bayesian analysis of mixture models with an unknown number of components an alternative to reversible jump methods richardson and green present a method of performing a bayesian analysis of data from a finite mixture distribution with an unknown number of components their method is a markov chain monte carlo mcmc approach which makes use of the reversible jump methodology described by green we describe an alternative mcmc method which views the parameters of the model as a marked point process extending methods suggested by ripley to create a markov birth death process with an appropriate stationary distribution our method is easy to implement even in the case of data in more than one dimension and we illustrate it on both univariate and bivariate data there appears to be considerable potential for applying these ideas to other contexts as an alternative to more general reversible jump methods and we conclude with a brief discussion of how this might be achieved

improvement on the 10 node tetrahedral element for three dimensional problems by decomposing the strain part of the conforming 10 node tetrahedral element t10 and relaxing the compatibility condition for the constant strain term the performance of the element can be improved by introducing the incompressible condition in the high order strain term the element can be made very efficient for the analysis of the nearly incompressible problem numerical results show that the modified element in general has better accuracy and reliability compared to the classical displacement based tetrahedral element t10 for a wide range of structural problems including the analysis of thin and slender structures

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

a robust refined quadrilateral plane element based on a rational choice of the internal incompatible displacement function and a special formulation of the a priori elimination of the internal non conforming displacement parameters a new refined quadrilateral plane element rq4 has been developed the present element can be shown to be computationally efficient accurate and free from locking and is better than other elements such as the plan s element hs the generalized hybrid element qcs6 and the refined hybrid element rgh4 etc several numerical examples are given to show the superior performances of the present element rq4

relative entropy and identification of gibbs measures in dynamical systems in this work we explore the idea of using the relative entropy of ergodic measures for the identification of gibbs measures in dynamical systems the question we face is how to estimate the thermodynamic potential together with a grammar from a sample produced by the corresponding gibbs state

large deviations for the empirical field of a gibbs measure on applique le principe de contraction pour obtenir un principe de grande deviation pour la distribution des distributions empiriques on donne une description detaillee de la fonction de taux resultante

estimation of allocation rates in a cluster analysis context abstract a sample of multivariate observations is assumed to be drawn from a mixture of a given number of underlying populations the mixture likelihood approach to clustering is used to allocate each individual in the sample to its population of origin on the basis of the estimated posterior probabilities of population membership estimation of the correct allocation rate is considered for individual populations as well as for the overall mixture by averaging functions of the maximum of these posterior probabilities the estimates of the correct allocation rates provide a means of assessing the performance of the mixture approach to clustering the bootstrap technique is investigated for its effectiveness in reducing the bias of the estimates so obtained results are reported for three real data sets and a simulation study it is demonstrated that the proposed estimates generally provide useful information on the unobservable allocation rates of the mixture approach encouraging results are obtained for

a fe meshfree quad4 element based on partition of unity a new 4 node quadrilateral element is developed by combining the shape functions of finite element and meshfree methods the objective is to synergise the attractive features of finite element and meshfree shape functions using the concepts of partition of unity pu methods the shape functions of the well known quad4 element are used for pu and the least square point interpolation for local approximation this enables the proposed element inherit the compatibility properties of finite element method and the quadratic polynomial completeness properties of meshfree methods numerical results for the bench mark problems show that the proposed element has a good tolerance to distorted meshes the element also seems to be free from the linear dependence problem which is known to plague some of the pu based elements

extrapolated fields in the formulation of the assumed strain elements part ii three dimensional problems abstract a new assumed strain quadrilateral element with accurate in plane bending behavior is presented the basic idea consists in introduction of a parallelogram domain associated with the given quadrilateral element development of the related assumed strain field for the parallelogram and subsequent extrapolation of this field to the domain of the original quadrilateral the assumed strain field for the parallelogram is constructed by identification of various modes of its deformation and then by proper modification of the strain field in some of these modes in particular the strain operator with respect to the so called in plane bending modes is modified so as to simulate the strain field resulting from the assumptions usually made in structural mechanics the modification of the strain fields leads to the assumed strain operator the proposed new assumed strain quadrilateral element exhibits remarkably accurate performance for both membrane and bending dominated problems even when severely distorted and high aspect ratio meshes are considered and when materials are nearly incompressible

