experiments with implicit upwind methods for the euler equations abstract a number of implicit integration schemes for the one dimensional euler equations with conservative upwind spatial differencing are tested on a problem of steady discontinuous flow fastest convergence quadratic for the first order backward euler scheme is obtained with the upwind switching provided by van leer s differentiable split fluxes which easily linearize in time with roe s nondifferentiable split flux differences the iterations may get trapped in a limit cycle this also happens in a second order scheme with split fluxes if the matrix coefficients arising in the implicit time linearization are not properly centered in space the use of second order terms computed from split fluxes degrades the accuracy of the solution especially if these are subjected to a limiter for the sake of monotonicity preservation second order terms computed from the characteristic variables perform best

order based dependent dirichlet processes in this article we propose a new framework for bayesian nonparametric modeling with continuous covariates in particular we allow the nonparametric distribution to depend on covariates through ordering the random variables building the weights in the stick breaking representation we focus mostly on the class of random distributions that induces a dirichlet process at each covariate value we derive the correlation between distributions at different covariate values and use a point process to implement a practically useful type of ordering two main constructions with analytically known correlation structures are proposed practical and efficient computational methods are introduced we apply our framework through mixtures of these processes to regression modeling the modeling of stochastic volatility in time series data and spatial geostatistical modeling

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

spatially dependent polya tree modeling for survival data with the proliferation of spatially oriented time to event data spatial modeling in the survival context has received increased recent attention a traditional way to capture a spatial pattern is to introduce frailty terms in the linear predictor of a semiparametric model such as proportional hazards or accelerated failure time we propose a new methodology to capture the spatial pattern by assuming a prior based on a mixture of spatially dependent polya trees for the baseline survival in the proportional hazards model thanks to modern markov chain monte carlo mcmc methods this approach remains computationally feasible in a fully hierarchical bayesian framework we compare the spatially dependent mixture of polya trees mpt approach to the traditional spatial frailty approach and illustrate the usefulness of this method with an analysis of iowan breast cancer survival data from the surveillance epidemiology and end results seer program of the national cancer institute our method provides better goodness of fit over the traditional alternatives as measured by log pseudo marginal likelihood lpml the deviance information criterion dic and full sample score fss statistics

on conditional and intrinsic autoregressions summary gaussian conditional autoregressions have been widely used in spatial statistics and bayesian image analysis where they are intended to describe interactions between random variables at fixed sites in euclidean space the main appeal of these distributions is in the markovian interpretation of their full conditionals intrinsic autoregressions are limiting forms that retain the markov property despite being improper they can have advantages over the standard autoregressions both conceptually and in practice for example they often avoid difficulties in parameter estimation without apparent loss or exhibit appealing invariances as in texture analysis however on small arrays and in nonlattice applications both forms of autoregression can lead to undesirable second order characteristics either in the variables themselves or in contrasts among them this paper discusses standard and intrinsic autoregressions and describes how the problems that arise can be alleviated using dempster s 1972 algorithm or an appropriate modification the approach represents a partial synthesis of standard geostatistical and gaussian markov random field formulations some nonspatial applications are also mentioned

some aspects of polya tree distributions for statistical modelling the definition and elementary properties of polya tree distributions are reviewed two theorems are presented showing that polya trees can be constructed to concentrate arbitrarily closely about any desired pdf and that polya tree priors can put positive mass in every relative entropy neighborhood of every positive density with finite entropy thereby satisfying a consistency condition such theorems are false for dirichlet processes models are constructed combining partially specified polya trees with other information such as monotonicity or unimodality it is shown how to compute bounds on posterior expectations over the class of all priors with the given specifications a numerical example is given a theorem of diaconis and freedman about dirichlet processes is generalized to polya trees allowing polya trees to be the models for errors in regression problems finally empirical bayes models using dirichlet processes are generalized to polya trees an example from berry and christensen is reanalyzed with a polya tree model

