rotation invariant nonrigid point set matching in cluttered scenes this paper addresses the problem of rotation invariant nonrigid point set matching the shape context sc feature descriptor is used because of its strong discriminative nature whereas edges in the graphs constructed by point sets are used to determine the orientations of scs similar to lengths or directions oriented scs constructed this way can be regarded as attributes of edges by matching edges between two point sets rotation invariance is achieved two novel ways of constructing graphs on a model point set are proposed aiming at making the orientations of scs as robust to disturbances as possible the structures of these graphs facilitate the use of dynamic programming dp for optimization the strong discriminative nature of sc the special structure of the model graphs and the global optimality of dp make our methods robust to various types of disturbances particularly clutters the extensive experiments on both synthetic and real data validated the robustness of the proposed methods to various types of disturbances they can robustly detect the desired shapes in complex and highly cluttered scenes

additive nonparametric regression with autocorrelated errors a bayesian approach is presented for nonparametric estimation of an additive regression model with autocorrelated errors each of the potentially non linear components is modelled as a regression spline using many knots while the errors are modelled by a high order stationary autoregressive process parameterized in terms of its autocorrelations the distribution of significant knots and partial autocorrelations is accounted for using subset selection our approach also allows the selection of a suitable transformation of the dependent variable all aspects of the model are estimated simultaneously by using the markov chain monte carlo method it is shown empirically that the approach proposed works well on several simulated and real examples

the generalized distributive law we discuss a general message passing algorithm which we call the generalized distributive law gdl the gdl is a synthesis of the work of many authors in information theory digital communications signal processing statistics and artificial intelligence it includes as special cases the baum welch algorithm the fast fourier transform fft on any finite abelian group the gallager tanner wiberg decoding algorithm viterbi s algorithm the bcjr algorithm pearl s belief propagation algorithm the shafer shenoy probability propagation algorithm and the turbo decoding algorithm although this algorithm is guaranteed to give exact answers only in certain cases the junction tree condition unfortunately not including the cases of gtw with cycles or turbo decoding there is much experimental evidence and a few theorems suggesting that it often works approximately even when it is not supposed to

decomposable graphical gaussian model determination we propose a methodology for bayesian model determination in decomposable graphical gaussian models to achieve this aim we consider a hyper inverse wishart prior distribution on the concentration matrix for each given graph to ensure compatibility across models such prior distributions are obtained by marginalisation from the prior conditional on the complete graph we explore alternative structures for the hyperparameters of the latter and their consequences for the model model determination is carried out by implementing a reversible jump markov chain monte carlo sampler in particular the dimension changing move we propose involves adding or dropping an edge from the graph we characterise the set of moves which preserve the decomposability of the graph giving a fast algorithm for maintaining the junction tree representation of the graph at each sweep as state variable we use the incomplete variance covariance matrix containing only the elements for which the corresponding element of the inverse is nonzero this allows all computations to be performed locally at the clique level which is a clear advantage for the analysis of large and complex datasets finally the statistical and computational performance of the procedure is illustrated by mean of both artificial and real datasets

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

joint mean covariance models with applications to longitudinal data unconstrained parameterisation summary we provide unconstrained parameterisation for and model a covariance using covariates the cholesky decomposition of the inverse of a covariance matrix is used to associate a unique unit lower triangular and a unique diagonal matrix with each covariance matrix the entries of the lower triangular and the log of the diagonal matrix are unconstrained and have meaning as regression coefficients and prediction variances when regressing a measurement on its predecessors an extended generalised linear model is introduced for joint modelling of the vectors of predictors for the mean and covariance subsuming the joint modelling strategy for mean and variance heterogeneity gabriel s antedependence models dempster s covariance selection models and the class of graphical models the likelihood function and maximum likelihood estimators of the covariance and the mean parameters are studied when the observations are normally distributed applications to modelling nonstationary dependence structures and multivariate data are discussed and illustrated using real data a graphical method similar to that based on the correlogram in time series is developed and used to identify parametric models for nonstationary covariances

nonparametric modeling of longitudinal covariance structure in functional mapping of quantitative trait loci estimation of the covariance structure of longitudinal processes is a fundamental prerequisite for the practical deployment of functional mapping designed to study the genetic regulation and network of quantitative variation in dynamic complex traits we present a nonparametric approach for estimating the covariance structure of a quantitative trait measured repeatedly at a series of time points specifically we adopt huang et al s 2006 biometrika 93 85 98 approach of invoking the modified cholesky decomposition and converting the problem into modeling a sequence of regressions of responses a regularized covariance estimator is obtained using a normal penalized likelihood with an l 2 penalty this approach embedded within a mixture likelihood framework leads to enhanced accuracy precision and flexibility of functional mapping while preserving its biological relevance simulation studies are performed to reveal the statistical properties and advantages of the proposed method a real example from a mouse genome project is analyzed to illustrate the utilization of the methodology the new method will provide a useful tool for genome wide scanning for the existence and distribution of quantitative trait loci underlying a dynamic trait important to agriculture biology and health sciences

a graduated assignment algorithm for graph matching a graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise by combining graduated nonconvexity two way assignment constraints and sparsity large improvements in accuracy and speed are achieved its low order computational complexity o lm where l and m are the number of links in the two graphs and robustness in the presence of noise offer advantages over traditional combinatorial approaches the algorithm not restricted to any special class of graph is applied to subgraph isomorphism weighted graph matching and attributed relational graph matching to illustrate the performance of the algorithm attributed relational graphs derived from objects are matched then results from twenty five thousand experiments conducted on 100 mode random graphs of varying types graphs with only zero one links weighted graphs and graphs with node attributes and multiple link types are reported no comparable results have been reported by any other graph matching algorithm before in the research literature twenty five hundred control experiments are conducted using a relaxation labeling algorithm and large improvements in accuracy are demonstrated

