nonparametric bayes conditional distribution modeling with variable selection this article considers a methodology for flexibly characterizing the relationship between a response and multiple predictors goals are 1 to estimate the conditional response distribution addressing the distributional changes across the predictor space and 2 to identify important predictors for the response distribution change both within local regions and globally we first introduce the probit stick breaking process psbp as a prior for an uncountable collection of predictor dependent random distributions and propose a psbp mixture psbpm of normal regressions for modeling the conditional distributions a global variable selection structure is incorporated to discard unimportant predictors while allowing estimation of posterior inclusion probabilities local variable selection is conducted relying on the conditional distribution estimates at different predictor points an efficient stochastic search sampling algorithm is proposed for posterior computation the methods are illustrated through simulation and applied to an epidemiologic study

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

on large deviations in the averaging principle for sdes with a full dependence we establish the large deviation principle for stochastic differential equations with averaging in the case when all coefficients of the fast component depend on the slow one including diffusion

averaging principle for slow fast stochastic differential equations with time dependent locally lipschitz coefficients abstract this paper is devoted to studying the averaging principle for stochastic differential equations with slow and fast time scales where the drift coefficients satisfy local lipschitz conditions with respect to the slow and fast variables and the coefficients in the slow equation depend on time t and making use of the techniques of time discretization and truncation we prove that the slow component strongly converges to the solution of the corresponding averaged equation

when where and how of efficiency estimation improved procedures for stochastic frontier modeling abstractthe issues of functional form distributions of the error components and endogeneity are for the most part still open in stochastic frontier models the same is true when it comes to imposition of restrictions of monotonicity and curvature making efficiency estimation an elusive goal in this paper we attempt to consider these problems simultaneously and offer practical solutions to the problems raised by stone 2002 and addressed in badunenko henderson and kumbhakar 2012 we provide major extensions to smoothly mixing regressions and fractional polynomial approximations for both the functional form of the frontier and the structure of inefficiency endogeneity is handled simultaneously using copulas we provide detailed computational experiments and an application to us banks to explore the posteriors of the new models we rely heavily on sequential monte carlo techniques

averaging principle for multiscale stochastic fractional schrodinger korteweg de vries system this work concerns the averaging principle for multiscale stochastic fractional schrodinger korteweg de vries system stochastic averaging principle is a powerful tool for studying qualitative analysis of stochastic dynamical systems with different time scales to be more precise under suitable conditions the multiscale system can be reduced to a single stochastic fractional korteweg de vries equation averaged equation with a modified coefficient the slow component of multiscale system towards to the solution of the averaged equation in moment in order to prove the averaging principle there are two key points uniform bounds for the solution and holder continuity of time variable for the slow component for this we need a crucial property smoothing effect of the fractional korteweg de vries semigroup but the traditional method can t help us obtain this property such analysis does not follow in a straightforward manner from results already available in the mathematical literature on the contrary it requires the introduction of some new ideas and techniques we try to overcome this difficulty by the duality method the interpolation arguments the energy estimate method and refined inequality technique

a sequential particle filter method for static models summary particle filter methods are complex inference procedures which combine importance sampling and monte carlo schemes in order to explore consistently a sequence of multiple distributions of interest we show that such methods can also offer an efficient estimation

averaging principle for one dimensional stochastic burgers equation abstract in this paper we consider the averaging principle for one dimensional stochastic burgers equation with slow and fast time scales under some suitable conditions we show that the slow component strongly converges to the solution of the corresponding averaged equation meanwhile when there is no noise in the slow component equation we also prove that the slow component weakly converges to the solution of the corresponding averaged equation with the order of convergence 1 r for any 0 r 1

one dimensional stochastic burgers equation driven by levy processes abstract in this paper we proved the global existence and uniqueness of the strong weak and mild solutions for one dimensional burgers equation perturbed by a poisson form process a poisson form and q wiener process with the dirichlet bounded condition we also proved the existence of the invariant measure of these models