a unified framework for fitting bayesian semiparametric models to arbitrarily censored survival data including spatially referenced data a comprehensive unified approach to modeling arbitrarily censored spatial survival data is presented for the three most commonly used semiparametric models proportional hazards proportional odds

on the flexibility of agglomeration based physical space discontinuous galerkin discretizations in this work we show that the flexibility of the discontinuous galerkin dg discretization can be fruitfully exploited to implement numerical solution strategies based on the use of elements with very general shapes thanks to the freedom in defining the mesh topology we propose a new h adaptive technique based on agglomeration coarsening of a fine mesh the possibility to enhance the error distribution over the computational domain is investigated on a poisson problem with the goal of obtaining a mesh independent discretization the main building block of our dg method consists of defining discrete polynomial spaces directly on physical frame elements for this purpose we orthonormalize with respect to the l 2 product a set of monomials relocated in a specific element frame and we introduce an easy way to reduce the cost related to numerical integration on agglomerated meshes to complete the dg formulation for second order problems two extensions of the br2 scheme to arbitrary polyhedral grids including an estimate of the stabilization parameter ensuring the coercivity property are here proposed

hp version composite discontinuous galerkin methods for elliptic problems on complicated domains in this paper we introduce the hp version discontinuous galerkin composite finite element method for the discretization of second order elliptic partial differential equations this class of methods allows for the approximation of problems posed on computational domains which may contain a huge number of local geometrical features or microstructures while standard numerical methods can be devised for such problems the computational effort may be extremely high as the minimal number of elements needed to represent the underlying domain can be very large in contrast the minimal dimension of the underlying composite finite element space is independent of the number of geometric features the key idea in the construction of this latter class of methods is that the computational domain omega is no longer resolved by the mesh instead the finite element basis or shape functions are adapted to the geometric details present in omega in this paper we extend these ideas to the discontinuous galer

gibbs sampling methods for stick breaking priors a rich and flexible class of random probability measures which we call stick breaking priors can be constructed using a sequence of independent beta random variables examples of random measures that have this characterization include the dirichlet process its two parameter extension the two parameter poisson dirichlet process finite dimensional dirichlet priors and beta two parameter processes the rich nature of stick breaking priors offers bayesians a useful class of priors for nonparametric problems while the similar construction used in each prior can be exploited to develop a general computational procedure for fitting them in this article we present two general types of gibbs samplers that can be used to fit posteriors of bayesian hierarchical models based on stick breaking priors the first type of gibbs sampler referred to as a polya urn gibbs sampler is a generalized version of a widely used gibbs sampling method currently employed for dirichlet process computing this method applies t

reml estimation for survival models with frailty a method of estimation for generalised mixed models is applied to the estimation of regression parameters in proportional hazards models for failure times when there are repeated observations of failure on each subject the subject effect is incorporated into the model as a random frailty term best linear unbiased predictors are used as an initial step in the computation of maximum likelihood and residual maximum likelihood estimates

a nonparametric bayesian modeling approach for cytogenetic dosimetry summary in cytogenetic dosimetry samples of cell cultures are exposed to a range of doses of a given agent in each sample at each dose level some measure of cell disability is recorded the objective is to develop models that explain cell response to dose such models can be used to predict response at unobserved doses more important such models can provide inference for unknown exposure doses given the observed responses typically cell disability is viewed as a poisson count but in the present work a more appropriate response is a categorical classification in the literature modeling in this case is very limited what exists is purely parametric we propose a fully bayesian nonparametric approach to this problem we offer comparison with a parametric model through a simulation study and the analysis of a real dataset modeling blood cultures exposed to radiation where classification is with regard to number of micronuclei per cell

