self delta equivalence for links whose milnor s isotopy invariants vanish for an n component link milnor s isotopy invariants are defined for each multi index i i 1 i 2 i m i j 1 n here m is called the length let r i denote the maximum number of times that any index appears in i it is known that milnor invariants with r 1 i e milnor invariants for all multi indices i with r i 1 are link homotopy invariant n habegger and x s lin showed that two string links are link homotopic if and only if their milnor invariants with r 1 coincide this gives us that a link in s 3 is link homotopic to a trivial link if and only if all milnor invariants of the link with r 1 vanish although milnor invariants with r 2 are not link homotopy invariants t fleming and the author showed that milnor invariants with r 2 are self equivalence invariants in this paper we give a self equivalence classification of the set of n component links in s 3 whose milnor invariants with length 2n 1 and r 2 vanish as a corollary we have that a link is self equivalent to a trivial link if and only if all milnor invariants of the link with r 2 vanish this is a geometric characterization for links whose milnor invariants with r 2 vanish the chief ingredient in our proof is habiro s clasper theory we also give an alternate proof of a link homotopy classification of string links by using clasper theory

measured early lateral energy fractions in concert halls and opera houses in the 30 years since early lateral reflections were first suggested as important for concert halls spatial impression and source broadening have become almost universally accepted as essential characteristics of halls with good acoustics two objective measures of source broadening have been proposed measured values of the best defined of these measures the early lateral energy fraction lf are considered here results from two independent measurement surveys are discussed comparisons of lf values by hall show a significant link between hall mean lf and hall width there is however considerable overlap between measured lf values in different halls so the relevance of describing halls by their mean early lateral energy fraction values is questionable the behaviour of lf values within auditoria is discussed for different concert hall plan forms and within opera houses a measure of source broadening including sound level is proposed and results considered in the context of auditorium design

statistical estimation in varying coefficient models varying coefficient models are a useful extension of classical linear models they arise naturally when one wishes to examine how regression coefficients change over different groups characterized by certain covariates such as age the appeal of these models is that the coef cient functions can easily be estimated via a simple local regression this yields a simple one step estimation procedure we show that such a one step method cannot be optimal when different coefficient functions admit different degrees of smoothness this drawback can be repaired by using our proposed two step estimation procedure the asymptotic mean squared error for the two step procedure is obtained and is shown to achieve the optimal rate of convergence a few simulation studies show that the gain by the two step procedure can be quite substantial the methodology is illustrated by an application to an environmental data set

dealing with label switching in mixture models summary in a bayesian analysis of finite mixture models parameter estimation and clustering are sometimes less straightforward than might be expected in particular the common practice of estimating parameters by their posterior mean and summarizing joint posterior distributions by marginal distributions often leads to nonsensical answers this is due to the so called label switching problem which is caused by symmetry in the likelihood of the model parameters a frequent response to this problem is to remove the symmetry by using artificial identifiability constraints we demonstrate that this fails in general to solve the problem and we describe an alternative class of approaches relabelling algorithms which arise from attempting to minimize the posterior expected loss under a class of loss functions we describe in detail one particularly simple and general relabelling algorithm and illustrate its success in dealing with the label switching problem on two examples

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

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

smoothing spline estimation in varying coefficient models summary smoothing spline estimators are considered for inference in varying coefficient models with one effect modifying covariate bayesian confidence intervals are developed for the coefficient curves and efficient computational methods are derived for computing the curve estimators fitted values posterior variances and data adaptive methods for selecting the levels of smoothing the efficacy and utility of the methodology proposed are demonstrated through a small simulation study and the analysis of a real data set

smoothing spline estimation for varying coefficient models with repeatedly measured dependent variables longitudinal samples i e datasets with repeated measurements over time are common in biomedical and epidemiological studies such as clinical trials and cohort observational studies an exploratory tool for the analyses of such data is the varying coefficient model y t xt t t t where y t and x t x 0 t x k t t are the response and covariates at time t t 0 t k t t are smooth coefficient curves of t and t is a mean zero stochastic process a special case that is of particular interest in many situations is data with time dependent response and time independent covariates we propose in this article a componentwise smoothing spline method for estimating 0 t k t nonparametrically based on the previous varying coefficient model and a longitudinal sample of t y t x with time independent covariates x x 0 x k t from n independent subjects a leave one subject out cross validation is suggested to choose the smoothing parameters asymptotic properties of our

