nonlocal diffusion equations with dynamical boundary conditions abstract in this paper we study nonlocal problems that are analogous to the local ones given by the laplacian or the p laplacian with dynamical boundary conditions we deal both with smooth and with singular kernels and show existence and uniqueness of solutions and study their asymptotic behaviour as t goes to infinity

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

elliptic 1 laplacian equations with dynamical boundary conditions abstract this paper is concerned with an evolution problem having an elliptic equation involving the 1 laplacian operator and a dynamical boundary condition we apply nonlinear semigroup theory to obtain existence and uniqueness results as well as a comparison principle our main theorem shows that the solution we found is actually a strong solution we also compare solutions with different data

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

a bayesian semiparametric survival model with longitudinal markers we consider inference for data from a clinical trial of treatments for metastatic prostate cancer patients joined the trial with diverse prior treatment histories the resulting heterogeneous patient population gives rise to challenging statistical inference problems when trying to predict time to progression on different treatment arms inference is further complicated by the need to include a longitudinal marker as a covariate to address these challenges we develop a semiparametric model for joint inference of longitudinal data and an event time the proposed approach includes the possibility of cure for some patients the event time distribution is based on a nonparametric polya tree prior for the longitudinal data we assume a mixed effects model incorporating a regression on covariates in a nonparametric event time model in general and for a polya tree model in particular is a challenging problem we exploit the fact that the covariate itself is a random variable we achieve an implementation of the desired regression by factoring the joint model for the event time and the longitudinal outcome into a marginal model for the event time and a regression of the longitudinal outcomes on the event time i e we implicitly model the desired regression by modeling the reverse conditional distribution

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

a new heterogeneous multidimensional unfolding procedure a variety of joint space multidimensional scaling mds methods have been utilized for the spatial analysis of two or three way dominance data involving subjects preferences choices considerations intentions etc so as to provide a parsimonious spatial depiction of the underlying relevant dimensions attributes stimuli and or subjects utility structures in the same joint space representation we demonstrate that care must be taken with respect to a key assumption in existent joint space mds models such that all estimated dimensions are utilized by each and every subject in the sample as this assumption can lead to serious distortions with respect to the derived joint spaces we develop a new bayesian dimension selection methodology for the multidimensional unfolding model which accommodates heterogeneity with respect to such dimensional utilization at the individual subject level for the analysis of two or three way dominance data a consumer psychology application regarding the preference for over the counter otc analgesics is provided we conclude by discussing the practical implications of the results as well as directions for future research

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

boundary fluxes for nonlocal diffusion abstract we study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary this problem may be seen as a generalization of the usual neumann problem for the heat equation first we prove existence uniqueness and a comparison principle next we study the behavior of solutions for some prescribed boundary data including blowing up ones finally we look at a nonlinear flux boundary condition

marginal likelihood from the metropolis hastings output this article provides a framework for estimating the marginal likelihood for the purpose of bayesian model comparisons the approach extends and completes the method presented in chib 1995 by overcoming the problems associated with the presence of intractable full conditional densities the proposed method is developed in the context of mcmc chains produced by the metropolis hastings algorithm whose building blocks are used both for sampling and marginal likelihood estimation thus economizing on prerun tuning effort and programming experiments involving the logit model for binary data hierarchical random effects model for clustered gaussian data poisson regression model for clustered count data and the multivariate probit model for correlated binary data are used to illustrate the performance and implementation of the method these examples demonstrate that the method is practical and widely applicable

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 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

new approach to bounding effective properties of random heterogeneous materials a new approach to bounding effective properties of random heterogeneous materials is developed in this paper the expectation material properties are computed for a stochastic unit cell to represent the random heterogeneous materials this stochastic unit cell is then used to compute the upper bound and lower bound of effective properties using the variational asymptotic method for unit cell homogenization a recently developed general purpose micromechanics code in comparison with other approaches the present approach has two main advantages 1 the numerical implementation is not restricted to statically homogeneous and isotropic microstructures 2 both the lower bound and upper bound converge to the effective properties of a deterministic unit cell with decreasing randomness of the stochastic unit cell to illustrate the application of this new approach various examples are analyzed and compared with existing theories