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

a low dissipation dg method for the under resolved simulation of low mach number turbulent flows abstract in recent years the use of high order discontinuous galerkin dg methods for the under resolved direct numerical simulations udns of turbulent flows has received special attention the suitability of the approach for this kind of applications is related to the dissipation and dispersion proprieties of the scheme while the dispersion errors are small over a broad range of frequencies a relevant dissipation error mainly acts at the smallest under resolved scales resembling a high frequency filter nevertheless it was recognized flad and gassner 2017 mengaldo et al 2018 that the choice of the interface convective numerical flux strongly affects this dissipation behaviour and ultimately the success of the udns approach in this regard the excess of numerical dissipation caused by some upwind numerical convective fluxes must be avoided in particular when dealing with low speed flows since this behaviour is exacerbated approaching the incompressibility limit fixes for the excess of numerical dissipation of these schemes have been proposed by several authors in the context of different numerical methods see for example weiss and smith 1995 in this work a simple modification of the dissipation term of the low mach preconditioned roe scheme proposed by weiss and smith is considered the aim is to reduce further the amount of numerical dissipation with the intent of improving the results of udns a spatial dg discretization coupled with a linearly implicit rosenbrock type time integrator is here considered as a numerical framework perfectly suited for the assessment and comparison of different numerical flux functions results on canonical turbulent flow problems as the taylor green vortex and the flow in a straight sided channel are presented the improved accuracy of the proposed flux function is demonstrated the new low dissipation flux can be useful also in the context of standard lower order finite volume methods

the κ word problem over drh abstract profinite techniques are explored in order to prove decidability of a word problem over a family of pseudovarieties of semigroups which is parameterized by pseudovarieties of groups let be the signature that naturally generalizes the usual signature on groups it consists of the multiplication and of the 1 power given a pseudovariety of groups h we denote by drh the pseudovariety all finite semigroups whose regular r classes lie in h we prove that the word problem for terms is decidable over drh provided it is decidable over h in general the word problem for terms is said to be decidable over a pseudovariety v if it is decidable whether two terms define the same element in every semigroup of v further we present a canonical form for elements in the free semigroup over drh based on the knowledge of a canonical form for elements in the free semigroup over h this extends work of almeida and zeitoun on the pseudovariety of all finite r trivial semigroups

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

robust untangling of curvilinear meshes this paper presents a technique that allows to untangle high order curvilinear meshes the technique makes use of unconstrained optimization where element jacobians are constrained to lie in a prescribed range through moving log barriers the untangling procedure starts from a possibly invalid curvilinear mesh and moves mesh vertices with the objective of producing elements that all have bounded jacobians bounds on jacobians are computed using the results of johnen et al 2012 2013 1 2 the technique is applicable to any kind of polynomial element for surface volume hybrid or boundary layer meshes a series of examples demonstrate both the robustness and the efficiency of the technique the final example involving a time explicit computation shows that it is possible to control the stable time step of the computation for curvilinear meshes through an alternative element deformation measure

semiparametric bayesian inference for stochastic frontier models in this paper we propose a semiparametric bayesian framework for the analysis of stochastic frontiers and efficiency measurement the distribution of inefficiencies is modelled nonparametrically through a dirichlet process prior we suggest prior distributions and implement a bayesian analysis through an efficient markov chain monte carlo sampler which allows us to deal with practically relevant sample sizes we also consider the case where the efficiency distribution varies with firm characteristics the methodology is applied to a cost frontier estimated from a panel data set on 382 u s hospitals

rank based inference in the proportional hazards model for interval censored data summary a marginal likelihood approach to fitting the proportional hazards model to interval censored or grouped data is proposed this approach maximises a likelihood that is the sum over all rankings of the data that are consistent with the observed censoring intervals as in the usual proportional hazards model the method does not require specification of the baseline hazard function the score equations determining the maximum marginal likelihood estimator can be written as the expected value of the score of the usual proportional hazards model with respect to a certain distribution of rankings a gibbs sampling scheme is given to generate rankings from this distribution and stochastic approximation is used to solve the score equations simulation results under various censoring schemes give point estimates that are close to estimates obtained using actual failure times