varying coefficient models we explore a class of regression and generalized regression models in which the coefficients are allowed to vary as smooth functions of other variables general algorithms are presented for estimating the models flexibly and some examples are given this class of models ties together generalized additive models and dynamic generalized linear models into one common framework when applied to the proportional hazards model for survival data this approach provides a new way of modelling departures from the proportional hazards assumption

mixtures of varying coefficient models for longitudinal data with discrete or continuous nonignorable dropout the analysis of longitudinal repeated measures data is frequently complicated by missing data due to informative dropout we describe a mixture model for joint distribution for longitudinal repeated measures where the dropout distribution may be continuous and the dependence between response and dropout is semiparametric specifically we assume that responses follow a varying coefficient random effects model conditional on dropout time where the regression coefficients depend on dropout time through unspecified nonparametric functions that are estimated using step functions when dropout time is discrete e g for panel data and using smoothing splines when dropout time is continuous inference under the proposed semiparametric model is hence more robust than the parametric conditional linear model the unconditional distribution of the repeated measures is a mixture over the dropout distribution we show that estimation in the semiparametric varying coefficient mixture model can proceed by fitting a parametric mixed effects model and can be carried out on standard software platforms such as sas the model is used to analyze data from a recent aids clinical trial and its performance is evaluated using simulations

finite mixture varying coefficient models for analyzing longitudinal heterogenous data this paper aims to develop a mixture model to study heterogeneous longitudinal data on the treatment effect of heroin use from a california civil addict program each component of the mixture is characterized by a varying coefficient mixed effect model we use the bayesian p splines approach to approximate the varying coefficient functions we develop markov chain monte carlo algorithms to estimate the smooth functions unknown parameters and latent variables in the model we use modified deviance information criterion to determine the number of components in the mixture a simulation study demonstrates that the modified deviance information criterion selects the correct number of components and the estimation of unknown quantities is accurate we apply the proposed model to the heroin treatment study furthermore we identify heterogeneous longitudinal patterns copyright 2011 john wiley sons ltd

homotopy invariants of links this paper answers a question originally asked by john milnor in 1957 it offers significant progress toward another question from that paper in m 1 an m 2 john milnor defined a collection of isotopy invariants of links stallings showed these were actually concordance i variants of the ink stallings work suggested that milnor s invariants were related to other algebraically defined invariants the massey products in the exterior of the link a connection made precise in tu and p thus the results in this paper can be reinterpreted as results about massey products in the link exterior recently mike freedman has suggested that some of these invariants may be the obstructions to the topological surgery theorem in dimension four f i if2 fl in this paper the approach to studying higher dimensional link concordance presented in o 1 is extended to the study of links in the 3 sphere a collection of new link invariants is defined and related to milnor s invariants one fundamental advantage of this approach is that these new invariants make explicit use of the three sphere containing the link the link exterior contains all the relations among milnor s invariants by accounting for the ambient sphere our invariants eliminate redundancy see theorem 15 we answer this question originally asked by milnor 1 to what extent are milnor s invariants independent of each other theorem 15 milnor also asked this question 2 can one extract invariants from the group rc n where 7r is the link group and n is the intersection of the lower central series of the link group theorem 15 answers question 1 partial results can be found in c 1 ma i on and t the only previously known results for two component links were k 2 8 where the number of linearly independent invariants are 0 1 0 5 0 6 and 4 respectively for links with three or more components tess was known

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

the classification of links up to link homotopy though the study of knots and links in dimension three has been with us for well over a century progress towards the ultimate goal of their classification has been slow various methods have been used in their study ranging from braid theory to the study of the link complement and its fundamental group braid theory succeeded in the classification of braids i e in solving the word and conjugacy problems in the braid groups an equivalence relation generated by markov moves on braids was found yielding the set of isotopy classes of links see b however the combinatorics of the markov moves are very difficult and braid theory has not yet led to the classification of links although recent work of birman and menasco shows progress in that direction bm on the other hand it has led to polynomial invariants via the work of jones and others j recently witten w has given a physical interpretation of these polynomials in terms of particle transmission possible relations with the results in this work are yet to be explored the study of the fundamental group of the complement of a link has led to link invariants of many types milnor m2 introduced higher order linking numbers called i invariants which have been shown see p and t to coincide with cohomological invariants ma of the link complement these invariants have proven inadequate for the classification of links in part due to a lack of understanding of their true indeterminancy several years prior to the publication of m2 milnor introduced the notion of link homotopy his terminology was simply homotopy in mi some link homotopy invariants of links were introduced there which turned out to be a subcollection of the i invariants in m2 it was hoped that modulo a certain appropriate indeterminancy these link homotopy invariants would be able to classify links up to link homotopy although this classification was achieved by milnor for links with two and three components mi it was only after more than thirty years that levine accomplished such a classification for links with four components le2 the classification of links up to link homotopy presented here represents a unification of the above two points of view as such it is a possible model for what the ultimate classification picture might look like see l for a general