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

semiparametric bayesian analysis of survival data abstract this review article investigates the potential of bayes methods for the analysis of survival data using semiparametric models based on either the hazard or the intensity function the nonparametric part of every model is assumed to be a realization of a stochastic process the parametric part which may include a regression parameter or a parameter quantifying the heterogeneity of a population is assumed to have a prior distribution with possibly unknown hyperparameters careful applications of some recently popular computational tools including sampling based algorithms are used to find posterior estimates of several quantities of interest even when dealing with complex models and unusual data structures the methodologies developed herein are motivated and aimed at analyzing some common types of survival data from different medical studies here we focus on univariate survival data in the presence of fixed and time dependent covariates multiple event time data for repeated nonfatal events

joint models for the association of longitudinal binary and continuous processes with application to a smoking cessation trial joint models for the association of a longitudinal binary and a longitudinal continuous process are proposed for situations in which their association is of direct interest the models are parameterized such that the dependence between the two processes is characterized by unconstrained regression coefficients bayesian variable selection techniques are used to parsimoniously model these coefficients a markov chain monte carlo mcmc sampling algorithm is developed for sampling from the posterior distribution using data augmentation steps to handle missing data several technical issues are addressed to implement the mcmc algorithm efficiently the models are motivated by and are used for the analysis of a smoking cessation clinical trial in which an important question of interest was the effect of the exercise treatment on the relationship between smoking cessation and weight gain

nested sampling algorithm for subsurface flow model selection uncertainty quantification and nonlinear calibration 1 calibration of subsurface flow models is an essential step for managing ground water aquifers designing of contaminant remediation plans and maximizing recovery from hydrocarbon reservoirs we investigate an efficient sampling algorithm known as nested sampling ns which can simultaneously sample the posterior distribution for uncertainty quantification and estimate the bayesian evidence for model selection model selection statistics such as the bayesian evidence are needed to choose or assign different weights to different models of different levels of complexities in this work we report the first successful application of nested sampling for calibration of several nonlinear subsurface flow problems the estimated bayesian evidence by the ns algorithm is used to weight different parameterizations of the subsurface flow models prior model selection the results of the numerical evaluation implicitly enforced occam s razor where simpler models with fewer number of parameters are favored over complex models the proper level of model complexity was automatically determined based on the information content of the calibration data and the data mismatch of the calibrated model

posterior simulation and bayes factors in panel count data models abstract this paper is concerned with the problems of posterior simulation and model choice for poisson panel data models with multiple random effects efficient algorithms based on markov chain monte carlo methods for sampling the posterior distribution are developed a new parameterization of the random effects and fixed effects is proposed and compared with a parameterization in common use and computation of marginal likelihoods and bayes factors via chib s 1995 method is also considered the methods are illustrated with two real data applications involving large samples and multiple random effects

efficient bayes factor estimation from the reversible jump output summary we propose a class of estimators of the bayes factor which is based on an extension of the bridge sampling identity of meng wong 1996 and makes use of the output of the reversible jump algorithm of green 1995 within this class we give the optimal estimator and also a suboptimal one which may be simply computed on the basis of the acceptance probabilities used within the reversible jump algorithm for jumping between models the proposed estimators are very easily computed and lead to a substantial gain of efficiency in estimating the bayes factor over the standard estimator based on the reversible jump output this is illustrated through a series of monte carlo simulations involving a linear and a logistic regression model

prediction via orthogonalized model mixing abstract we introduce an approach and algorithms for model mixing in large prediction problems with correlated predictors we focus on the choice of predictors in linear models and mix over possible subsets of candidate predictors our approach is based on expressing the space of models in terms of an orthogonalization of the design matrix advantages are both statistical and computational statistically orthogonalization often leads to a reduction in the number of competing models by eliminating correlations computationally large model spaces cannot be enumerated recent approaches are based on sampling models with high posterior probability via markov chains based on orthogonalization of the space of candidate predictors we can approximate the posterior probabilities of models by products of predictor specific terms this leads to an importance sampling function for sampling directly from the joint distribution over the model space without resorting to markov chains compared to the latter ortho

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

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

how to approximate the heat equation with neumann boundary conditions by nonlocal diffusion problems we present a model for nonlocal diffusion with neumann boundary conditions in a bounded smooth domain prescribing the flux through the boundary we study the limit of this family of nonlocal diffusion operators when a rescaling parameter related to the kernel of the nonlocal operator goes to zero we prove that the solutions of this family of problems converge to a solution of the heat equation with neumann boundary conditions