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 metric entropy of diffeomorphisms part i characterization of measures satisfying pesin s entropy formula soit m une variete de riemann compacte soit f m m un diffeomorphisme et soit m une mesure de probabilite de borel f invariante sur m on identifie les mesures pour lesquelles l inegalite de margulis et ruelle qui relie l entropie aux exposants de lyapunov atteint l egalite on demontre une formule valable pour toutes les mesures invariantes

geometrically nonlinear dynamic formulation for three dimensional co rotational solid elements abstract this study presents a three dimensional nonlinear dynamic formulation based on a co rotational cr approach for solid elements the cr formulation is relatively efficient but it is based on the assumption of small strains during large displacement the novel idea of the present formulation involves the use of the cr formulation through a three dimensional solid element for inertial quantities in addition to an internal force vector and a stiffness matrix the present dynamic formulation is derived from lagrange s equation of motion in this procedure the cr formulation i e element independent cr is one of the most attractive features that is strongly manifested in an efficient manner consequently this obtains the governing equation of motion including motion driven inertial components physical quantities induced by the prescribed motion four examples are presented to demonstrate the accuracy of the present dynamic formulation finally the results are compared with those obtained by abaqus and the findings reveal that the proposed dynamic formulation is in good agreement with existing predictions

variational principles for non conforming finite element methods variational principles with relaxed inter element continuity requirement for non conforming element methods in linear and non linear analyses are developed based on the principles any non conforming element displacement can be used directly to derive the explicit expressions of non conforming displacement function which can ensure the passage of the patch test c for the requirement of convergence copyright 2001 john wiley sons ltd

development and testing of stable invariant isoparametric curvilinear 2 and 3 d hybrid stress elements abstract linear and quadratic serendipity hybrid stress elements are examined in respect of stability coordinate invariance and optimality a formulation based upon symmetry group theory successfully addresses these issues in undistorted geometries and is fully detailed for plane elements the resulting least order stable invariant stress polynomials can be applied as astute approximations in distorted cases through a variety of tensor components and variational principles a distortion sensitivity study for two and three dimensional elements provides favourable numerical comparisons with the assumed displacement method

an 8 node brick finite element an 8 node brick element based on the assumed stress hybrid formulation is described with three additional stress fields the element stiffness matrix now has the required rank of 18 and the bending response is exact with rectangular elements surprisingly the 2 2 2 gauss rule suffices for all numerical integrations to satisfy the constant stress patch test

three dimensional hybrid trefftz stress elements the stress model of the hybrid trefftz finite element formulation is applied to the linear elastostatic analysis of solids the stresses are approximated in the domain of the element and displacements on its boundary complete linearly independent hierarchical polynomial approximation functions are used in both domain and boundary approximations the displacement basis is defined independently on each inter element surface continuity at the edges and on the corners of the elements is not enforced a priori the stress basis is constrained to solve locally the beltrami governing differential equation it is derived from the associated papkovitch neuber elastic displacement solution generalized variables are used to ensure that the approximations are independent of the geometric description of the elements the solving system is derived directly from the fundamental relations of elastostatics the solving system is symmetric when the same property applies to the local elasticity condition sparse described by boundary integral arrays and well suited to p refinement and parallel processing the numerical implementation of these equations is discussed and numerical tests are presented to illustrate the performance of the finite element formulation copyright 2000 john wiley sons ltd

