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

using mixture models to detect sex bias in health outcomes in bangladesh abstract many interesting economic hypotheses entail differences in behaviors of groups within a population but analyses of pooled samples shed only partial light on underlying segmentations finite mixture models are considered as an alternative to methods based on pooling robustness checks using t regressions and a bayesian analogue to the likelihood ratio test for model evaluation are developed the methodology is used to investigate pro son bias in child health outcomes in bangladesh while regression analysis on the entire sample appears to wash out evidence of bias the mixture models reveal systematic girl boy differences in health outcomes

getting it right joint distribution tests of posterior simulators analytical or coding errors in posterior simulators can produce reasonable but incorrect approximations of posterior moments this article develops simple tests of posterior simulators that detect both kinds of errors and uses them to detect and correct errors in two previously published articles the tests exploit the fact that a bayesian model specifies the joint distribution of observables data and unobservables parameters there are two joint distribution simulators the marginal conditional simulator draws unobservables from the prior and then observables conditional on unobservables the successive conditional simulator alternates between the posterior simulator and an observables simulator formal comparison of moment approximations of the two simulators reveals existing analytical or coding errors in the posterior simulator

smoothly mixing regressions this paper extends the conventional bayesian mixture of normals model by permitting state probabilities to depend on observed covariates the dependence is captured by a simple multinomial probit model a conventional and rapidly mixing mcmc algorithm provides access to the posterior distribution at modest computational cost this model is competitive with existing econometric models as documented in the paper s illustrations the first illustration studies quantiles of the distribution of earnings of men conditional on age and education and shows that smoothly mixing regressions are an attractive alternative to nonbayesian quantile regression the second illustration models serial dependence in the s p 500 return and shows that the model compares favorably with arch models using out of sample likelihood criteria

efficient estimation of conditional variance functions in stochastic regression author s fan jianqing yao qiwei abstract conditional heteroscedasticity has been often used in modelling and understanding the variability of statistical data under a general setup which includes the nonlinear time series model as a special case we propose an e cient and adaptive method for estimating the conditional variance the basic idea is to apply a local linear regression to the squared residuals we demonstrate that without knowing the regression function we can estimate the conditional variance asymptotically as well as if the regression were given this asymptotic result established under the assumption that the observations are made from a strictly stationary and absolutely regular process is also veri ed via simulation further the asymptotic result paves the way for adapting an automatic bandwidth selection scheme an application with nancial data illustrates the usefulness of the proposed techniques

divergence free preserving high order schemes for magnetohydrodynamics an artificial magnetic resistivity method abstract this paper proposes a new strategy that is very simple divergence free high order accurate yet has an effective discontinuous capturing capability for simulating compressible magnetohydrodynamics mhd the new strategy is to construct artificial diffusion terms in a physically consistent manner such that the artificial terms act as a diffusion term only in the curl of magnetic field to capture numerical discontinuities in the magnetic field while not affecting the divergence field thus maintaining divergence free constraint the physically consistent artificial diffusion terms are built into the induction equations in a conservation law form at a partial differential equation level the proposed method may be viewed as adding an artificial magnetic resistivity to the induction equations and is inherently divergence free both ideal and resistive mhd with and without shock waves and also both inviscid and viscous flows the method is based on finite difference method with co located variable arrangement and we show that any linear finite difference scheme in an arbitrary order of accuracy can be used to discretize the modified governing equations to ensures the divergence free and the global conservation constraints numerically at the discretization level the artificial magnetic resistivity is designed to localize automatically in regions of discontinuity in the curl of magnetic field and vanish wherever the flow is sufficiently smooth with respect to the grid scale thereby maintaining the desirable high order accuracy of the employed discretization scheme in smooth regions two dimensional smooth and non smooth ideal mhd problems are considered to validate the capability of the proposed method