smoothed aggregation multigrid for the discontinuous galerkin method the aim of this paper is to investigate theoretically as well as experimentally an algebraic multilevel algorithm for the solution of the linear systems that arise from the discontinuous galerkin method the smoothed aggregation multigrid introduced by vanek for the conforming finite element method is applied to low order discretizations of convection diffusion equations for the elliptic model problem the algorithm is shown to be quasi optimal adjustments for the case of nonvanishing advection such as directionally implicit smoothing and a suitable splitting of the operator are discussed several numerical experiments are presented for two dimensional problems including a newton type linearization of the compressible navier stokes equations

a flexible inner outer preconditioned gmres algorithm a variant of the gmres algorithm is presented that allows changes in the preconditioning at every step there are many possible applications of the new algorithm some of which are briefly discussed in particular a result of the flexibility of the new variant is that any iterative method can be used as a preconditioner for example the standard gmres algorithm itself can be used as a preconditioner as can cgnr or cgne the conjugate gradient method applied to the normal equations however the more appealing utilization of the method is in conjunction with relaxation techniques possibly multilevel techniques the possibility of changing preconditioners may be exploited to develop efficient iterative methods and to enhance robustness a few numerical experiments are reported to illustrate this fact

an anova model for dependent random measures we consider dependent nonparametric models for related random probability distributions for example the random distributions might be indexed by a categorical covariate indicating the treatment levels in a clinical trial and might represent random effects distributions under the respective treatment combinations we propose a model that describes dependence across random distributions in an analysis of variance anova type fashion we define a probability model in such a way that marginally each random measure follows a dirichlet process dp and use the dependent dirichlet process to define the desired dependence across the related random measures the resulting probability model can alternatively be described as a mixture of anova models with a dp prior on the unknown mixing measure the main features of the proposed approach are ease of interpretation and computational simplicity because the model follows the standard anovastructure interpretation and inference parallels conventions for anova mode

a multilevel discontinuous galerkin method a variable v cycle preconditioner for an interior penalty finite element discretization for elliptic problems is presented an analysis under a mild regularity assumption shows that the preconditioner is uniform the interior penalty method is then combined with a discontinuous galerkin scheme to arrive at a discretization scheme for an advection diffusion problem for which an error estimate is proved a multigrid algorithm for this method is presented and numerical experiments indicating its robustness with respect to diffusion coefficient are reported

modeling spatial survival data using semiparametric frailty models we propose a new class of semiparametric frailty models for spatially correlated survival data specifically we extend the ordinary frailty models by allowing random effects accommodating spatial correlations to enter into the baseline hazard function multiplicatively we prove identifiability of the models and give sufficient regularity conditions we propose drawing inference based on a marginal rank likelihood no parametric forms of the baseline hazard need to be assumed in this semiparametric approach monte carlo simulations and the laplace approach are used to tackle the intractable integral in the likelihood function different spatial covariance structures are explored in simulations and the proposed methods are applied to the east boston asthma study to detect prognostic factors leading to childhood asthma

predictive model selection we consider the problem of selecting one model from a large class of plausible models a predictive bayesian viewpoint is advocated to avoid the specification of prior probabilities for the candidate models and the detailed interpretation of the parameters in each model using criteria derived from a certain predictive density and a prior specification that emphasizes the observables we implement the proposed methodology for three common problems arising in normal linear models variable subset selection selection of a transformation of predictor variables and estimation of a parametric variance function interpretation of the relative magnitudes of the criterion values for various models is facilitated by a calibration of the criteria relationships between the proposed criteria and other well known criteria are examined

asymptotic theory for the frailty model the frailty model is a generalization of cox s proportional hazards model which includes a random effect nielsen gill andersen and sorensen 1992 proposed an em algorithm to estimate the cumulative baseline hazard and the variance of the random effect here the asymptotic distribution of the estimators is given along with a consistent estimator of the asymptotic variance

multigrid algorithms for hp discontinuous galerkin discretizations of elliptic problems we present w cycle h p and hp multigrid algorithms for the solution of the linear system of equations arising from a wide class of hp version discontinuous galerkin discretizations of elliptic problems starting from a classical framework in geometric multigrid analysis we define a smoothing and an approximation property which are used to prove uniform convergence of the w cycle scheme with respect to the discretization parameters and the number of levels provided the number of smoothing steps is chosen of order p 2 mu where p is the polynomial approximation degree and mu 0 1 a discussion on the effects of employing inherited or noninherited sublevel solvers is also presented numerical experiments confirm the theoretical results

consistency in a proportional hazards model incorporating a random effect supported in part by the north atlantic treaty organization under a grant awarded in 1990 conducted at the mathematical institute of the university of utrecht the netherlands