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

hierarchical mixtures of experts and the em algorithm we present a tree structured architecture for supervised learning the statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models glim s learning is treated as a maximum likelihood problem in particular we present an expectation maximization em algorithm for adjusting the parameters of the architecture we also develop an on line learning algorithm in which the parameters are updated incrementally comparative simulation results are presented in the robot dynamics domain

bayesian inference in mixtures of experts and hierarchical mixtures of experts models with an application to speech recognition abstract machine classification of acoustic waveforms as speech events is often difficult due to context dependencies here a vowel recognition task with multiple speakers is studied via the use of a class of modular and hierarchical systems referred to as mixtures of experts and hierarchical mixtures of experts models the statistical model underlying the systems is a mixture model in which both the mixture coefficients and the mixture components are generalized linear models a full bayesian approach is used as a basis of inference and prediction computations are performed using markov chain monte carlo methods a key benefit of this approach is the ability to obtain a sample from the posterior distribution of any functional of the parameters of the given model in this way more information is obtained than can be provided by a point estimate also avoided is the need to rely on a normal approximation to the posterior as the basis of inference this is particularly important in cases where the posteri

error bounds for the asymptotic expansion of the hurwitz zeta function in this paper we reconsider the large a asymptotic expansion of the hurwitz zeta function s a new representations for the remainder term of the asymptotic expansion are found and used to obtain sharp and realistic error bounds applications to the asymptotic expansions of the polygamma functions the gamma function the barnes g function and the s derivative of the hurwitz zeta function s a are provided a detailed discussion on the sharpness of our error bounds is also given

strong convergence rate in averaging principle for stochastic fitzhugh nagumo system with two time scales abstract this article deals with averaging principle for stochastic fitzhugh nagumo system with different time scales under suitable conditions the existence of an averaging equation eliminating the fast variable for this coupled system is proved and as a consequence the system can be reduced to a single stochastic ordinary equation with a modified coefficient moreover the rate of convergence for the slow component towards the solution of the averaging equation is of order 1 2

estimation and inference in two stage semi parametric models of production processes many papers have regressed non parametric estimates of productive efficiency on environmental variables in two stage procedures to account for exogenous factors that might affect firms performance none of these have described a coherent data generating process dgp moreover conventional approaches to inference employed in these papers are invalid due to complicated unknown serial correlation among the estimated efficiencies we first describe a sensible dgp for such models we propose single and double bootstrap procedures both permit valid inference and the double bootstrap procedure improves statistical efficiency in the second stage regression we examine the statistical performance of our estimators using monte carlo experiments

statistical inference for dea estimators of directional distances in productivity and efficiency analysis the technical efficiency of a production unit is measured through its distance to the efficient frontier of the production set the most familiar non parametric methods use farrell debreu shephard or hyperbolic radial measures these approaches require that inputs and outputs be non negative which can be problematic when using financial data recently chambers et al 1998 have introduced directional distance functions which can be viewed as additive rather than multiplicative measures efficiency directional distance functions are not restricted to non negative input and output quantities in addition the traditional input and output oriented measures are nested as special cases of directional distance functions consequently directional distances provide greater flexibility however until now only free disposal hull fdh estimators of directional distances and their conditional and robust extensions have known statistical properties simar and vanhems 2012 this paper develops the statistical properties of directional d estimators which are especially useful when the production set is assumed convex we first establish that the directional data envelopment analysis dea estimators share the known properties of the traditional radial dea estimators we then use these properties to develop consistent bootstrap procedures for statistical inference about directional distance estimation of confidence intervals and bias correction the methods are illustrated in some empirical examples

analysis of multiscale methods for stochastic differential equations we analyze a class of numerical schemes proposed in 26 for stochastic differential equations with multiple time scales both advective and diffusive time scales are considered weak as well as strong convergence theorems are proven most of our results are optimal they in turn allow us to provide a thorough discussion on the efficiency as well as optimal strategy for the method c 2005 wiley periodicals inc

generalized linear models with varying dispersion summary generalized linear models are further generalized to include a linear predictor for the dispersion as well as for the mean it is shown how the convenient structure of generalized linear models can be carried over to this more general setting by considering the mean and dispersion structure separately mean and dispersion submodels are formulated for this the dependent variable for the dispersion submodel being the deviance components of the mean submodel the fact that both submodels are essentially generalized linear models themselves is used to derive simple expressions for the likelihood equations and for asymptotic tests estimation algorithms are proposed which have good convergence properties the results apply mainly to the normal inverse gaussian and gamma distributions but can be extended to discrete distributions by using quasi likelihoods the methods developed are applied to a well known data set

ergodicity of 2d navier stokes equations with random forcing and large viscosity the stochastically forced two dimensional incompressable navier stokes equations are shown to possess an unique invariant measure if the viscosity is taken large enough this result follows from a stronger result showing that at high viscosity there is a unique stationary solution which attracts solutions started from arbitrary initial conditions that is to say the system has a trivial random attractor along the way results controling the expectation and averaging time of the energy and enstrophy are given

