the em algorithm an old folk song sung to a fast new tune celebrating the 20th anniversary of the presentation of the paper by dempster laird and rubin which popularized the em algorithm we investigate after a brief historical account strategies that aim to make the em algorithm converge faster while maintaining its simplicity and stability e g automatic monotone convergence in likelihood first we introduce the idea of a working parameter to facilitate the search for efficient data augmentation schemes and thus fast em implementations second summarizing various recent extensions of the em algorithm we formulate a general alternating expectation conditional maximization algorithm aecm that couples flexible data augmentation schemes with model reduction schemes to achieve efficient computations we illustrate these methods using multivariate t models with known or unknown degrees of freedom and poisson models for image reconstruction we show through both empirical and theoretical evidence the potential for a dramatic reduction in computational time with little increase in human effort we also discuss the intrinsic connection between em type algorithms and the gibbs sampler and the possibility of using the techniques presented here to speed up the latter the main conclusion of the paper is that with the help of statistical considerations it is possible to construct algorithms that are simple stable and fast

an isogeometric method for the reissner mindlin plate bending problem we present a new isogeometric method for the discretization of the reissner mindlin plate bending problem the proposed scheme follows a recent theoretical framework that makes possible the construction of a space of smooth discrete deflections wh and a space of smooth discrete rotations h such that the kirchhoff constraint is exactly satisfied at the limit therefore we obtain a formulation which is natural from the theoretical mechanical viewpoint and locking free by construction we prove that the method is uniformly stable and satisfies optimal convergence estimates finally the theoretical results are fully supported by numerical tests

isogeometric structural shape optimization an old dilemma in structural shape optimization is the needed tight link between design model or geometric description and analysis model the intention of this paper is to show that isogeometric analysis offers a potential and promising way out of this dilemma to this end we show a structural shape optimization framework based on the isogeometric analysis approach with the discretization based on non uniform rational b splines nurbs the analysis model represents the structural geometry exactly furthermore nurbs enable efficient geometry control together with smooth boundaries they are the de facto standard in cad systems but are also widely used in a shape optimal design context to define the geometry representation and the design variables with the presented isogeometric approach to shape optimization the analysis model is inherently merged with the design model omitting the typically involved interplay between both we derive analytical sensitivities for nurbs discretizations which allow application of efficient gradient based optimization algorithms the present contribution is restricted to two dimensional problems of linear elasticity but the extension to three dimensions and other problem classes is straightforward some representative examples demonstrate and validate the methodology further the potential of boundary continuity control within isogeometric structural shape optimization is explored to trigger smooth or less smooth angular designs

isogeometric analysis using t splines we explore t splines a generalization of nurbs enabling local refinement as a basis for isogeometric analysis we review t splines as a surface design methodology and then develop it for engineering analysis applications we test t splines on some elementary two dimensional and three dimensional fluid and structural analysis problems and attain good results in all cases we summarize the current status of t splines their limitations and future possibilities

parameter expansion to accelerate em the px em algorithm summary the em algorithm and its extensions are popular tools for modal estimation but ar e often criticised for their slow convergence we propose a new method that can often make em much faster the intuitive idea is to use a covariance adjustment to correct the analysis of the m step capitalising on extra information captured in the imputed complete data the way we accomplish this is by parameter expansion we expand the complete data model while preserving the observed data model and use the expanded complete data model to generate em this parameter expanded ei m px em algorithm shares the simplicity and stability of ordinary em but has a faster rate of convergence since its m step performs a more efficient analysis the px em algorithm is illustrated for the multivariate t distribution a random effects model factor analysis probit regression and a poisson imaging model

isogeometric boundary element analysis using unstructured t splines we couple collocated isogeometric boundary element methods and unstructured analysis suitable t spline surfaces for linear elastostatic problems we extend the definition of analysis suitable t splines to encompass unstructured control grids unstructured meshes and develop basis functions which are smooth rational polynomials defined in terms of the bezier extraction framework and which pass standard patch tests we then develop a collocation procedure which correctly accounts for sharp edges and corners extraordinary points and t junctions this approach is applied to several three dimensional problems including a real world t spline model of a propeller we believe this work clearly illustrates the power of combining new analysis suitable computer aided design technologies with established analysis methodologies in this case the boundary element method