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

impact of redundant checks on the lp decoding thresholds of ldpc codes feldman et al 11 asked whether the performance of the linear programming lp decoder can be improved by adding redundant parity checks to tighten the lp relaxation we prove in this paper that for low density parity check codes even if we include all redundant parity checks asymptotically there is no gain in the lp decoder threshold on the binary symmetric channel under certain conditions on the base tanner graph first we show that if the tanner graph has bounded check degree and satisfies a condition which we call asymptotic strength then including high degree redundant parity checks in the lp does not significantly improve the threshold of the lp decoder in the following sense for each constant delta 0 there is a constant k 0 such that the threshold of the lp decoder containing all redundant checks of degree at most k improves by at most delta upon adding to the lp all redundant checks of degree larger than k we conclude that if the graph satisfies an additional condition which we call rigidity then including all redundant checks does not improve the threshold of the base lp we call the graph asymptotically strong if the lp decoder corrects a constant fraction of errors even if the log likelihood ratios of the correct variables are arbitrarily small by building on a construction due feldman et al 9 and its recent improvement by viderman 24 we show that asymptotic strength follows from sufficiently large variable to check expansion we also give a geometric interpretation of asymptotic strength in terms pseudocodewords we call the graph rigid if the minimum weight of a sum of check nodes involving a cycle tends to infinity as the block length tends to infinity under the assumptions that the graph girth is logarithmic and the minimum check degree is at least 3 rigidity is equivalent to the nondegeneracy property that adding at least logarithmically many checks does not give a constant weight check we argue that nondegeneracy is a typical property of random check regular tanner graphs

on the posterior distribution of the number of components in a finite mixture the posterior distribution of the number of components k in a finite mixture satisfies a set of inequality constraints the result holds irrespective of the parametric form of the mixture components and under assumptions on the prior distribution weaker than those routinely made in the literature on bayesian analysis of finite mixtures the inequality constraints can be used to perform an internal consistency check of mcmc estimates of the posterior distribution of k and to provide improved estimates which are required to satisfy the constraints bounds on the posterior probability of k components are derived using the constraints implications on prior distribution specification and on the adequacy of the posterior distribution of k as a tool for selecting an adequate number of components in the mixture are also explored

a bayesian model averaging approach with non informative priors for cost effectiveness analyses we consider the problem of assessing new and existing technologies for their cost effectiveness in the case where data on both costs and effects are available from a clinical trial and we address it by means of the cost effectiveness acceptability curve the main difficulty in these analyses is that cost data usually exhibit highly skew and heavy tailed distributions so that it can be extremely difficult to produce realistic probabilistic models for the underlying population distribution here in order to integrate the uncertainty about the model into the analysis of cost data and into cost effectiveness analyses we consider an approach based on bayesian model averaging bma in the particular case of weak prior informations about the unknown parameters of the different models involved in the procedure the main consequence of this assumption is that the marginal densities required by bma are undetermined however in accordance with the theory of partial bayes factors and in particular of fractional bayes factors we suggest replacing each marginal density with a ratio of integrals that can be efficiently computed via path sampling

on the laplace equation with dynamical boundary conditions of reactive diffusive type this paper deals with the laplace equation in a bounded regular domain of rn n 2 coupled with a dynamical boundary condition of reactive diffusive type in particular we study the problem u 0in 0 ut ku l uon 0 u 0 x u0 x on where u u t x t 0 x x denotes the laplacian operator with respect to the space variable while denotes the laplace beltrami operator on is the outward normal to and k and l are given real constants well posedness is proved for any given initial distribution u0 on together with the regularity of the solution moreover the fourier method is applied to represent it in term of the eigenfunctions of a related eigenvalue problem

bayesian model selection for incomplete data using the posterior predictive distribution summary we explore the use of a posterior predictive loss criterion for model selection for incomplete longitudinal data we begin by identifying a property that most model selection criteria for incomplete data should consider we then show that a straightforward extension of the gelfand and ghosh 1998 biometrika 85 1 11 criterion to incomplete data has two problems first it introduces an extra term in addition to the goodness of fit and penalty terms that compromises the criterion second it does not satisfy the aforementioned property we propose an alternative and explore its properties via simulations and on a real dataset and compare it to the deviance information criterion dic in general the dic outperforms the posterior predictive criterion but the latter criterion appears to work well overall and is very easy to compute unlike the dic in certain classes of models for missing data

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

bayesian wavelet regression on curves with application to a spectroscopic calibration problem motivated by calibration problems in near infrared nir spectroscopy we consider the linear regression setting in which the many predictor variables arise from sampling an essentially continuous curve at equally spaced points and there may be multiple predictands we tackle this regression problem by calculating the wavelet transforms of the discretized curves then applying a bayesian variable selection method using mixture priors to the multivariate regression of predictands on wavelet coefficients for prediction purposes we average over a set of likely models applied to a particular problem in nir spectroscopy this approach was able to find subsets of the wavelet coefficients with overall better predictive performance than the more usual approaches in the application the available predictors are measurements of the nir reflectance spectrum of biscuit dough pieces at 256 equally spaced wavelengths the aim is to predict the composition i e the fat flour sugar and water content of the doug