estimation of a covariance matrix using the reference prior estimation of a covariance matrix sum is a notoriously difficult problem the standard unbiased estimator can be substantially suboptimal we approach the problem from a noninformative prior bayesian perspective developing the reference noninformative prior for a covariance matrix and obtaining expressions for the resulting bayes estimators these expressions involve the computation of high dimensional posterior expectations which is done using a recent markov chain simulation tool the hit and run sampler frequentist risk comparisons with previously suggested estimators are also given and determination of the accuracy of the estimators is addressed

correspondence propagation with weak priors for the problem of image registration the top few reliable correspondences are often relatively easy to obtain while the overall matching accuracy may fall drastically as the desired correspondence number increases in this paper we present an efficient feature matching algorithm to employ sparse reliable correspondence priors for piloting the feature matching process first the feature geometric relationship within individual image is encoded as a spatial graph and the pairwise feature similarity is expressed as a bipartite similarity graph between two feature sets then the geometric neighborhood of the pairwise assignment is represented by a categorical product graph along which the reliable correspondences are propagated and finally a closed form solution for feature matching is deduced by ensuring the feature geometric coherency as well as pairwise feature agreements furthermore our algorithm is naturally applicable for incorporating manual correspondence priors for semi supervised feature matching extensive experiments on both toy examples and real world applications demonstrate the superiority of our algorithm over the state of the art feature matching techniques

thermodynamics of the general diffusion process time reversibility and entropy production we introduce an axiomatic thermodynamic theory for the general diffusion process and prove a theorem concerning entropy and irreversibility the equivalence among time reversibility zero entropy production symmetricity of the stationary diffusion process and a potential condition

nonconjugate bayesian estimation of covariance matrices and its use in hierarchical models abstract the problem of estimating a covariance matrix in small samples has been considered by several authors following early work by stein this problem can be especially important in hierarchical models where the standard errors of fixed and random effects depend on estimation of the covariance matrix of the distribution of the random effects we propose a set of hierarchical priors hps for the covariance matrix that produce posterior shrinkage toward a specified structure here we examine shrinkage toward diagonality we then address the computational difficulties raised by incorporating these priors and nonconjugate priors in general into hierarchical models we apply a combination of approximation gibbs sampling possibly with a metropolis step and importance reweighting to fit the models and compare this hybrid approach to alternative markov chain monte carlo methods our investigation involves three alternative hps the first works with the spectral decomposition of the covariance matrix an

interpolation of stochastic and deterministic reduced dynamics abstract there are roughly speaking the two extreme types of dynamical density functional theories one is deterministic without noise and another is fully stochastic with noise we attempt to interpolate these extreme limiting theories for general reduced description of time evolution by making use of a series of projection operators which generalize the so called kawasaki gunton operator this helps to clarify though in a formal way the controversies or confusions surrounding the current dynamical density functional theories

parsimonious covariance matrix estimation for longitudinal data this article proposes a data driven method to identify parsimony in the covariance matrix of longitudinal data and to exploit any such parsimony to produce a statistically efficient estimator of the covariance matrix the approach parameterizes the covariance matrix through the cholesky decomposition of its inverse for longitudinal data this is a one step ahead predictive representation and the cholesky factor is likely to have off diagonal elements that are zero or close to zero a hierarchical bayesian model is used to identify any such zeros in the cholesky factor similar to approaches that have been successful in bayesian variable selection the model is estimated using a markov chain monte carlo sampling scheme that is computationally efficient and can be applied to covariance matrices of high dimension it is demonstrated through simulations that the proposed method compares favorably in terms of statistical efficiency with a highly regarded competing approach the estimator is applied to three

nonparametric function estimation subject to monotonicity convexity and other shape constraints this paper uses free knot and fixed knot regression splines in a bayesian context to develop methods for the nonparametric estimation of functions subject to shape constraints in models with log concave likelihood functions the shape constraints we consider include monotonicity convexity and functions with a single minimum a computationally efficient mcmc sampling algorithm is developed that converges faster than previous methods for non gaussian models simulation results indicate the monotonically constrained function estimates have good small sample properties relative to i unconstrained function estimates and ii function estimates obtained from other constrained estimation methods when such methods exist also asymptotic results show the methodology provides consistent estimates for a large class of smooth functions two detailed illustrations exemplify the ideas

a bayesian approach to additive semiparametric regression abstract we present a bayesian approach to estimating an additive semiparametric regression model which is robust to outliers the unknown curves are estimated by posterior means and are shown to be smoothing splines by using markov chain monte carlo an o mn algorithm is produced where n is the sample size and m is the total number of markov chain iterations previous exact approaches required o n3 operations making the estimation of large data sets impractical efficient methods for estimating the posterior means using mixture and backfitting estimates are developed the properties of the curve estimates are studied empirically using both simulated and real examples