geometry independent field approximation cad analysis integration geometrical exactness and adaptivity in isogeometric analysis iga the same spline representation is employed for both the geometry of the domain and approximation of the unknown fields over this domain this identity of the geometry and field approximation spaces was put forward in the now classic 2005 paper 20 as a key advantage on the way to the integration of computer aided design cad and subsequent analysis in computer aided engineering cae 20 claims indeed that any change to the geometry of the domain is automatically inherited by the approximation of the field variables without requiring the regeneration of the mesh at each change of the domain geometry yet in finite element versions of iga a parameterization of the interior of the domain must still be constructed since cad only provides information about the boundary the identity of the boundary and field representation decreases the flexibility in which this parameterization can be generated and somewhat constrains the modeling and simulation process because an approximation able to represent the domain geometry accurately need not be adequate to also approximate the field variables accurately in particular when the solution is not smooth we propose here a new paradigm called geometry independent field approximation gift where the spline spaces used for the geometry and the field variables can be chosen and adapted independently while preserving geometric exactness and tight cad integration gift has the following features 1 it is possible to flexibly

subdivision surfaces a new paradigm for thin shell finite element analysis we develop a new paradigm for thin shell finite element analysis based on the use of subdivision surfaces for i describing the geometry of the shell in its undeformed configuration and ii generating smooth interpolated displacement fields possessing bounded energy within the strict framework of the kirchhoff love theory of thin shells the particular subdivision strategy adopted here is loop s scheme with extensions such as required to account for creases and displacement boundary conditions the displacement fields obtained by subdivision are h2 and consequently have a finite kirchhoff love energy the resulting finite elements contain three nodes and element integrals are computed by a one point quadrature the displacement field of the shell is interpolated from nodal displacements only in particular no nodal rotations are used in the interpolation the interpolation scheme induced by subdivision is non local i e the displacement field over one element depend on the nodal displacements of the element nodes and all nodes of immediately neighbouring elements however the use of subdivision surfaces ensures that all the local displacement fields thus constructed combine conformingly to define one single limit surface numerical tests including the belytschko et al 10 obstacle course of benchmark problems demonstrate the high accuracy and optimal convergence of the method

rotation free isogeometric thin shell analysis using pht splines this paper presents a novel approach for isogeometric analysis of thin shells using polynomial splines over hierarchical t meshes pht splines the method exploits the flexibility of t meshes for local refinement the main advantage of the pht splines in the context of thin shell theory is that it achieves c1 continuity so the kirchhoff love theory can be used in pristine form no rotational degrees of freedom are needed numerical results show the excellent performance of the present method

random effects diagonal metric multidimensional scaling models by assuming a distribution for the subject weights in a diagonal metric indscal multidimensional scaling model the subject weights become random effects including random effects in multidimensional scaling models offers several advantages over traditional diagonal metric models such as those fitted by the indscal alscal and other multidimensional scaling programs unlike traditional models the number of parameters does not increase with the number of subjects and because the distribution of the subject weights is modeled the construction of linear models of the subject weights and the testing of those models is immediate here we define a random effects diagonal metric multidimensional scaling model give computational algorithms describe our experiences with these algorithms and provide an example illustrating the use of the model and algorithms

shape preserving additions of fuzzy intervals abstract triangular norm based additions preserving the lr shape of lr fuzzy intervals are studied the connection between t norm based additions preserving the linearity of fuzzy intervals and additions preserving lr shape for invertible shapes l and r is given a possibility of controlling the growth of the spread during the calculations with lr fuzzy intervals is shown

an answer to an open problem on triangular norms in this paper we shall give an example to show that an open problem of fodor on triangular norm which is collected by klement et al in problems on triangular norms and related operators fuzzy sets and systems 145 2004 471 479 has a negative solution

an isogeometric analysis approach for the study of the gyrokinetic quasi neutrality equation in this work a new discretization scheme for the gyrokinetic quasi neutrality equation is proposed it is based on isogeometric analysis the iga which relies on nurbs functions accommodates arbitrary coordinates and the use of complicated computation domains moreover arbitrary high order degree of basis functions can be used and their regularity enables the use of a low number of elements here this approach is successfully tested on elliptic problems like the quasi neutrality equation arising in gyrokinetic models in this last application when polar coordinates are considered a fast solver can be used and the non locality is dealt with a suitable decomposition which reduces the resolution of the gyrokinetic quasi neutrality equation to a sequence of local 2d elliptic problems

finite mixture distributions sequential likelihood and the em algorithm a popular way to account for unobserved heterogeneity is to assume that the data are drawn from a finite mixture distribution a barrier to using finite mixture models is that parameters that could previously be estimated in stages must now be estimated jointly using mixture distributions destroys any additive separability of the log likelihood function we show however that an extension of the em algorithm reintroduces additive separability thus allowing one to estimate parameters sequentially during each maximization step in establishing this result we develop a broad class of estimators for mixture models returning to the likelihood problem we show that relative to full information maximum likelihood our sequential estimator can generate large computational savings with little loss of efficiency