time varying effect models for ordinal responses with applications in substance abuse research ordinal responses are very common in longitudinal data collected from substance abuse research or other behavioral research this study develops a new statistical model with free sas macro s that can be applied to characterize time varying effects on ordinal responses our simulation study shows that the ordinal scale time varying effects model has very low estimation bias and sometimes offers considerably better performance when fitting data with ordinal responses than a model that treats the response as continuous contrary to a common assumption that an ordinal scale with several levels can be treated as continuous our results indicate that it is not so much the number of levels on the ordinal scale but rather the skewness of the distribution that makes a difference on relative performance of linear versus ordinal models we use longitudinal data from a well known study on youth at high risk for substance abuse as a motivating example to demonstrate that the proposed model can characterize the time varying effect of negative peer influences on alcohol use in a way that is more consistent with the developmental theory and existing literature in comparison to the linear time varying effect model

penalized clustering of large scale functional data with multiple covariates in this article we propose a penalized clustering method for large scale data with multiple covariates through a functional data approach in our proposed method responses and covariates are linked together through nonparametric multivariate functions fixed effects which have great flexibility in modeling various function features such as jump points branching and periodicity functional anova is used to further decompose multivariate functions in a reproducing kernel hilbert space and provide associated notions of main effect and interaction parsimonious random effects are used to capture various correlation structures the mixed effects models are nested under a general mixture model in which the heterogeneity of functional data is characterized we propose a penalized henderson s likelihood approach for model fitting and design a rejection controlled em algorithm for the estimation our method selects smoothing parameters through generalized cross validation furthermore bayesian confidence in

bayesian identification selection and estimation of semiparametric functions in high dimensional additive models in this paper we propose an approach to both estimate and select unknown smooth functions in an additive model with potentially many functions each function is written as a linear combination of basis terms with coefficients regularized by a proper linearly constrained gaussian prior given any potentially rank deficient prior precision matrix we show how to derive linear constraints so that the corresponding effect is identified in the additive model this allows for the use of a wide range of bases and precision matrices in priors for regularization by introducing indicator variables each constrained gaussian prior is augmented with a point mass at zero thus allowing for function selection posterior inference is calculated using markov chain monte carlo and the smoothness in the functions is both the result of shrinkage through the constrained gaussian prior and model averaging we show how using non degenerate priors on the shrinkage parameters enables the application of substantially more computationally efficient sampling schemes than would otherwise be the case we show the favourable performance of our approach when compared to two contemporary alternative bayesian methods to highlight the potential of our approach in high dimensional settings we apply it to estimate two large seemingly unrelated regression models for intra day electricity load both models feature a variety of different univariate and bivariate functions which require different levels of smoothing and where component selection is meaningful priors for the error disturbance covariances are selected carefully and the empirical results provide a substantive contribution to the electricity load modelling literature in their own right

spatial modeling with spatially varying coefficient processes in many applications the objective is to build regression models to explain a response variable over a region of interest under the assumption that the responses are spatially correlated in nearly all of this work the regression coefficients are assumed to be constant over the region however in some applications coefficients are expected to vary at the local or subregional level here we focus on the local case although parametric modeling of the spatial surface for the coefficient is possible here we argue that it is more natural and flexible to view the surface as a realization from a spatial process we show how such modeling can be formalized in the context of gaussian responses providing attractive interpretation in terms of both random effects and explaining residuals we also offer extensions to generalized linear models and to spatio temporal setting we illustrate both static and dynamic modeling with a dataset that attempts to explain log selling price of single family houses