exponentially improved asymptotics for the gamma function by expressing the error term in truncation of the asymptotic expansion in terms of a mellin barnes integral we obtain an exponentially improved asymptotic expansion for z as z in arg z we describe the need for such an expansion arising in applications the result is compared with formal results of dingle obtained via borel summation and rigorous methods of olver using laplace integrals for a different class of functions

error bounds and exponential improvement for the asymptotic expansion of the barnes g function in this paper we establish new integral representations for the remainder term of the known asymptotic expansion of the logarithm of the barnes g function using these representations we obtain e

bayesian mixture of splines for spatially adaptive nonparametric regression summary a bayesian approach is presented for spatially adaptive nonparametric regression where the regression function is modelled as a mixture of splines each component spline in the mixture has associated with it a smoothing parameter which is defined over a local region of the covariate space these local regions overlap such that individual data points may lie simultaneously in multiple regions consequently each component spline has attached to it a weight at each point of the covariate space and by allowing the weight of each component spline to vary across the covariate space a spatially adaptive estimate of the regression function is obtained the number of mixing components is chosen using a modification of the bayesian information criteria we study the procedure analytically and show by simulation that it compares favourably to three competing techniques these techniques are the bayesian regression splines estimator of smith kohn 1996 the hybrid adaptive spline estimator of luo wahba 1997 and the automatic bayesian curve fitting estimator of denison et al 1998 the methodology is illustrated by modelling global air temperature anomalies all the computations are carried out efficiently using markov chain monte carlo

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

smooth approximations to monotone concave functions in production analysis an alternative to nonparametric concave least squares abstract estimation of banking efficiency and productivity is essential for regulatory purposes and for testing various theories in the context of banking such as the quiet life hypothesis the bad management hypothesis etc in such studies it is therefore important to place as few restrictions as possible on the functional forms subject to global satisfaction of the theoretical properties relating to monotonicity and concavity in this paper we propose an alternative to nonparametric segmented concave least squares we use a differentiable approximation to an arbitrary functional form based on smoothly mixing cobb douglas anchor functions over the data space estimation is based on bayesian techniques organized around markov chain monte carlo the approximation properties of the new functional form are investigated in a monte carlo experiment where the true functional form is a symmetric generalized mcfadden the new techniques are applied to a large u s banking data set as well as a global banking data set

hierarchical mixtures of experts for exponential family regression models approximation and maximum likelihood estimation we consider hierarchical mixtures of experts hme models where exponential family regression models with generalized linear mean functions of the form x t are mixed here is the inverse link function suppose the true response y follows an exponential family regression model with mean function belonging to a class of smooth functions of the form h x where h w 2 k0 a sobolev class over 0 1 s it is shown that the hme probability density functions can approximate the true density at a rate of o m 2 s in hellinger distance and at a rate of o m 4 s in kullback leibler divergence where m is the number of experts and s is the dimension of the predictor x we also provide conditions under which the mean square error of the estimated mean response obtained from the maximum likelihood method converges to zero as the sample size and the number of experts both increase

large deviations and approximations for slow fast stochastic reaction diffusion equations abstract a large deviation principle is derived for a class of stochastic reaction diffusion partial differential equations with slow fast components the result shows that the rate function is exactly that of the averaged equation plus the fluctuating deviation which is a stochastic partial differential equation with small gaussian perturbation this result also confirms the effectiveness of the approximation of the averaged equation plus the fluctuating deviation to the slow fast stochastic partial differential equations

averaging principle for a class of stochastic reaction diffusion equations we consider the averaging principle for stochastic reaction diffusion equations under some assumptions providing existence of a unique invariant measure of the fast motion with the frozen slow component we calculate limiting slow motion the study of solvability of kolmogorov equations in hilbert spaces and the analysis of regularity properties of solutions allow to generalize the classical approach to finite dimensional problems of this type in the case of spde s

regression density estimation using smooth adaptive gaussian mixtures we model a regression density flexibly so that at each value of the covariates the density is a mixture of normals with the means variances and mixture probabilities of the components changing smo