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

bayesian density regression summary the paper considers bayesian methods for density regression allowing a random probability distribution to change flexibly with multiple predictors the conditional response distribution is expressed as a non parametric mixture of regression models with the mixture distribution changing with predictors a class of weighted mixture of dirichlet process priors is proposed for the uncountable collection of mixture distributions it is shown that this specification results in a generalized polya urn scheme which incorporates weights that are dependent on the distance between subjects predictor values to allow local dependence in the mixture distributions we propose a kernel based weighting scheme a gibbs sampling algorithm is developed for posterior computation the methods are illustrated by using simulated data examples and an epidemiologic application

maximum likelihood estimation for the proportional odds model with random effects in this article we study the semiparametric proportional odds model with random effects for correlated right censored failure time data we establish that the maximum likelihood estimators for the parameters of this model are consistent and asymptotically gaussian furthermore the limiting variances achieve the semiparametric efficiency bounds and can be consistently estimated simulation studies show that the asymptotic approximations are accurate for practical sample sizes and that the efficiency gains of the proposed estimators over those of cai cheng and wei can be substantial a real example is provided to illustrate the proposed methods

a bayesian semiparametric accelerated failure time model a bayesian semiparametric approach is described for an accelerated failure time model the error distribution is assigned a polya tree prior and the regression parameters a noninformative hierarchical prior two cases are considered the first assumes error terms are exchangeable the second assumes that error terms are partially exchangeable a markov chain monte carlo algorithm is described to obtain a predictive distribution for a future observation given both uncensored and censored data

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

hierarchical generalized linear models and frailty models with bayesian nonparametric mixing summary this paper proposes bayesian nonparametric mixing for some well known and popular models the distribution of the observations is assumed to contain an unknown mixed effects term which includes a fixed effects term a function of the observed covariates and an additive or multiplicative random effects term typically these random effects are assumed to be independent of the observed covariates and independent and identically distributed from a distribution from some known parametric family this assumption may be suspect if either there is interaction between observed covariates and unobserved covariates or the fixed effects predictor of observed covariates is misspecified another cause for concern might be simply that the covariates affect more than just the location of the mixed effects distribution as a consequence the distribution of the random effects could be highly irregular in modality and skewness leaving parametric families unable to model the distribution adequately this paper therefore proposes a bayesian nonparametric prior for the random effects to capture possible deviances in modality and skewness and to explore the observed covariates effect on the distribution of the mixed effects

combining information from several experiments with nonparametric priors summary this paper considers combining information from several experiments when the experiments can be summarised via a parameter value the structure of this set of parameters in terms of independence exchangeability partial exchangeability etc is assumed to be unknown and a finite number of possible structures are entertained each with an associated prior weight representing the degree of belief in that structure crucial is the criterion by which these structures are selected the final inference for the parameter values is taken to be the average with respect to the posterior weights of the values obtained from each structure this is performed within a bayesian nonparametric framework where the form of the prior distribution for the parameters is unrestricted therefore we do not assume that the distributions associated with a partial structure are from the same family different types of experiment suggest different types of distributions of parameters associated with each type of experiment