a bayesian analysis of quantal bioassay experiments incorporating historical controls via bayes factors this paper addresses model based bayesian inference in the analysis of data arising from bioassay experiments in such experiments increasing doses of a chemical substance are given to treatment groups usually rats or mice for a fixed period of time usually 2 years the goal of such an experiment is to determine whether an increased dosage of the chemical is associated with increased probability of an adverse effect usually presence of adenoma or carcinoma the data consists of dosage survival time and the occurrence of the adverse event for each unit in the study to determine whether such relationship exists this paper proposes using bayes factors to compare two probit models the model that assumes increasing dose effects and the model that assumes no dose effect these models account for the survival time of each unit through a poly k type correction in order to increase statistical power the proposed approach allows the incorporation of information from control groups from previous studies the proposed method is able to handle data with very few occurrences of the adverse event the proposed method is compared with a variation of the peddada test via simulation and is shown to have higher power we demonstrate the method by applying it to the two bioassay experiment datasets previously analyzed by other authors copyright 2017 john wiley sons ltd

imputation and variable selection in linear regression models with missing covariates across multiply imputed data sets variable selection methods such as stepwise regression and other criterion based strategies that include or exclude particular variables typically result in models with different selected predictors thus presenting a problem for combining the results from separate complete data analyses here drawing on a bayesian framework we propose two alternative strategies to address the problem of choosing among linear regression models when there are missing covariates one approach which we call impute then select its involves initially performing multiple imputation and then applying bayesian variable selection to the multiply imputed data sets a second strategy is to conduct bayesian variable selection and missing data imputation simultaneously within one gibbs sampling process which we call simultaneously impute and select sias the methods are implemented and evaluated using the bayesian procedure known as stochastic search variable selection for multivariate normal data sets but both strategies offer general frameworks within which different bayesian variable selection algorithms could be used for other types of data sets a study of mental health services utilization among children in foster care programs is used to illustrate the techniques simulation studies show that both its and sias outperform complete case analysis with stepwise variable selection and that sias slightly outperforms its

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

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

local boundedness of solutions to non local parabolic equations modeled on the fractional p laplacian abstract we state and prove estimates for the local boundedness of subsolutions of non local possibly degenerate parabolic integro differential equations of the form t u x t p v r n k x y t u x t u y t p 2 u x t u y t d y 0 x t r n r where p v means in the principle value sense p 1 and the kernel obeys k x y t x y n p s for some s 0 1 uniformly in x y t r n r n r

real parameter evolutionary monte carlo with applications to bayesian mixture models we propose an evolutionary monte carlo algorithm to sample from a target distribution with real valued parameters the attractive features of the algorithm include the ability to learn from the samples obtained in previous steps and the ability to improve the mixing of a system by sampling along a temperature ladder the effectiveness of the algorithm is examined through three multimodal examples and bayesian neural networks the numerical results confirm that the real coded evolutionary algorithm is a promising general approach for simulation and optimization

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

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

bounded h_ infty calculus for pseudodifferential operators and applications to the dirichlet neumann operator operators of the form a a x d k with a pseudodifferential symbol x belonging to the hormander class s m 1 m 0 0 1 and certain perturbations k are shown to possess a bounded h calculus in besov triebel lizorkin and certain subspaces of holder spaces provided a is suitably elliptic applications concern pseudodifferential operators with mildly regular symbols and operators on manifolds of low regularity an example is the dirichlet neumann operator for a compact domain with c 1 r bounda r y

dynamical boundary conditions in a non cylindrical domain for the laplace equation abstract in this paper we study existence uniqueness and asymptotic behavior of the laplace equation with dynamical boundary conditions on regular non cylindrical domains we write the problem as a non autonomous dirichlet to neumann operator and use form methods in a more general framework to accomplish our goal a class of non autonomous elliptic problems with dynamical boundary conditions on lipschitz domains is also considered in this same context

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

extending conventional priors for testing general hypotheses in linear models summary we consider that observations come from a general normal linear model and that it is desirable to test a simplifying null hypothesis about the parameters we approach this problem from an objective bayesian model selection perspective crucial ingredients for this approach are proper objective priors to be used for deriving the bayes factors jeffreys zellner siow priors have good properties for testing null hypotheses defined by specific values of the parameters in full rank linear models we extend these priors to deal with general hypotheses in general linear models not necessarily of full rank the resulting priors which we call conventional priors are expressed as a generalization of recently introduced partially informative distributions the corresponding bayes factors are fully automatic easily computed and very reasonable the methodology is illustrated for the change point problem and the equality of treatments effects problem we compare the conventional priors derived for these problems with other objective bayesian proposals like the intrinsic priors it is concluded that both priors behave similarly although interesting subtle differences arise we adapt the conventional priors to deal with nonnested model selection as well as multiple model comparison finally we briefly address a generalization of conventional priors to nonnormal scenarios