on the correct convergence of the em algorithm for gaussian mixtures it is well known that the em algorithm generally converges to a local maximum likelihood estimate however there have been many evidences to show that the em algorithm can converge correctly to the true parameters as long as the overlap of gaussians in the sample data is small enough this paper studies this correct convergence problem asymptotically on the em algorithm for gaussian mixtures it has been proved that the em algorithm becomes a contraction mapping of the parameters within a neighborhood of the consistent solution of the maximum likelihood when the measure of average overlap among gaussians in the original mixture is small enough and the number of samples is large enough that is if the initial parameters are set within the neighborhood the em algorithm will always converge to the consistent solution i e the expected result moreover the simulation results further demonstrate that this correct convergence neighborhood becomes larger as the average overlap becomes smaller

diagonals of continuous triangular norms diagonals of continuous t norms are studied the characterization of all functions being diagonals of continuous t norms is given to a given diagonal the class of all continuous t norms with this diagonal is characterized

lipschitz continuity of triangular subnorms this paper deals with the lipschitz property of triangular subnorms unlike the case of triangular norms for these operations the problem is still open and presents an interesting variety of situations we provide some characterization results by weakening the notion of convexity introducing two generalized versions of convexity for real functions called a lower convexity and sub convexity the a lower convex and sub convex real mappings present characteristics quite different from the usual convex real mappings we will discuss the link between such kind of functions and the generators and their pseudo inverse of continuous archimedean triangular subnorms

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

nonorthogonal analysis of variance using a generalized conjugate gradient algorithm abstract a method is developed that computes an exact nonorthogonal analysis of variance using cell means the method is iterative and does not require that the non orthogonal design matrix be stored or formed at each stage in the process a balanced analysis of variance problem must be solved a monotonicity property for the estimates of the regression sum of squares is derived that could be used to minimize iteration in hypothesis testing an application of the algorithm to the solution of analysis of covariance problems is also given

factor analysis by instrumental variables methods three alternative estimation procedures for factor analysis based on the instrumental variables method are presented these procedures are justified by the method of least squares formulas for asymptotic standard errors of factor loadings are derived the procedures are empirically compared to the method of maximum likelihood the conclusion based on the data used in this study is that two of the procedures seem to work well

t sum of l r fuzzy numbers abstract the sum of l r fuzzy numbers based on a given archimedian continuous t norm t is studied a series of improving sufficient conditions of several authors ensuring an analytical form of the output sum is completed by a sufficient and necessary condition i e the best sufficient condition some applications are indicated

an em algorithm for nonlinear random effects models the pharmaceutical industry is currently interested in the population approach and population models also known as mixed effects models and random effects models depending on the precise form population models are useful in that they can account for both withinand between individual sources of variability and serial correlation within individual observations when analyzing unbalanced repeated measures data the modelling of population pharmacodynamic or pharmacokinetic profiles typically involves nonlinear random effects models each individual s observations are modelled by identical up to unknown parameter values nonlinear regression models with the distribution of the observations or a transformation of the observations about expected responses taken to be normal with the degree of variability described by a variance model between individual variability is modelled by a population distribution for the individual regression parameter values random effects in a parametric analysis the population distribution is taken to be normal the parameters of which along with the parameters of the variance model are known as the population parameters maximum likelihood estimation of the population parameters for nonlinear random effects models was pioneered by beal and sheiner 1979 and since then a number of algorithms have appeared for approximate maximum likelihood including steimer et al 1984 lindstrom and bates 1990 beal and sheiner 1992 and mentre and gomeni 1995 all of these algorithms are approximate in some way for a summary see beal and sheiner 1992 wolfinger 1993 pinheiro and bates 1994 and davidian and giltinan 1995 in this paper an em algorithm for exact maximum likelihood estimation is introduced an em algorithm obtaining maximum likelihood estimates for linear random effects models was introduced by dempster laird and rubin 1977 laird and ware 1982 lindstrom and bates 1988 jennrich and schluchter 1986 and liu and rubin 1994 all describe hybrid em algorithms for the linear random effects model a true em algorithm for the linear model is described by jamshidian and jennrich 1993 mentre and gomeni 1995 describe an approximate em algorithm for nonlinear random effects models and from the algorithm given in this paper it can be seen clearly how their approximations arise the present algorithm uses monte carlo methods to perform the e step a strategy previously adopted in an altogether different model by guo and thompson 1994 guo and thompson require a gibbs sampler that is a markov chain monte carlo method for their e step but the present algorithm uses independent samples in section 2 of this paper the nonlinear random effects model is described section 3 gives the em algorithm without random effect covariates while section 4 gives the modified algorithm in the