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

latent variable models with nonparametric interaction effects of latent variables renal disease is one of the common complications of diabetes especially for asian populations moreover cardiovascular and renal diseases share common risk factors this paper proposes a latent variable model with nonparametric interaction effects of latent variables for a study based on the hong kong diabetes registry which was established in 1995 as part of a continuous quality improvement program at the prince of wales hospital in hong kong renal outcome outcome latent variable is regressed in terms of cardiac function and diabetes explanatory latent variables through an additive structural equation formulated using a series of unspecified univariate and bivariate smooth functions the bayesian p splines approach along with a markov chain monte carlo algorithm is proposed to estimate smooth functions unknown parameters and latent variables in the model the performance of the developed methodology is demonstrated via a simulation study the effect of the nonparametric interaction of cardiac function and diabetes on renal outcome is investigated using the proposed methodology copyright 2013 john wiley sons ltd

graph based point drift the problem of point set registration often arises in pattern recognition whenever one needs to match information available in images such as feature locations landmarks or points representing a surface of an object it is a challenging task and a widely explored topic in stereo vision image alignment medical imaging and other fields many of those problems have been addressed using graph theory by taking advantage of the structural information available in graphs in this paper graph centralities are explored in the point set registration problem for the first time we propose a variant of the coherent point drift cpd by integrating the degree betweenness closeness eigenvector and pagerank centralities the centrality values bring topological information used during the computation of correspondence between points we analyse the performance on several datasets and our results indicate that the registration can converge faster when the centrality is combined with the spatial information in the traditional probabilistic framework our novel contribution introduces the social network centralities as a good source of prior information for the registration problem and it demonstrates how one can take advantage of such information highlightswe introduce the graph centrality into the point set registration problem integrating centrality with spatial information can improve the convergence speed we discuss the importance of the graph edges for the registration we compare the performance of five centrality variants with the cpd algorithm

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

a zernike moment phase based descriptor for local image representation and matching a local image descriptor robust to the common photometric transformations blur illumination noise and jpeg compression and geometric transformations rotation scaling translation and viewpoint is crucial to many image understanding and computer vision applications in this paper the representation and matching power of region descriptors are to be evaluated a common set of elliptical interest regions is used to evaluate the performance the elliptical regions are further normalized to be circular with a fixed size the normalized circular regions will become affine invariant up to a rotational ambiguity here a new distinctive image descriptor to represent the normalized region is proposed which primarily comprises the zernike moment zm phase information an accurate and robust estimation of the rotation angle between a pair of normalized regions is then described and used to measure the similarity between two matching regions the discriminative power of the new zm phase descriptor is compared with five major existing region descriptors sift gloh pca sift complex moments and steerable filters based on the precision recall criterion the experimental results involving more than 15 million region pairs indicate the proposed zm phase descriptor has generally speaking the best performance under the common photometric and geometric transformations both quantitative and qualitative analyses on the descriptor performances are given to account for the performance discrepancy first the key factor for its striking performance is due to the fact that the zm phase has accurate estimation accuracy of the rotation angle between two matching regions second the feature dimensionality and feature orthogonality also affect the descriptor performance third the zm phase is more robust under the nonuniform image intensity fluctuation finally a time complexity analysis is provided

n sift n dimensional scale invariant feature transform we propose the n dimensional scale invariant feature transform n sift method for extracting and matching salient features from scalar images of arbitrary dimensionality and compare this method s performance to other related features the proposed features extend the concepts used for 2 d scalar images in the computer vision sift technique for extracting and matching distinctive scale invariant features we apply the features to images of arbitrary dimensionality through the use of hyperspherical coordinates for gradients and multidimensional histograms to create the feature vectors we analyze the performance of a fully automated multimodal medical image matching technique based on these features and successfully apply the technique to determine accurate feature point correspondence between pairs of 3 d mri images and dynamic 3d time ct data

an efficient globally optimal algorithm for asymmetric point matching although the robust point matching algorithm has been demonstrated to be effective for non rigid registration there are several issues with the adopted deterministic annealing optimization technique first it is not globally optimal and regularization on the spatial transformation is needed for good matching results second it tends to align the mass centers of two point sets to address these issues we propose a globally optimal algorithm for the robust point matching problem in the case that each model point has a counterpart in scene set by eliminating the transformation variables we show that the original matching problem is reduced to a concave quadratic assignment problem where the objective function has a low rank hessian matrix this facilitates the use of large scale global optimization techniques we propose a modified normal rectangular branch and bound algorithm to solve the resulting problem where multiple rectangles are simultaneously subdivided to increase the chance of shrinking the rectangle containing the global optimal solution in addition we present an efficient lower bounding scheme which has a linear assignment formulation and can be efficiently solved extensive experiments on synthetic and real datasets demonstrate the proposed algorithm performs favorably against the state of the art methods in terms of robustness to outliers matching accuracy and run time

bayes model averaging with selection of regressors when a number of distinct models contend for use in prediction the choice of a single model can offer rather unstable predictions in regression stochastic search variable selection with bayesian model averaging offers a cure for this robustness issue but at the expense of requiring very many predictors here we look at bayes model averaging incorporating variable selection for prediction this offers similar mean square errors of prediction but with a vastly reduced predictor space this can greatly aid the interpretation of the model it also reduces the cost if measured variables have costs the development here uses decision theory in the context of the multivariate general linear model in passing this reduced predictor space bayes model averaging is contrasted with single model approximations a fast algorithm for updating regressions in the markov chain monte carlo searches for posterior inference is developed allowing many more variables than observations to be contemplated we discuss the merits of absolute rather than proportionate shrinkage in regression especially when there are more variables than observations the methodology is illustrated on a set of spectroscopic data used for measuring the amounts of different sugars in an aqueous solution