nonparametric smoothing estimates of time varying coefficient models with longitudinal data this paper considers nonparametric estimation in a varying coefficient model with repeated measurements y ij x ij t ij for i 1 n and j 1 n i where x ij x ij x ijk t and y ij x ij t ij denote the jth outcome covariate and time design points respectively of the ith subject the model considered here is y ij x ij t t ij e i t ij where t 0 t k t t for k 0 are smooth nonparametric functions of interest and e i t is a zero mean stochastic process the measurements are assumed to be independent for different subjects but can be correlated at different time points within each subject two nonparametric estimators of t namely a smoothing spline and a locally weighted polynomial are derived for such repeatedly measured data a crossvalidation criterion is proposed for the selection of the corresponding smoothing parameters asymptotic properties such as consistency rates of convergence and asymptotic mean squared errors are established for kernel estimators a special case of the local polynomials these asymptotic results give useful insights into the reliability of our general estimation methods an example of predicting the growth of children born to hiv infected mothers based on gender hiv status and maternal vitamin a levels shows that this model and the corresponding nonparametric estimators are useful in epidemiological studies

on bayesian analysis of mixtures with an unknown number of components discussion author s reply 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

markov chain monte carlo estimation of classical and dynamic switching and mixture models bayesian estimation of a very general model class where the distribution of the observations depends on a latent process taking values in a discrete state space is discussed in this article this model class covers finite mixture modeling markov switching autoregressive modeling and dynamic linear models with switching the consequences the unidentifiability of this type of model has on markov chain monte carlo mcmc estimation are explicitly dealt with joint bayesian estimation of all latent variables model parameters and parameters that determine the probability law of the latent process is carried out by a new mcmc method called permutation sampling the permutation sampler first samples from the unconstrained posterior which often can be done in a convenient multimove manner and then applies a permutation of the current labeling of the states of the latent process in a first run the random permutation sampler used selected the permutation randomly the mcmc output of the random permutation s

generalized gauss maps and integrals for three component links toward higher helicities for magnetic fields and fluid flows to each three component link in the 3 sphere we associate a generalized gauss map from the 3 torus to the 2 sphere and show that the pairwise linking numbers and milnor triple linking number that classify the link up to link homotopy correspond to the pontryagin invariants that classify its generalized gauss map up to homotopy we view this as a natural extension of the familiar situation for two component links in 3 space where the linking number is the degree of the classical gauss map from the 2 torus to the 2 sphere the generalized gauss map like its prototype is geometrically natural in the sense that it is equivariant with respect to orientation preserving isometries of the ambient space thus positioning it for application to physical situations when the pairwise linking numbers of a three component link are all zero we give an integral formula for the triple linking number analogous to the gauss integral for the pairwise linking numbers this new integral is also geometrically natural like its prototype in the sense that the integrand is invariant under orientation preserving isometries of the ambient space versions of this integral have been applied by komendarczyk in special cases to problems of higher order helicity and derivation of lower bounds for the energy of magnetic fields we have set this entire paper in the 3 sphere because our generalized gauss map is easiest to present here but in a subsequent paper we will give the corresponding maps and integral formulas in euclidean 3 space

an approach to homotopy classification of links a reformulation and refinement of the i invariants of milnor are used to give a homotopy classification of 4 component linlis and suggest a possible general homotopy classification the main idea is to use the reduced group of a link and its geometric automorphisms to define the precise indeterminacy of these invariants introduction in 1954 milnor m introduced the concept of link homotopy a notion considerably weaker than the usual notion of link type in fact it is also weaker than the relations of pl and topological isotopy and i equivalence introduced later see r go g1 but equivalent to the apparently weaker relation which asks for disjoint singular cylinders in i x s3 connecting the links see li recently link homotopy has come up in a reformulation of the 4 dimensional topological surgery conjecture see fl unlike usual link type the classification problem for link homotopy seems quite tractable in m milnor gives a complete homotopy classification of links with 3 or fewer components and shows that a link is homotopically trivial if and only if a certain collection of numerical invariants is defined and vanishes alternatively this can be interpreted in terms of the reduced link group 9 l defined in m see below the numerical homotopy invariants used in m are part of a wider collectionthe u invariants which appear in m1 and are there shown to be invariants of topological isotopy in s they are shown to be invariants of topological iequivalence but are not except for the subset used in m homotopy invariants although the u invariants do not serve to classify links under i equivalence it is still an open question whether a link with trivial u invariants is cobordant to a boundary link a boundary link is one whose components bound disjoint surfaces in s3 they have trivial u invariants and include all split links links whose components lie in disjoint balls in s3 and parallel links links formed by several parallel copies of a single knot as already mentioned the homotopy u invariants are trivial if and only if the link is homotopy trivial but it is not true that any links with the same u invariants are homotopic l their indeterminacy is too large in l a classification of links up to surgery equivalences is given using certain of the homotopy u invariants with a refinement of their indeterminacy in fact it seems implicit in m that one should be able to use the u invariants to give a general homotopy classification it is shown in m p that the u invariants received by the editors december 12 1986 1980 mathematics subject classification 1985 revision primary 57m25 partially supported by the national science foundation r 1988 american mathematical society 0002 9947 88 1 00 25 per page