adaptive sampling for bayesian variable selection our paper proposes adaptive monte carlo sampling schemes for bayesian variable selection in linear regression that improve on standard markov chain methods we do so by considering metropolis hastings proposals that make use of accumulated information about the posterior distribution obtained during sampling adaptation needs to be done carefully to ensure that sampling is from the correct ergodic distribution we give conditions for the validity of an adaptive sampling scheme in this problem and for simulating from a distribution on a finite state space in general and suggest a class of adaptive proposal densities which uses best linear prediction to approximate the gibbs sampler our sampling scheme is computationally much faster per iteration than the gibbs sampler and when this is taken into account the efficiency gains when using our sampling scheme compared to alternative approaches are substantial in terms of precision of estimation of posterior quantities of interest for a given amount of computation time we compare our method with other sampling schemes for examples involving both real and simulated data the methodology developed in the paper can be extended to variable selection in more general problems

on the estimation of technical inefficiency in the stochastic frontier production function model abstract the error term in the stochastic frontier model is of the form v u where v is a normal error term representing pure randomness and u is a non negative error term representing technical inefficiency the entire v u is easily estimated for each observation but a previously unsolved problem is how to separate it into its two components v and u this paper suggests a solution to this problem by considering the expected value of u conditional on v u an explicit formula is given for the half normal and exponential cases

the stokes phenomenon associated with the hurwitz zeta function ζ s a we examine the exponentially improved asymptotic expansion of the hurwitz zeta function s a for large complex values of a with s regarded as a parameter it is shown that an infinite number of subdominant exponential terms switch on across the stokes lines arg a

technical and allocative efficiency in a panel stochastic production frontier system model abstract in this paper we consider a state of the art panel stochastic production frontier model and estimate it using a system that includes both technical and allocative inefficiency the system consists of the optimal input choice rule the first order conditions focs under cost minimization together with the production function the focs are used to take care of endogeneity of inputs allocative inefficiency is modeled as non fulfillment of the focs we use distributional assumptions on the noise and inefficiency components and estimate the model parameters using the maximum likelihood method in estimating technical and allocative inefficiency components and costs therefrom we control for fixed firm effects in each equation of the system we also correct for the incidental parameter bias by using the half panel jackknife estimator

strong convergence in stochastic averaging principle for two time scales stochastic partial differential equations abstract the theory of stochastic averaging principle provides an effective approach for the qualitative analysis of stochastic systems with different time scales and is relatively mature for stochastic ordinary differential equations in this paper we study the averaging principle for a class of stochastic partial differential equations with two separated time scales driven by scalar noises under suitable assumptions it is shown that the slow component strongly converges to the solution of the corresponding averaged equation

stochastic burgers equations and their semi classical expansions in this paper we use the hopf cole logarithmic transformation and the stochastic hamilton jacobi theory to study stochastic heat equations and burgers equations before the caustics the stochastic inviscid burgers equation gives the first term of our semi classical expansion i e the inviscid limit of the viscous stochastic burgers equation in order to push our results beyond the inviscid limit we construct solutions for iterated stochastic hamilton jacobi continuity equations then we give the semi classical asymptotic expansions for stochastic heat equations and burgers equations by using nelson s stochastic mechanical processes with drifts given by the solution of the iterated stochastic hamilton jacobi continuity equations the explicit formula for the remainder term is given by a path integral

uniform asymptotic smoothing of stokes s discontinuities across a stokes line where one exponential in an asymptotic expansion maximally dominates another the multiplier of the small exponential changes rapidly if the expansion is truncated near its least term the change is not discontinuous but smooth and moreover universal in form in terms of the singulant f the difference between the larger and smaller exponents and real on the stokes line the change in the multiplier is the error function pi frac 1 2 int sigma infty dt exp t 2 text where sigma imf 2ref frac 1 2 the derivation requires control of exponentially small terms in the dominant series this is achieved with dingle s method of borel summation of late terms starting with the least term in numerical illustrations the multiplier is extracted from dawson s integral erfi and the airy function of the second kind bi the small exponential emerges in the predicted universal manner from the dominant one which can be 10 10 times larger

on stochastic diffusion equations and stochastic burgers equations in this paper we construct a strong solution for the stochastic hamilton jacobi equation by using stochastic classical mechanics before the caustics we thereby obtain the viscosity solution for a certain class of inviscid stochastic burgers equations this viscosity solution is not continuous beyond the caustics of the corresponding hamilton jacobi equation the hopf cole transformation is used to identify the stochastic heat equation and the viscous stochastic burgers equation the exact solutions for the above two equations are given in terms of the stochastic hamilton jacobi function under a no caustic condition we construct the heat kernel for the stochastic heat equation for zero potentials in hyperbolic space and for harmonic oscillator potentials in euclidean space thereby obtaining the stochastic mehler formula