the effect of interference of coloured additive and multiplicative white noises on escape rate in this paper we have calculated the escape rate from a meta stable state for coloured and correlated noise driven open systems based on the fokker planck description of the stochastic process we consider the effect of two correlation times due to the additive coloured noise and the correlation between additive coloured and multiplicative white noises the effect of the noise correlation strength on the rate has also been investigated

matching by linear programming and successive convexification we present a novel convex programming scheme to solve matching problems focusing on the challenging problem of matching in a large search range and with cluttered background matching is formulated as metric labeling with l1 regularization terms for which we propose a novel linear programming relaxation method and an efficient successive convexification implementation the unique feature of the proposed relaxation scheme is that a much smaller set of basis labels is used to represent the original label space this greatly reduces the size of the searching space a successive convexification scheme solves the labeling problem in a coarse to fine manner importantly the original cost function is reconvexified at each stage in the new focus region only and the focus region is updated so as to refine the searching result this makes the method well suited for large label set matching experiments demonstrate successful applications of the proposed matching scheme in object detection motion estimation and tracking

bayesian variable selection in linear regression abstract this article is concerned with the selection of subsets of predictor variables in a linear regression model for the prediction of a dependent variable it is based on a bayesian approach intended to be as objective as possible a probability distribution is first assigned to the dependent variable through the specification of a family of prior distributions for the unknown parameters in the regression model the method is not fully bayesian however because the ultimate choice of prior distribution from this family is affected by the data it is assumed that the predictors represent distinct observables the corresponding regression coefficients are assigned independent prior distributions for each regression coefficient subject to deletion from the model the prior distribution is a mixture of a point mass at 0 and a diffuse uniform distribution elsewhere that is a spike and slab distribution the random error component is assigned a normal distribution with mean 0 and standard deviation

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

nonparametric regression using bayesian variable selection abstract this paper estimates an additive model semiparametrically while automatically selecting the significant independent variables and the appropriate power transformation of the dependent variable the nonlinear variables are modeled as regression splines with significant knots selected from a large number of candidate knots the estimation is made robust by modeling the errors as a mixture of normals a bayesian approach is used to select the significant knots the power transformation and to identify outliers using the gibbs sampler to carry out the computation empirical evidence is given that the sampler works well on both simulated and real examples and that in the univariate case it compares favorably with a kernel weighted local linear smoother the variable selection algorithm in the paper is substantially faster than previous bayesian variable selection algorithms

a performance evaluation of local descriptors in this paper we compare the performance of descriptors computed for local interest regions as for example extracted by the harris affine detector mikolajczyk k and schmid c 2004 many different descriptors have been proposed in the literature it is unclear which descriptors are more appropriate and how their performance depends on the interest region detector the descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations we compare shape context belongie s et al april 2002 steerable filters freeman w and adelson e setp 1991 pca sift ke y and sukthankar r 2004 differential invariants koenderink j and van doorn a 1987 spin images lazebnik s et al 2003 sift lowe d g 1999 complex filters schaffalitzky f and zisserman a 2002 moment invariants van gool l et al 1996 and cross correlation for different types of interest regions we also propose an extension of the sift descriptor and show that it outperforms the original method furthermore we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the sift based descriptors perform best moments and steerable filters show the best performance among the low dimensional descriptors

bayesian model averaging for linear regression models abstract we consider the problem of accounting for model uncertainty in linear regression models conditioning on a single selected model ignores model uncertainty and thus leads to the underestimation of uncertainty when making inferences about quantities of interest a bayesian solution to this problem involves averaging over all possible models i e combinations of predictors when making inferences about quantities of interest this approach is often not practical in this article we offer two alternative approaches first we describe an ad hoc procedure occam s window which indicates a small set of models over which a model average can be computed second we describe a markov chain monte carlo approach that directly approximates the exact solution in the presence of model uncertainty both of these model averaging procedures provide better predictive performance than any single model that might reasonably have been selected in the extreme case where there are many candidate predictors but

bayesian nonparametric regression analysis of data with random effects covariates from longitudinal measurements we consider nonparametric regression analysis in a generalized linear model glm framework for data with covariates that are the subject specific random effects of longitudinal measurements the usual assumption that the effects of the longitudinal covariate processes are linear in the glm may be unrealistic and if this happens it can cast doubt on the inference of observed covariate effects allowing the regression functions to be unknown we propose to apply bayesian nonparametric methods including cubic smoothing splines or p splines for the possible nonlinearity and use an additive model in this complex setting to improve computational efficiency we propose the use of data augmentation schemes the approach allows flexible covariance structures for the random effects and within subject measurement errors of the longitudinal processes the posterior model space is explored through a markov chain monte carlo mcmc sampler the proposed methods are illustrated and compared to other approaches the naive approach and the regression calibration via simulations and by an application that investigates the relationship between obesity in adulthood and childhood growth curves

spike and slab priors for function selection in structured additive regression models structured additive regression star provides a general framework for complex gaussian and non gaussian regression models with predictors comprising arbitrary combinations of nonlinear functions and surfaces spatial effects varying coefficients random effects and further regression terms the large flexibility of star makes function selection a challenging and important task aiming at 1 selecting the relevant covariates 2 choosing an appropriate and parsimonious representation of the impact of covariates on the predictor and 3 determining the required interactions we propose a spike and slab prior structure for function selection that allows to include or exclude single coefficients as well as blocks of coefficients representing specific model terms a novel multiplicative parameter expansion is required to obtain good mixing and convergence properties in a markov chain monte carlo simulation approach and is shown to induce desirable shrinkage properties in simulation studies and with re