an artificial compressibility flux for the discontinuous galerkin solution of the incompressible navier stokes equations discontinuous galerkin dg methods have proved to be well suited for the construction of robust high order numerical schemes on unstructured and possibly nonconforming grids for a variety of problems their application to the incompressible navier stokes ins equations has also been recently considered although the subject is far from being fully explored in this work we propose a new approach for the dg numerical solution of the ins equations written in conservation form the inviscid numerical fluxes both in the continuity and in the momentum equation are computed using the values of velocity and pressure provided by the exact solution of the riemann problem associated with a local artificial compressibility perturbation of the equations unlike in most of the existing methods artificial compressibility is here introduced only at the interface flux level therefore resulting in a consistent discretization of the ins equations irrespectively of the amount of artificial compressibility introduced the discretization of the viscous term follows the well established dg scheme named br2 the performance and the accuracy of the method are demonstrated by computing the kovasznay flow and the two dimensional lid driven cavity flow for a wide range of reynolds numbers and for various degrees of polynomial approximation

parametric spatial cure rate models for interval censored time to relapse data summary several recent papers e g chen ibrahim and sinha 1999 journal of the american statistical association94 909 919 ibrahim chen and sinha 2001a biometrics57 383 388 have described statistical methods for use with time to event data featuring a surviving fraction i e a proportion of the population that never experiences the event such cure rate models and their multivariate generalizations are quite useful in studies of multiple diseases to which an individual may never succumb or from which an individual may reasonably be expected to recover following treatment e g various types of cancer in this article we extend these models to allow for spatial correlation estimable via zip code identifiers for the subjects as well as interval censoring our approach is bayesian where posterior summaries are obtained via a hybrid markov chain monte carlo algorithm we compare across a broad collection of rather high dimensional hierarchical models using the deviance information criterion a tool recently developed for just this purpose we apply our approach to the analysis of a smoking cessation study where the subjects reside in 53 southeastern minnesota zip codes in addition to the usual posterior estimates our approach yields smoothed zip code level maps of model parameters related to the relapse rates over time and the ultimate proportion of quitters the cure rates

bayesian nonparametric spatial modeling with dirichlet process mixing customary modeling for continuous point referenced data assumes a gaussian process that is often taken to be stationary when such models are fitted within a bayesian framework the unknown parameters of the process are assumed to be random so a random gaussian process results here we propose a novel spatial dirichlet process mixture model to produce a random spatial process that is neither gaussian nor stationary we first develop a spatial dirichlet process model for spatial data and discuss its properties because of familiar limitations associated with direct use of dirichlet process models we introduce mixing by convolving this process with a pure error process we then examine properties of models created through such dirichlet process mixing in the bayesian framework we implement posterior inference using gibbs sampling spatial prediction raises interesting questions but these can be handled finally we illustrate the approach using simulated data as well as a dataset involving precipitati

asymptotic theory for the correlated gamma frailty model the frailty model is a generalization of cox s proportional hazard model where a shared unobserved quantity in the intensity induces a positive correlation among the survival times murphy showed consistency and asymptotic normality of the nonparametric maximum likelihood estimator npmle for the shared gamma frailty model without covariates in this paper we extend this result to the correlated gamma frailty model and we allow for covariates we discuss the definition of the nonparametric likelihood function in terms of a classical proof of consistency for the maximum likelihood estimator which goes back to wald our proof of the consistency for the npmle is essentially the same as the classical proof for the maximum likelihood estimator a new central limit theorem for processes of bounded variation is given furthermore we prove that a consistent estimator for the asymptotic variance of the npmle is given by the inverse of a discrete observed information matrix

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

a bayesian hierarchical model for related densities by using polya trees bayesian hierarchical models are used to share information between related samples and to obtain more accurate estimates of sample level parameters common structure and variation between samples when the parameter of interest is the distribution or density of a continuous variable a hierarchical model for continuous distributions is required various such models have been described in the literature using extensions of the dirichlet process and related processes typically as a distribution on the parameters of a mixing kernel we propose a new hierarchical model based on the polya tree which enables direct modelling of densities and enjoys some computational advantages over the dirichlet process the polya tree also enables more flexible modelling of the variation between samples providing more informed shrinkage and permitting posterior inference on the dispersion function which quantifies the variation between sample densities we also show how the model can be extended to cluster samples in situations where the observed samples are believed to have been drawn from several latent populations