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

dynamic conditionally linear mixed models for longitudinal data we develop a new class of models dynamic conditionally linear mixed models for longitudinal data by decomposing the within subject covariance matrix using a special cholesky decomposition here dynamic means using past responses as covariates and conditional linearity means that parameters entering the model linearly may be random but nonlinear parameters are nonrandom this setup offers several advantages and is surprisingly similar to models obtained from the first order linearization method applied to nonlinear mixed models first it allows for flexible and computationally tractable models that include a wide array of covariance structures these structures may depend on covariates and hence may differ across subjects this class of models includes e g all standard linear mixed models antedependence models and vonesh carter models second it guarantees the fitted marginal covariance matrix of the data is positive definite we develop methods for bayesian inference and motivate the usefulness of these models using a series of longitudinal depression studies for which the features of these new models are well suited

homotopy on spatial graphs and the sato levine invariant edge homotopy and vertex homotopy are equivalence relations on spatial graphs which are generalizations of milnor s link homotopy we introduce some edge resp vertex homotopy invariants of spatial graphs by applying the sato levine invariant for the 2 component constituent algebraically split links and show examples of non splittable spatial graphs up to edge resp vertex homotopy all of whose constituent links are link homotopically trivial

varying coefficient models and basis function approximations for the analysis of repeated measurements summary a global smoothing procedure is developed using basis function approximations for estimating the parameters of a varying coefficient model with repeated measurements inference procedures based on a resampling subject bootstrap are proposed to construct confidence regions and to perform hypothesis testing conditional biases and variances of our estimators and their asymptotic consistency are developed explicitly finite sample properties of our procedures are investigated through a simulation study application of the proposed approach is demonstrated through an example in epidemiology in contrast to the existing methods this approach applies whether or not the covariates are timeinvariant and does not require binning of the data when observations are sparse at distinct observation times

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

bayesian smoothing and regression splines for measurement error problems in the presence of covariate measurement error estimating a regression function nonparametrically is extremely difficult the problem being related to deconvolution various frequentist approaches exist for this problem but to date there has been no bayesian treatment in this article we describe bayesian approaches to modeling a flexible regression function when the predictor variable is measured with error the regression function is modeled with smoothing splines and regression p splines two methods are described for exploration of the posterior the first called the iterative conditional modes icm is only partially bayesian icm uses a componentwise maximization routine to find the mode of the posterior it also serves to create starting values for the second method which is fully bayesian and uses markov chain monte carlo mcmc techniques to generate observations from the joint posterior distribution use of the mcmc approach has the advantage that interval estimates that directly model and

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

a bayesian modeling approach for generalized semiparametric structural equation models in behavioral biomedical and psychological studies structural equation models sems have been widely used for assessing relationships between latent variables regression type structural models based on parametric functions are often used for such purposes in many applications however parametric sems are not adequate to capture subtle patterns in the functions over the entire range of the predictor variable a different but equally important limitation of traditional parametric sems is that they are not designed to handle mixed data types continuous count ordered and unordered categorical this paper develops a generalized semiparametric sem that is able to handle mixed data types and to simultaneously model different functional relationships among latent variables a structural equation of the proposed sem is formulated using a series of unspecified smooth functions the bayesian p splines approach and markov chain monte carlo methods are developed to estimate the smooth functions and the unknown parameters moreover we examine the relative benefits of semiparametric modeling over parametric modeling using a bayesian model comparison statistic called the complete deviance information criterion dic the performance of the developed methodology is evaluated using a simulation study to illustrate the method we used a data set derived from the national longitudinal survey of youth