nonlinear langevin equations and the time dependent density functional method to study the time dependent density functional method tddfm two streaming velocity reversible terms are reformulated in the nonlinear langevin equation mori s prog theor phys 33 423 1965 projection operator method shows a variety of nonlinear langevin equations this is because the equations depend on the choice of phase space functions employed in the projection if phase space functions include particular functions however the streaming velocity term has an invariable form the form is independent of the choice of other phase space functions since the invariable streaming velocity term does not introduce the tddfm the second viewpoint is presented in this the linearization of the streaming velocity term agrees with the frequency term in the linear langevin equation since only the second streaming velocity term introduces the tddfm one needs to be cautious in the derivation of the tddfm

levy flights in confining potentials we analyze confining mechanisms for levy flights when they evolve in suitable external potentials their variance may exist and show signatures of a superdiffusive transport two classes of stochastic jump type processes are considered those driven by langevin equation with levy noise and those named topological levy processes occurring in systems with topological complexity such as folded polymers or complex networks whose langevin representation is unknown and possibly nonexistent our major finding is that both above classes of processes stay in affinity and may share common stationary probability density even if their detailed dynamical behavior look different this near equilibrium observation seems to be generic to a broad class of levy noise driven processes such as e g superdiffusion on folded polymers geophysical flows and even climatic changes

semiparametric estimates of the relation between weather and electricity sales abstract a nonlinear relationship between electricity sales and temperature is estimated using a semiparametric regression procedure that easily allows linear transformations of the data this accommodates introduction of covariates timing adjustments due to the actual billing schedules and serial correlation the procedure is an extension of smoothing splines with the smoothness parameter estimated from minimization of the generalized cross validation criterion introduced by craven and wahba 1979 estimates are presented for residential sales for four electric utilities and are compared with models that represent the weather using only heating and cooling degree days or with piecewise linear splines

entropy production in nonequilibrium statistical mechanics we consider systems of nonequilibrium statistical mechanics driven by nonconservative forces and in contact with an ideal thermostat these are smooth dynamical systems for which one can define natural stationary states srb in the simplest case and entropy production e minus the sum of the lyapunov exponents in the simplest case we give exact and explicit definitions of the entropy production e for the various situations of physical interest we prove that e 0 and indicate cases where e 0 the novelty of the approach is that we do not try to compute entropy production directly but make it depend on the identification of a natural stationary state for the system

principle of maximum entropy and reduced dynamics a new method to obtain a series of reduced dynamics at various stages of coarse graining is proposed this ranges from the most coarse grained one which agrees with the deterministic time evolution equation for averages of the relevant variables to the least coarse grained one which is the generalized fokker planck equation for the probability distribution function of the relevant variables the method is based on the extention of the kawasaki gunton operator with the help of the principle of maximum entropy

a new approach to cholesky based covariance regularization in high dimensions summary in this paper we propose a new regression interpretation of the cholesky factor of the covariance matrix as opposed to the well known regression interpretation of the cholesky factor of the inverse covariance which leads to a new class of regularized covariance estimators suitable for high dimensional problems regularizing the cholesky factor of the covariance via this regression interpretation always results in a positive definite estimator in particular one can obtain a positive definite banded estimator of the covariance matrix at the same computational cost as the popular banded estimator of bickel levina 2008b which is not guaranteed to be positive definite we also establish theoretical connections between banding cholesky factors of the covariance matrix and its inverse and constrained maximum likelihood estimation under the banding constraint and compare the numerical performance of several methods in simulations and on a sonar data example

hybrid adaptive splines abstract an adaptive spline method for smoothing is proposed that combines features from both regression spline and smoothing spline approaches one of its advantages is the ability to vary the amount of smoothing in response to the inhomogeneous curvature of true functions at different locations this method can be applied to many multivariate function estimation problems which is illustrated by an application to smoothing temperature data on the globe the method s performance in a simulation study is found to be comparable to the wavelet shrinkage methods proposed by donoho and johnstone the problem of how to count the degrees of freedom for an adaptively chosen set of basis functions is addressed this issue arises also in the mars procedure proposed by friedman and other adaptive regression spline procedures

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

variable selection and function estimation in additive nonparametric regression using a data based prior abstract a hierarchical bayesian approach is proposed for variable selection and function estimation in additive nonparametric gaussian regression models and additive nonparametric binary regression models the prior for each component function is an integrated wiener process resulting in a posterior mean estimate that is a cubic smoothing spline each of the explanatory variables is allowed to be in or out of the model and the regression functions are estimated by model averaging to allow variable selection and model averaging data based priors are used for the smoothing parameter and the slope at 0 of each component function a two step markov chain monte carlo method is used to efficiently obtain the data based prior and to carry out variable selection and function estimation it is shown by simulation that significant improvements in the function estimators can be obtained over an approach that estimates all the unknown functions simultaneously the methodology is illustrated for a binary regressio

bayesian analysis of binary and polychotomous response data abstract a vast literature in statistics biometrics and econometrics is concerned with the analysis of binary and polychotomous response data the classical approach fits a categorical response regression model using maximum likelihood and inferences about the model are based on the associated asymptotic theory the accuracy of classical confidence statements is questionable for small sample sizes in this article exact bayesian methods for modeling categorical response data are developed using the idea of data augmentation the general approach can be summarized as follows the probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data values of the latent data can be simulated from suitable truncated normal distributions if the latent data are known then the posterior distribution of the parameters can be computed using standard results for normal linear models draws from this posterior are used to sample new latent data and t