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

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

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

local linear quantile regression abstract in this article we study nonparametric regression quantile estimation by kernel weighted local linear fitting two such estimators are considered one is based on localizing the characterization of a regression quantile as the minimizer of e pp y a x x where p is the appropriate check function the other follows by inverting a local linear conditional distribution estimator and involves two smoothing parameters rather than one our aim is to present fully operational versions of both approaches and to show that each works quite well although either might be used in practice we have a particular preference for the second our automatic smoothing parameter selection method is novel the main regression quantile smoothing parameters are chosen by rule of thumb adaptations of state of the art methods for smoothing parameter selection for regression mean estimation the techniques are illustrated by application to two datasets and compared in simulations

bayesian semiparametric estimation of proportional hazards models abstract this paper proposes a semiparametric analysis of proportional hazards models this approach consists in specifying the relation between a duration and explanatory variables without specifying the data distribution the parameters involved in this relation are then considered as parameters of interest and the data distribution is treated as a nuisance parameter we propose a bayesian estimation method the principle of which is to specify a prior distribution on the nuisance parameter we then obtain semiparametric estimators for the parameters of interest by computing their posterior distribution conditional on the data and integrated with respect to the nuisance parameter

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

local polynomial estimators of the volatility function in nonparametric autoregression abstract in this paper we consider a class of dynamic models in which both the conditional mean and the conditional variance volatility are unknown functions of the past we first derive probabilistic conditions under which nonparametric estimation of these functions is possible we then construct an estimator based on local polynomial fitting we examine the rates of convergence of these estimators and give a result on their asymptotic normality the local polynomial fitting of the volatility function is applied to different foreign exchange rate series we find an asymmetric u shaped smiling face form of the volatility function

computational and inferential difficulties with mixture posterior distributions abstract this article deals with both exploration and interpretation problems related to posterior distributions for mixture models the specification of mixture posterior distributions means that the presence of k modes is known immediately standard markov chain monte carlo mcmc techniques usually have difficulties with well separated modes such as occur here the mcmc sampler stays within a neighborhood of a local mode and fails to visit other equally important modes we show that exploration of these modes can be imposed using tempered transitions however if the prior distribution does not distinguish between the different components then the posterior mixture distribution is symmetric and standard estimators such as posterior means cannot be used we propose alternatives for bayesian inference for permutation invariant posteriors including a clustering device and alternative appropriate loss functions

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

bayesian variants of some classical semiparametric regression techniques abstract this paper develops new bayesian methods for semiparametric inference in the partial linear normal regression model y z f x e where f is an unknown function these methods draw solely on the normal linear regression model with natural conjugate prior hence posterior results are available which do not suffer from some problems which plague the existing literature such as computational complexity methods for testing parametric regression models against semiparametric alternatives are developed we discuss how these methods can at some cost in terms of computational complexity be extended to other models e g qualitative choice models or those involving censoring or truncation and provide precise details for a semiparametric probit model we show how the assumption of normal errors can easily be relaxed

smoothness priors and nonlinear regression abstract smoothness priors represent prior information that an unknown function does not change slope quickly and hence that the function describes a simple curve e g wahba 1978 in this article such priors for the multiple nonlinear regression model are developed in such a way that estimates and standard errors can be obtained as a natural and conceptually straightforward extension of linear multiple regression estimation with the addition of dummy variables and dummy observations relations to spline and polynomial interpolation are described an illustrative example of cost function estimation is provided

bayesian curve fitting using multivariate normal mixtures summary problems of regression smoothing and curve fitting are addressed via predictive inference in a flexible class of mixture models multidimensional density estimation using dirichlet mixture models provides the theoretical basis for semi parametric regression methods in which fitted regression functions may be deduced as means of conditional predictive distributions these bayesian regression functions have features similar to generalised kernel regression estimates but the formal analysis addresses problems of multivariate smoothing parameter estimation and the assessment of uncertainties about regression functions naturally computations are based on multidimensional versions of existing markov chain simulation analysis of univariate dirichlet mixture models

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