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

generalized smooth finite mixtures we propose a general class of models and a unified bayesian inference methodology for flexibly estimating the density of a response variable conditional on a possibly high dimensional set of covari

probabilistic characterization of directional distances and their robust versions in productivity analysis the performance of production units is measured through the distance of the individual decision making units dmu to the technology which is defined as the frontier of the production set most of the existing methods farrell debreu and shephard radial measures input or output oriented and hyperbolic distance functions rely on multiplicative measures of the distance and so require to deal with strictly positive inputs and outputs this can be critical when the data contain zero or negative values as in financial data bases for the measure of funds performances directional distance function is an alternative that can be viewed as an additive measure of e ciency we show in this paper that using a probabilistic formulation of the production process the directional distance can be expressed as simple radial or hyperbolic distance up to a simple transformation of the inputs outputs space this allows to propose simple methods of estimation but also to transfer easily most of the known properties of the estimators shared by the radial and hyperbolic distances in addition the formulation allows to define robust directional distances in the lines of quantileor order m partial frontiers finally we can also define conditional directional distance functions conditional to environmental factors to illustrate the methodology we show how it can be implemented using a mutual funds database

an averaging principle for diffusions in foliated spaces consider an sde on a foliated manifold whose trajectories lay on compact leaves we investigate the effective behavior of a small transversal perturbation of order e an average principle is shown to hold such that the component transversal to the leaves converges to the solution of a deterministic ode according to the average of the perturbing vector field with respect to invariant measures on the leaves as e goes to zero an estimate of the rate of convergence is given these results generalize the geometrical scope of previous approaches including completely integrable stochastic hamiltonian system

infinitely many stokes smoothings in the gamma function the stokes lines for gamma z are the positive and negative imaginary axes where all terms in the divergent asymptotic expansion for ln gamma z have the same phase on crossing these lines from the right to the left half plane infinitely many subdominant exponentials appear rather than the usual one the exponentials increase in magnitude towards the negative real axis anti stokes line where they add to produce the poles of gamma z corresponding to each small exponential is a separate component asymptotic series in the expansion for ln gamma z if each is truncated near its least term its exponential switches on smoothly across the stokes lines according to the universal error function law by appropriate subtractions from ln gamma z the switching on of successively smaller exponentials can be revealed the procedure is illustrated by numerical computations

on bayesian analysis of mixtures with an unknown number of components with discussion new methodology for fully bayesian mixture analysis is developed making use of reversible jump markov chain monte carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture a sample from the full joint distribution of all unknown variables is thereby generated and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution the methodology is applied here to the analysis of univariate normal mixtures using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context

average and deviation for slow fast stochastic partial differential equations abstract averaging is an important method to extract effective macroscopic dynamics from complex systems with slow modes and fast modes this article derives an averaged equation for a class of stochastic partial differential equations without any lipschitz assumption on the slow modes the rate of convergence in probability is obtained as a byproduct importantly the stochastic deviation between the original equation and the averaged equation is also studied a martingale approach proves that the deviation is described by a gaussian process this gives an approximation to errors of order o instead of order o attained in previous averaging

averaging principle for stochastic korteweg de vries equation abstract averaging principle is a powerful tool for studying qualitative analysis of nonlinear dynamical systems in this paper we will establish an averaging principle for stochastic korteweg de vries equation under a general averaging condition with the help of this averaging principle we can establish an effective approximation for the solution of stochastic korteweg de vries equation this can tell us the asymptotic behavior of the solution and make the interaction between nonlinearity uncertainty and multiple scales more clear in order to obtain this averaging principle we need to establish the smoothing effect for the third order operator

limit behavior of two time scale diffusions revisited abstract this work is concerned with diffusions with two time scales or singularly perturbed diffusions asymptotic expansions of the solution of the associated cauchy problem for parabolic partial differential equation are obtained and the desired error bounds are derived these asymptotic expansions are then used to analyze related limit distributions of normalized integral functionals

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

likelihood based inference for regular functions with fractional polynomial approximations abstract this paper shows that regular fractional polynomials can approximate regular cost production and utility functions and their first two derivatives on closed compact subsets of the strictly positive orthant of euclidean space arbitrarily well these functions therefore can provide reliable approximations to demand functions and other economically relevant characteristics of tastes and technology using canonical cost function data it shows that full bayesian inference for these approximations can be implemented using standard markov chain monte carlo methods