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

multigrid algorithms for symmetric discontinuous galerkin methods on graded meshes we study a class of symmetric discontinuous galerkin methods on graded meshes optimal order error estimates are derived in both the energy norm and the l 2 norm and we establish the uniform convergence of v cycle f cycle and w cycle multigrid algorithms for the resulting discrete problems numerical results that confirm the theoretical results are also presented

data augmentation priors for bayesian and semi bayes analyses of conditional logistic and proportional hazards regression data augmentation priors have a long history in bayesian data analysis formulae for such priors have been derived for generalized linear models but their accuracy depends on two approximation steps this note presents a method for using offsets as well as scaling factors to improve the accuracy of the approximations in logistic regression this method produces an exceptionally simple form of data augmentation that allows it to be used with any standard package for conditional logistic or proportional hazards regression to perform bayesian and semi bayes analyses of matched and survival data the method is illustrated with an analysis of a matched case control study of diet and breast cancer

sc hyperdecidability of r a class tc x of x graphs is introduced and an algorithmic property of labellings of finite strongly connected graphs by rational languages is shown to be decidable this property named as tc inevitability is a language theoretic analogue of the r inevitability of labellings of finite strongly connected graphs by finite monoids as a consequence the pseudovariety r of all finite r trivial monoids is shown to be hyperdecidable relative to the class of labellings of finite strongly connected graphs by finite monoids strong decidability of the dual pseudovariety l follows as a corollary and a few applications to decidability results are provided

kernel estimation of hazard functions when observations have dependent and common covariates abstract we propose a hazard model where dependence between events is achieved by assuming dependence between covariates this model allows for correlated variables specific to observations as well as macro variables which all observations share this setup better fits many economic and financial applications where events are not independent nonparametric estimation of the hazard function is then studied kernel estimators proposed in nielsen and linton 1995 and linton et al 2003 are shown to have similar asymptotic properties compared with the i i d case mixing conditions ensure the asymptotic results follow these results depend on adjustments to bandwidth conditions simulations are conducted which verify the impact of dependence on estimators bandwidth selection accounting for dependence is shown to improve performance in an empirical application trade intensity in high frequency financial data is estimated

estimation of multivariate frailty models using penalized partial likelihood summary there exists a growing literature on the estimation of gamma distributed multiplicative shared frailty models there is however often a need to model more complicated frailty structures but attempts to extend gamma frailties run into complications motivated by hip replacement data with a more complicated dependence structure we propose a model based on multiplicative frailties with a multivariate log normal joint distribution we give a justification and an estimation procedure for this generally structured frailty model which is a generalization of the one presented by mcgilchrist 1993 biometrics49 221 225 the estimation is based on laplace approximation of the likelihood function this leads to estimating equations based on a penalized fixed effects partial likelihood where the marginal distribution of the frailty terms determines the penalty term the tuning parameters of the penalty function i e the frailty variances are estimated by maximizing an approximate profile likelihood the performance of the approximation is evaluated by simulation and the frailty model is fitted to the hip replacement data

h multigrid agglomeration based solution strategies for discontinuous galerkin discretizations of incompressible flow problems abstract in this work we exploit agglomeration based h multigrid preconditioners to speed up the iterative solution of discontinuous galerkin discretizations of the stokes and navier stokes equations as a distinctive feature h coarsened mesh sequences are generated by recursive agglomeration of a fine grid admitting arbitrarily unstructured grids of complex domains and agglomeration based discontinuous galerkin discretizations are employed to deal with agglomerated elements of coarse levels both the expense of building coarse grid operators and the performance of the resulting multigrid iteration are investigated for the sake of efficiency coarse grid operators are inherited through element by element l 2 projections avoiding the cost of numerical integration over agglomerated elements specific care is devoted to the projection of viscous terms discretized by means of the br2 dg method we demonstrate that enforcing the correct amount of stabilization on coarse grids levels is mandatory for achieving uniform convergence with respect to the number of levels the numerical solution of steady and unsteady linear and non linear problems is considered tackling challenging 2d test cases and 3d real life computations on parallel architectures significant execution time gains are documented

