution framework for the identification of model parameters and their spatially variability from noisy measurements of the response or output such parameters are frequently encountered in pde based models and correspond to quantities such as density or pressure fields elasto plastic moduli and internal variables in solid mechanics conductivity fields in heat diffusion problems permeability fields in fluid flow through porous media etc the proposed model has all the advantages of traditional bayesian formulations such as the ability to produce measures of confidence for the inferences made and providing not only predictive estimates but also quantitative measures of the predictive uncertainty in contrast to existing approaches it utilizes a parsimonious non parametric formulation that favors sparse representations and whose complexity can be determined from the data the proposed framework in non intrusive and makes use of a sequence of forward solvers operating at various resolutions as a result inexpensive coarse solvers are used to identify the most salient features of the unknown field s which are subsequently enriched by invoking solvers operating at finer resolutions this leads to significant computational savings particularly in problems involving computationally demanding forward models but also improvements in accuracy it is based on a novel adaptive scheme based on sequential monte carlo sampling which is embarrassingly parallelizable and circumvents issues with slow mixing encountered in markov chain monte carlo schemes the capabilities of the proposed methodology are illustrated in problems from nonlinear solid mechanics with special attention to cases where the data is contaminated with random noise and the scale of variability of the unknown field is smaller than the scale of the grid where observations are collected

hierarchical analysis of sur models with extensions to correlated serial errors and time varying parameter models we consider the use of markov chain monte carlo methods to analyze hierarchical versions of zellner s sur model in this context the questions of bayes estimation and model adequacy checking are considered the approach is extended to sur model with vector autoregressive and vector moving average errors of the first order finally an efficient algorithm is developed to estimate a markov time varying parameter sur model the ideas are applied to both simulated and real data

a statistical model for positron emission tomography abstract positron emission tomography pet still in its research stages is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner much as in x ray transmission tomography and other modes of computerized tomography the quality of the reconstructed image in pet is very sensitive to the mathematical algorithm to be used for reconstruction in this article we tailor a mathematical model to the physics of positron emissions and we use the model to describe the basic image reconstruction problem of pet as a standard problem in statistical estimation from incomplete data we describe various estimation procedures such as the maximum likelihood ml method using the em algorithm the method of moments and the least squares method a computer simulation of a pet experiment is then used to demonstrate the ml and the least squares reconstructions the main purposes of this article are to report on what we believe is an

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

variable selection via gibbs sampling abstract a crucial problem in building a multiple regression model is the selection of predictors to include the main thrust of this article is to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets this procedure entails embedding the regression setup in a hierarchical normal mixture model where latent variables are used to identify subset choices in this framework the promising subsets of predictors can be identified as those with higher posterior probability the computational burden is then alleviated by using the gibbs sampler to indirectly sample from this multinomial posterior distribution on the set of possible subset choices those subsets with higher probability the promising ones can then be identified by their more frequent appearance in the gibbs sample

the non analytic growth bound of a c0 semigroup and inhomogeneous cauchy problems abstract the non analytic growth bound t of a c0 semigroup t measures the extent to which t can be approximated by a holomorphic function and it is related to spectral properties of the generator a in regions of c far from the real axis we show that t can be characterised by means of fourier multiplier properties of the resolvent of a far from the real axis and also by existence and uniqueness of mild solutions of inhomogeneous cauchy problems of the form u t au t f t on r where the carleman spectra of f and u are far from the origin the corresponding results for the exponential growth bound 0 t have been established earlier by other authors

a bayesian approach to model selection in stochastic coefficient regression models and structural time series models abstract a bayesian model selection procedure is proposed for a stochastic coefficient regression model to determine which coefficients are fixed and which are time varying the posterior probabilities are computed by gaussian quadrature using the kalman filter it is shown empirically that the model selection approach works well on both simulated and real data a similar approach can be used to select a model from a class of state space models in particular for a trend plus seasonal structural time series model we show how to determine if the trend and or seasonal component is deterministic or stochastic

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

variable selection and functional form uncertainty in cross country growth regressions regression analyses of cross country economic growth data are complicated by two main forms of model uncertainty the uncertainty in selecting explanatory variables and the uncertainty in specifying the functional form of the regression function most discussions in the literature address these problems independently yet a joint treatment is essential we present a new framework that makes such a joint treatment possible using flexible nonlinear models specified by gaussian process priors and addressing the variable selection problem by means of bayesian model averaging using this framework we extend the linear model to allow for parameter heterogeneity of the type suggested by new growth theory while taking into account the uncertainty in selecting explanatory variables controlling for variable selection uncertainty we confirm the evidence in favor of parameter heterogeneity presented in several earlier studies however controlling for functional form uncertainty we find that the effects of many of the explanatory variables identified in the literature are not robust across countries and variable selections

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

a bayesian approach to characterizing uncertainty in inverse problems using coarse and fine scale information the bayesian approach allows one to easily quantify uncertainty at least in theory in practice however the markov chain monte carlo mcmc method can be computationally expensive particularly in complicated inverse problems we present a methodology for improving the speed and efficiency of an mcmc analysis by combining runs on different scales by using a coarser scale the chain can run faster particularly when there is an external forward simulator involved in the likelihood evaluation and better explore the posterior being less likely to become stuck in local maxima we discuss methods for linking the coarse chain back to the original fine scale chain of interest the resulting coupled chain can thus be run more efficiently without sacrificing the accuracy achieved at the finer scale