reference priors for the orbit in a group model for a group model in which the group mathbf g acts freely on the parameter space mathbf omega this paper considers a prior which is a product of right haar measure on mathbf g and a limiting form of jeffreys prior for the maximal invariant when the parameter of interest is the orbit of mathbf g in mathbf omega it is shown that such a prior is the reference prior defined by bernardo a method of calculating this reference prior is given which avoids the necessity of working in a parameterization of mathbf omega which expresses mathbf omega as a product of mathbf g and a cross section examples of the multivariate normal distribution with the parameter of interest being the correlation matrix or the eigenvalues of the covariance matrix are discussed

langevin equation for the density of a system of interacting langevin processes we present a simple derivation of the stochastic equation obeyed by the density function for a system of langevin processes interacting via a pairwise potential the resulting equation is considerably different from the phenomenological equations usually used to describe the dynamics of non conserved model a and conserved model b particle systems the major feature is that the spatial white noise for this system appears not additively but multiplicatively this simply expresses the fact that the density cannot fluctuate in regions devoid of particles the steady state for the density function may however still be recovered formally as a functional integral over the coursed grained free energy of the system as in models a and b

benchmark priors for bayesian model averaging in contrast to a posterior analysis given a particular sampling model posterior model probabilities in the context of model uncertainty are typically rather sensitive to the speciflcation of the prior in particular difiuse priors on model speciflc parameters can lead to quite unexpected consequences here we focus on the practically relevant situation where we need to entertain a large number of sampling models and we have or wish to use little or no subjective prior information we aim at providing an automatic or benchmark prior structure that can be used in such cases we focus on the normal linear regression model with uncertainty in the choice of re gressors we propose a partly noninformative prior structure related to a natural conjugate g prior speciflcation where the amount of subjective information requested from the user is limited to the choice of a single scalar hyperparameter g0j the consequences of difierent choices for g0j are examined we investigate theoretical properties such as consistency of the implied bayesian procedure links with classical information criteria are provided in addition we examine the flnite sample implications of several choices of g0j in a simulation study the use of the mc 3 algorithm of madigan and york 1995 combined with e cient coding in fortran makes it feasible to conduct large simulations in addition to posterior criteria we shall also compare the predictive performance of difierent priors a classic exam ple concerning the economics of crime will also be provided and contrasted with results in the literature the main flndings of the paper will lead us to propose a benchmark prior speciflcation in a linear regression context with model uncertainty

stochastic operators information and entropy for a stochastic operatoru on andl1 space i eu is linear positive and norm preserving on the positive cone ofl1 it is shown thatu decreases relative information between two nonnegativel1 functions furthermore it is shown that the following properties ofu are closely related u is energy decreasing energy preserving u ish decreasing whereh is boltzmann sh functional and the maxwell distributions are fixed points ofu

improving shape retrieval by spectral matching and meta similarity we propose two computational approaches for improving the retrieval of planar shapes first we suggest a geometrically motivated quadratic similarity measure that is optimized by way of spectral relaxation of a quadratic assignment by utilizing state of the art shape descriptors and a pairwise serialization constraint we derive a formulation that is resilient to boundary noise articulations and nonrigid deformations this allows both shape matching and retrieval we also introduce a shape meta similarity measure that agglomerates pairwise shape similarities and improves the retrieval accuracy when applied to the mpeg 7 shape dataset in conjunction with the proposed geometric matching scheme we obtained a retrieval rate of 92 5

maximum likelihood estimation of generalised linear models for multivariate normal covariance matrix the positive definiteness constraint is the most awkward stumbling block in modelling the covariance matrix pourahmadi s 1999 unconstrained parameterisation models covariance using covariates in a similar manner to mean modelling in generalised linear models the new covariance parameters have statistical interpretation as the regression coefficients and logarithms of prediction error variances corresponding to regressing a response on its predecessors in this paper the maximum likelihood estimators of the parameters of a generalised linear model for the covariance matrix their consistency and their asymptotic normality are studied when the observations are normally distributed these results along with the likelihood ratio test and penalised likelihood criteria such as bic for model and variable selection are illustrated using a real dataset

on the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds we prove convergence to equilibrium with explicit rates for various kinetic equations with relatively bad control of the distribution tails in particular boltzmann type equations with smoothed soft potentials we compensate the lack of uniform in time estimates by the use of precise logarithmic sobolev type inequalities and the assumption that the initial datum decays rapidly at large velocities our method not only gives explicit results on the times of convergence but is also able to cover situations in which compactness arguments apparently do not apply even mere convergence to equilibrium was an open problem for soft potentials

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

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

inference in semiparametric dynamic models for binary longitudinal data this article deals with the analysis of a hierarchical semiparametric model for dynamic binary longitudinal responses the main complicating components of the model are an unknown covariate function and serial correlation in the errors existing estimation methods for models with these features are of o n3 where n is the total number of observations in the sample therefore nonparametric estimation is largely infeasible when the sample size is large as in typical in the longitudinal setting here we propose a new o n markov chain monte carlo based algorithm for estimation of the nonparametric function when the errors are correlated thus contributing to the growing literature on semiparametric and nonparametric mixed effects models for binary data in addition we address the problem of model choice to enable the formal comparison of our semiparametric model with competing parametric and semiparametric specifications the performance of the methods is illustrated with detailed studies involving simul