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

entropy production fluctuations of finite markov chains for almost every trajectory segment over a finite time span of a finite markov chain with any given initial distribution the logarithm of the ratio of its probability to that of its time reversal converges exponentially to the entropy production rate of the markov chain the large deviation rate function has a symmetry of gallavotti cohen type which is called the fluctuation theorem moreover similar symmetries also hold for the rate functions of the joint distributions of general observables and the logarithmic probability ratio

a simple discrete model of brownian motors time periodic markov chains in this paper we consider periodically inhomogeneous markov chains which can be regarded as a simple version of physical model brownian motors we introduce for them the concepts of periodical reversibility detailed balance entropy production rate and circulation distribution we prove the equivalence of the following statements the time periodic markov chain is periodically reversible it is in detailed balance kolmogorov s cycle condition is satisfied its entropy production rate vanishes every circuit and its reversed circuit have the same circulation weight hence in our model of markov chains the directed transport phenomenon of brownian motors i e the existence of net circulation can occur only in nonequilibrium and irreversible systems moreover we verify the large deviation property and the gallavotti cohen fluctuation theorem of sample entropy production rates of the markov chain

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

three dimensional 8 node and 20 node refined hybrid isoparametric elements in this paper a new hybrid variational principle with independent variables of strain stress and displacement and with a weaker constraint condition of interelement continuity is proposed based on this functional a general formulation of a refined hybrid isoparametric element method has been established by the orthogonal approach the present formulation is a rational approach to be adopted for deriving high performance three dimensional hybrid isoparametric elements even up to the higher order 20 node element several numerical examples are presented to show that the present elements rgh8 8 node and rgh20 20 node have high accuracy excellent computational efficiency and less sensitivity to mesh distortion

deviations of trajectory averages and the defect in pesin s formula for anosov diffeomorphisms a large deviation theorem at the donsker varadhan level three is obtained for the convergence of trajectory averages of anosov diffeomorphisms it is possible to provide an explicit description of the rate function

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

chaotic hypothesis onsager reciprocity and fluctuation dissipation theorem it is shown that the chaoticity hypothesis recently introduced in statistical mechanics which is analogous to ruelle s principle for turbulence implies the onsager reciprocity and the fluctuation dissipation theorem in various reversible models for coexisting transport phenomena

entropy production and information gain in axiom a systems anosov systems are mathematical models for chaotic systems in statistical mechanics and fluid dynamics most of these systems enjoy the property of positive entropy production we introduce the concept of specific information gain or specific relative entropy h in anosov systems and prove that it is identical to the entropy production rate e p defined by ruelle and gallavotti in anosov systems from this point of view the entropy production rate e p characterizes the degree of macroscopic irreversibility of the system

estimation of finite mixture distributions through bayesian sampling summary a formal bayesian analysis of a mixture model usually leads to intractable calculations since the posterior distribution takes into account all the partitions of the sample we present approximation methods which evaluate the posterior distribution and bayes estimators by gibbs sampling relying on the missing data structure of the mixture model the data augmentation method is shown to converge geometrically since a duality principle transfers properties from the discrete missing data chain to the parameters the fully conditional gibbs alternative is shown to be ergodic and geometric convergence is established in the normal case we also consider non informative approximations associated with improper priors assuming that the sample corresponds exactly to a k component mixture

relations between incompatible displacement model and hybrid stress model an examination of the variational formulations confirms the similarity between the incompatible displacement model and the assumed stress hybrid model that was pointed out by irons in 1972 but the basic differences between the two are also identified for 8 node solid elements the assumed stress terms obtained through a rational procedure also agree with those deduced by irons purely from his physical insight

on fast supervised learning for normal mixture models with missing information it is an important research issue to deal with mixture models when missing values occur in the data in this paper computational strategies using auxiliary indicator matrices are introduced for efficiently handling mixtures of multivariate normal distributions when the data are missing at random and have an arbitrary missing data pattern meaning that missing data can occur anywhere we develop a novel em algorithm that can dramatically save computation time and be exploited in many applications such as density estimation supervised clustering and prediction of missing values in the aspect of multiple imputations for missing data we also offer a data augmentation scheme using the gibbs sampler our proposed methodologies are illustrated through some real data sets with varying proportions of missing values