a high order discontinuous galerkin method for the unsteady incompressible navier stokes equations we present a high order discontinuous galerkin discretization of the unsteady incompressible navier stokes equations in convection dominated flows using triangular and tetrahedral meshes the scheme is based on a semi explicit temporal discretization with explicit treatment of the nonlinear term and implicit treatment of the stokes operator the nonlinear term is discretized in divergence form by using the local lax friedrichs fluxes thus local conservativity is inherent spatial discretization of the stokes operator has employed both equal order p k p k and mixed order p k p k 1 velocity and pressure approximations a second order approximate algebraic splitting is used to decouple the velocity and pressure calculations leading to an algebraic helmholtz equation for each component of the velocity and a consistent poisson equation for the pressure the consistent poisson operator is replaced by an equivalent in stability and convergence operator namely that arising from the interior penalty discretization of the standard poisson operator with appropriate boundary conditions this yields a simpler and more efficient method characterized by a compact stencil size we show the temporal and spatial behavior of the method by solving some popular benchmarking tests for an unsteady stokes problem second order temporal convergence is obtained while for the taylor vortex test problem on both semi structured and fully unstructured triangular meshes spectral convergence with respect to the polynomial degree k is obtained by studying the orr sommerfeld stability problem we demonstrate that the p k p k method yields a stable solution while the p k p k 1 formulation leads to unphysical instability the good performance of the method is further shown by simulating vortex shedding in flow past a square cylinder we conclude that the proposed discontinuous galerkin method with the p k p k formulation is an efficient scheme for accurate and stable solution of the unsteady navier stokes equations in convection dominated flows

mixtures of polya trees for flexible spatial frailty survival modelling mixtures of polya trees offer a very flexible nonparametric approach for modelling time to event data many such settings also feature spatial association that requires further sophistication either at the point level or at the lattice level in this paper we combine these two aspects within three competing survival models obtaining a data analytic approach that remains computationally feasible in a fully hierarchical bayesian framework using markov chain monte carlo methods we illustrate our proposed methods with an analysis of spatially oriented breast cancer survival data from the surveillance epidemiology and end results program of the national cancer institute our results indicate appreciable advantages for our approach over competing methods that impose unrealistic parametric assumptions ignore spatial association or both

modeling regression error with a mixture of polya trees we model the error distribution in the standard linear model as a mixture of absolutely continuous polya trees constrained to have median 0 by considering a mixture we smooth out the partitioning effects of a simple polya tree and the predictive error density has a derivative everywhere except 0 the error distribution is centered around a standard parametric family of distributions and thus may be viewed as a generalization of standard models in which important data driven features such as skewness and multimodality are allowed by marginalizing the polya tree exact inference is possible up to markov chain monte carlo error

semiparametric regression for count data we introduce a class of bayesian semiparametric models for regression problems in which the response variable is a count our goal is to provide a flexible easy to implement and robust extension of generalised linear models for datasets of moderate or large size our approach is based on modelling the distribution of the response variable using a dirichlet process whose mean distribution function is itself random and is given a parametric form such as a generalised linear model the effects of the explanatory variables on the response are modelled via both the parameters of the mean distribution function of the dirichlet process and the total mass parameter we discuss modelling options and relationships with other approaches we derive in closed form the marginal posterior distribution of the regression coefficients and discuss its use in inference and computing we illustrate the benefits of our approach with a prognostic model for early breast cancer patients

mixed hp dgfem for incompressible flows we consider several mixed discontinuous galerkin approximations of the stokes problem and propose an abstract framework for their analysis using this framework we derive a priori error estimates for hp approximations on tensor product meshes we also prove a new stability estimate for the discrete divergence bilinear form