spatially adaptive smoothing splines summary we use a reproducing kernel hilbert space representation to derive the smoothing spline solution when the smoothness penalty is a function a t of the design space t thereby allowing the model to adapt to various degrees of smoothness in the structure of the data we propose a convenient form for the smoothness penalty function and discuss computational algorithms for automatic curve fitting using a generalised crossvalidation measure of order m where m is typically taken to be two the smoothing spline solution uses a global smoothing parameter il which implies that the true underlying mean process has a constant degree of smoothness in this paper we suggest a more general spatially adaptive framework that accommodates varying degrees of roughness by seeking solutions where the smoothness penalty a t is now a function of the design t we derive the solution within a reproducing kernel hilbert space gu 2002 ch 2 wahba 1990 ch 1 when applying the method to data we propose a piecewise constant model for the smoothing function a t this provides a convenient computational framework with closed form solutions for the corresponding reproducing kernels of the hilbert space these kernels show similarities to regression splines in that the use of a piecewise constant i t induces breaks in the mth 2m l1 th derivatives at the changepoints in l t

bayesian nonparametric longitudinal data analysis abstractpractical bayesian nonparametric methods have been developed across a wide variety of contexts here we develop a novel statistical model that generalizes standard mixed models for longitudinal data that include flexible mean functions as well as combined compound symmetry cs and autoregressive ar covariance structures ar structure is often specified through the use of a gaussian process gp with covariance functions that allow longitudinal data to be more correlated if they are observed closer in time than if they are observed farther apart we allow for ar structure by considering a broader class of models that incorporates a dirichlet process mixture dpm over the covariance parameters of the gp we are able to take advantage of modern bayesian statistical methods in making full predictive inferences and about characteristics of longitudinal profiles and their differences across covariate combinations we also take advantage of the generality of our model which provides for estimation

noise and conditional entropy evolution abstract we study the convergence properties of the conditional kullback leibler entropy in stochastic systems we have proved general results showing that asymptotic stability is a necessary and sufficient condition for the monotone convergence of the conditional entropy to its maximal value of zero additionally we have made specific calculations of the rate of convergence of this entropy to zero in a one dimensional situation illustrated by ornstein uhlenbeck and rayleigh processes higher dimensional situations and a two dimensional ornstein uhlenbeck process with a stochastically perturbed harmonic oscillator and colored noise as examples we also apply our general results to the problem of conditional entropy convergence in the presence of dichotomous noise in both the one dimensional and multidimensional cases we show that the convergence of the conditional entropy to zero is monotone and at least exponential in the specific cases of the ornstein uhlenbeck and rayleigh processes as well as the stochastically perturbed harmonic oscillator and colored noise examples we obtain exact formulae for the temporal evolution of the conditional entropy starting from a concrete initial distribution the rather surprising result in this case is that the rate of convergence of the entropy to zero is independent of the noise amplitude

fluctuations and non equilibrium thermodynamics abstract a closed macroscopic system with fluctuating local properties is treated as a thermodynamic system with internal degrees of freedom gibb s entropy postulate is used to define the systems entropy as a functional of the probability density in internal coordinate space it is shown that application of the scheme of thermodynamics of irreversible processes then leads directly to the theory of fluctuations as markov processes described by a multivariate fokker planck equation in this perspective fluctuation theory may be said to have become integrated into non equilibrium thermodynamics

robust point matching for nonrigid shapes by preserving local neighborhood structures in previous work on point matching a set of points is often treated as an instance of a joint distribution to exploit global relationships in the point set for nonrigid shapes however the local relationship among neighboring points is stronger and more stable than the global one in this paper we introduce the notion of a neighborhood structure for the general point matching problem we formulate point matching as an optimization problem to preserve local neighborhood structures during matching our approach has a simple graph matching interpretation where each point is a node in the graph and two nodes are connected by an edge if they are neighbors the optimal match between two graphs is the one that maximizes the number of matched edges existing techniques are leveraged to search for an optimal solution with the shape context distance used to initialize the graph matching followed by relaxation labeling updates for refinement extensive experiments show the robustness of our approach under deformation noise in point locations outliers occlusion and rotation it outperforms the shape context and tps rpm algorithms on most scenarios

representation and detection of deformable shapes we describe some techniques that can be used to represent and detect deformable shapes in images the main difficulty with deformable template models is the very large or infinite number of possible nonrigid transformations of the templates this makes the problem of finding an optimal match of a deformable template to an image incredibly hard using a new representation for deformable shapes we show how to efficiently find a global optimal solution to the nonrigid matching problem the representation is based on the description of objects using triangulated polygons our matching algorithm can minimize a large class of energy functions making it applicable to a wide range of problems we present experimental results of detecting shapes in medical images and images of natural scenes we also consider the problem of learning a nonrigid shape model for a class of objects from examples we show how to learn good models while constraining them to be in the form required by the matching algorithm

a random coefficient approach to the estimation of residential end use load profiles abstract this paper develops some extensions to the statistical approach to the estimation of residential end use load curves and provides a substantive application of these developments to a sample of households importantly the typical assumption that the coefficients of the appliance dummies are fixed ignores two important sources of variation during any particular hour the intensity of use of a particular appliance will vary from household to household also the dummies indicate only absence or presence of the appliance and do not allow for variations in size or capacity our treatment of the coefficients of appliance dummies as random rather than fixed provides a structure for the heteroskedasticity that has been observed in previous studies of this kind also included in the analysis is the utilization of other sources of information in particular from direct metering and a sample of diaries the resultant single equation specifications for individual hours are then pooled and jointly estimated using an sur structure