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

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

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

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

the dirichlet problem for the fractional p laplacian evolution equation abstract we consider a model of fractional diffusion involving a natural nonlocal version of the p laplacian operator we study the dirichlet problem posed in a bounded domain of r n with zero data outside of for which the existence and uniqueness of strong nonnegative solutions is proved and a number of quantitative properties are established a main objective is proving the existence of a special separate variable solution u x t t 1 p 2 f x called the friendly giant which produces a universal upper bound and explains the large time behaviour of all nontrivial nonnegative solutions in a sharp way moreover the spatial profile f of this solution solves an interesting nonlocal elliptic problem we also prove everywhere positivity of nonnegative solutions with any nontrivial data a property that separates this equation from the standard p laplacian equation

hybrid nested sampling algorithm for bayesian model selection applied to inverse subsurface flow problems a hybrid nested sampling hns algorithm is proposed for efficient bayesian model calibration and prior model selection the proposed algorithm combines nested sampling ns algorithm hybrid monte carlo hmc sampling and gradient estimation using stochastic ensemble method sem ns is an efficient sampling algorithm that can be used for bayesian calibration and estimating the bayesian evidence for prior model selection nested sampling has the advantage of computational feasibility within the nested sampling algorithm a constrained sampling step is performed for this step we utilize hmc to reduce the correlation between successive sampled states hmc relies on the gradient of the logarithm of the posterior distribution which we estimate using a stochastic ensemble method based on an ensemble of directional derivatives sem only requires forward model runs and the simulator is then used as a black box and no adjoint code is needed the developed hns algorithm is successfully applied for bayesian calibration and prior model selection of several nonlinear subsurface flow problems

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

multivariate bayesian variable selection and prediction the multivariate regression model is considered with p regressors a latent vector with p binary entries serves to identify one of two types of regression coefficients those close to 0 and those not specializing our general distributional setting to the linear model with gaussian errors and using natural conjugate prior distributions we derive the marginal posterior distribution of the binary latent vector fast algorithms aid its direct computation and in high dimensions these are supplemented by a markov chain monte carlo approach to sampling from the known posterior distribution problems with hundreds of regressor variables become quite feasible we give a simple method of assigning the hyperparameters of the prior distribution the posterior predictive distribution is derived and the approach illustrated on compositional analysis of data involving three sugars with 160 near infra red absorbances as regressors

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 p dirichlet to neumann operator with applications to elliptic and parabolic problems abstract in this paper we investigate the dirichlet to neumann operator associated with second order quasi linear operators of p laplace type for 1 p which acts on the boundary of a bounded lipschitz domain in r d for d 2 we establish well posedness and holder continuity with uniform estimates of weak solutions of some elliptic boundary value problems involving the dirichlet to neumann operator by employing these regularity results of weak solutions of elliptic problems we show that the semigroup generated by the negative dirichlet to neumann operator on l q enjoys an l q c 0 smoothing effect and the negative dirichlet to neumann operator on the set of continuous functions on the boundary of the domain generates a strongly continuous and order preserving semigroup moreover we establish convergence in large time with decay rates of all trajectories of the semigroup and in the singular case 1 e 2 d d 2 p 2 for some e 0 we give upper estimates of the finite time of extinction

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 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

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 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

a bayesian approach to prospective binary outcome studies with misclassification in a binary risk factor misclassification in a binary exposure variable within an unmatched prospective study may lead to a biased estimate of the disease exposure relationship it usually gives falsely small credible intervals because uncertainty in the recorded exposure is not taken into account when there are several other perfectly measured covariates interrelationships may introduce further potential for bias bayesian methods are proposed for analysing binary outcome studies in which an exposure variable is sometimes misclassified but its correct values have been validated for a random subsample of the subjects this bayesian approach can model relationships between explanatory variables and between exploratory variables and the probabilities of misclassification three logistic regressions are used to relate disease to true exposure misclassified exposure to true exposure and true exposure to other covariates credible intervals may be used to make decisions about whether certain parameters are unnecessary and hence whether the model can be reduced in complexity in the disease exposure model for parameters representing coefficients related to perfectly measured covariates the precision of posterior estimates is only slightly lower than would be found from data with no misclassification for the risk factor which has misclassification the estimates of model coefficients obtained are much less biased than those with misclassification ignored

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