nonparametric seemingly unrelated regression abstract a method is presented for simultaneously estimating a system of nonparametric regressions which may seem unrelated but where the errors are potentially correlated between equations we show that the advantage of estimating such a seemingly unrelated system of nonparametric regressions is that less observations can be required to obtain reliable function estimates than if each of the regression equations is estimated separately and the correlation ignored this increase in efficiency is investigated empirically using both simulated and real data the method uses a bayesian hierarchical framework where each regression function is represented as a linear combination of a large number of basis terms all the regression coefficients and the variance matrix of the errors are estimated simultaneously by their posterior means the computation is carried out using a markov chain monte carlo sampling scheme that employs a focused sampling step to combat the high dimensional representation of the unknown regression functions the methodology extends easily to other nonparametric multivariate regression models

dynamical density functional theory for interacting brownian particles stochastic or deterministic we aim to clarify confusions in the literature as to whether or not dynamical density functional theories for the one body density of a classical brownian fluid should contain a stochastic noise term we point out that a stochastic as well as a deterministic equation of motion for the density distribution can be justified depending on how the fluid one body density is defined i e whether it is an ensemble averaged density distribution or a spatially and or temporally coarse grained density distribution

a smooth nonparametric estimate of a mixing distribution using mixtures of gaussians abstract we propose a method of estimating mixing distributions using maximum likelihood over the class of arbitrary mixtures of gaussians subject to the constraint that the component variances be greater than or equal to some minimum value h this approach can lead to estimates of many shapes with smoothness controlled by parameter h we show that the resulting estimate will always be a finite mixture of gaussians each having variance h the nonparametric maximum likelihood estimate can be viewed as a special case with h 0 the method can be extended to estimate multivariate mixing distributions examples and the results of a simulation study are presented

automatic bayesian curve fitting summary a method of estimating a variety of curves by a sequence of piecewise polynomials is proposed motivated by a bayesian model and an appropriate summary of the resulting posterior distribution a joint distribution is set up over both the number and the position of the knots defining the piecewise polynomials throughout we use reversible jump markov chain monte carlo methods to compute the posteriors the methodology has been successful in giving good estimates for smooth functions i e continuous and differentiable as well as functions which are not differentiable and perhaps not even continuous at a finite number of points the methodology is extended to deal with generalized additive models

cholesky decomposition of a hyper inverse wishart matrix the canonical parameter of a covariance selection model is the inverse covariance matrix 1 whose zero pattern gives the conditional independence structure characterising the model in this paper we consider the upper triangular matrix obtained by the cholesky decomposition 1 t this provides an interesting alternative parameterisation of decomposable models since its upper triangle has the same zero structure as 1 and its elements have an interpretation as parameters of certain conditional distributions for a distribution for the strong hyper markov property is shown to be characterised by the mutual independence of the rows of this is further used to generalise to the hyper inverse wishart distribution some well known properties of the inverse wishart distribution in particular we show that a hyper inverse wishart matrix can be decomposed into independent normal and chi squared random variables and we describe a family of transformations under which the family of hyper inverse wishart distributions is closed

variable selection via gibbs sampling abstract a crucial problem in building a multiple regression model is the selection of predictors to include the main thrust of this article is to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets this procedure entails embedding the regression setup in a hierarchical normal mixture model where latent variables are used to identify subset choices in this framework the promising subsets of predictors can be identified as those with higher posterior probability the computational burden is then alleviated by using the gibbs sampler to indirectly sample from this multinomial posterior distribution on the set of possible subset choices those subsets with higher probability the promising ones can then be identified by their more frequent appearance in the gibbs sample

microscopic derivation of time dependent density functional methods time dependent density functional methods tddfm are studied from the microscopic viewpoint using projection operator methods in classical liquids a density field is defined without averaging so that a time evolution equation of the density field is derived with a random force the derived equation includes a free energy functional which is different from that defined in the tddfm the projection operator method provides the exact expression of the free energy functional another definition of the density field by an average leads to the equation of the tddfm in addition an equation describing fluctuations is also derived

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

bayesian radial basis functions of variable dimension a bayesian framework for the analysis of radial basis functions rbf is proposed that accommodates uncertainty in the dimension of the model a distribution is defined over the space of all rbf models of a given basis function and posterior densities are computed using reversible jump markov chain monte carlo samplers green 1995 this alleviates the need to select the architecture during the modeling process the resulting networks are shown to adjust their size to the complexity of the data

nonparametric bayesian testing for monotonicity this paper adopts a nonparametric bayesian approach to testing whether a function is monotone two new families of tests are constructed the first uses constrained smoothing splines with a hierarchical stochastic process prior that explicitly controls the prior probability of monotonicity the second uses regression splines together with two proposals for the prior over the regression coefficients via simulation the finite sample performance of the tests is shown to improve upon existing frequentist and bayesian methods the asymptotic properties of the bayes factor for comparing monotone versus nonmonotone regression functions in a gaussian model are also studied our results significantly extend those currently available which chiefly focus on determining the dimension of a parametric linear model

temporal behavior of the conditional and gibbs entropies we study the temporal approach to equilibrium of the gibbs and conditional entropies for stochastic systems in the presence of white noise the conditional entropy will either remain constant or monotonically increase to its maximum of zero however the gibbs entropy may have a variety of patterns of approach to its final value ranging from a monotone increase or decrease to an oscillatory approach we have illustrated all of these behaviors using examples in which both entropy dynamics can be determined analytically

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