standard errors for em estimation log likelihood the well known sem algorithm uses the second approach we consider three additional algorithms one that uses the first approach and two that use the second we evaluate the complexity and precision of these three and the sem algorithm in seven examples the first is a single parameter example used to give insight the others are three examples in each of two areas of em application poisson mixture models and the estimation of covariance from incomplete data the examples show that there are algorithms that are much simpler and more accurate than the sem algorithm hopefully their simplicity will increase the availability of standard error estimates in em applications it is shown that as previously conjectured a symmetry diagnostic can accurately estimate errors arising from numerical differentiation some issues related to the speed of the em algorithm and algorithms that differentiate the em operator are identified

state space models from the em algorithm to a gradient approach slow convergence is observed in the em algorithm for linear state space models we propose to circumvent the problem by applying any off the shelf quasi newton type optimizer which operates on the gradient of the log likelihood function such an algorithm is a practical alternative due to the fact that the exact gradient of the log likelihood function can be computed by recycling components of the expectation maximization em algorithm we demonstrate the efficiency of the proposed method in three relevant instances of the linear state space model in high signal to noise ratios where em is particularly prone to converge slowly we show that gradient based learning results in a sizable reduction of computation time

combining standardized mean differences using the method of maximum likelihood a maximum likelihood procedure for combining standardized mean differences based on a noncentratt distribution is proposed with a proper data augmentation technique an em algorithm is developed information and likelihood ratio statistics are discussed in detail for reliable inference simulation results favor the proposed procedure over both the existing normal theory maximum likelihood procedure and the commonly used generalized least squares procedure

solution of an open problem for associative copulas an open problem on triangular norms recently posed by klement et al fuzzy sets and systems 145 2004 471 is discussed in the class of associative copulas

isogeometric analysis using lr b splines abstract the recently proposed locally refined b splines denoted lr b splines by dokken et al 2013 6 may have the potential to be a framework for isogeometric analysis to enable future interoperable computer aided design and finite element analysis in this paper we propose local refinement strategies for adaptive isogeometric analysis using lr b splines and investigate its performance by doing numerical tests on well known benchmark cases the theory behind lr b spline is not presented in full details but the main conceptual ingredients are explained and illustrated by a number of examples

schur concave triangular norms characterization and application in pfcsp the concept of priority is often used in real time systems schur concave t norms are used to capture this concept within prioritized fuzzy constraint satisfaction problems pfcsps we are dealing with a very strict notion of priority which favors the constraint with the larger priority regardless of its value also some results on the characterization of schur concave t norms are given

kullback proximal algorithms for maximum likelihood estimation accelerated algorithms for maximum likelihood image reconstruction are essential for emerging applications such as three dimensional 3 d tomography dynamic tomographic imaging and other high dimensional inverse problems in this paper we introduce and analyze a class of fast and stable sequential optimization methods for computing maximum likelihood estimates and study its convergence properties these methods are based on a proximal point algorithm implemented with the kullback liebler kl divergence between posterior densities of the complete data as a proximal penalty function when the proximal relaxation parameter is set to unity one obtains the classical expectation maximization em algorithm for a decreasing sequence of relaxation parameters relaxed versions of em are obtained which can have much faster asymptotic convergence without sacrifice of monotonicity we present an implementation of the algorithm using more s 1983 trust region update strategy for illustration the method is applied to a nonquadratic inverse problem with poisson distributed data

the dynamic expectation conditional maximization either algorithm summary the expectation conditional maximization either ecme algorithm has proven to be an effective way of accelerating the expectation maximization algorithm for many problems recognizing the limitation of using prefixed acceleration subspaces in the ecme algorithm we propose a dynamic ecme decme algorithm which allows the acceleration subspaces to be chosen dynamically the simplest decme implementation is what we call decme 1 which uses the line that is determined by the two most recent estimates as the acceleration subspace the investigation of decme 1 leads to an efficient simple stable and widely applicable decme implementation which uses two dimensional acceleration subspaces and is referred to as decme 2 the fast convergence of decme 2 is established by the theoretical result that in a small neighbourhood of the maximum likelihood estimate it is equivalent to a conjugate direction method the remarkable accelerating effect of decme 2 and its variant is also demonstrated with several numerical examples

a computational approach to handle complex microstructure geometries in multiscale analysis of components there is usually a need to solve microstructures with complex geometries in this paper we use the extended finite element method x fem to solve scales involving complex geometries the x fem allows one to use meshes not necessarily matching the physical surface of the problem while retaining the accuracy of the classical finite element approach for material interfaces this is achieved by introducing a new enrichment strategy although the mesh does not need to conform to the physical surfaces it needs to be fine enough to capture the geometry of these surfaces a simple algorithm is described to adaptively refine the mesh to meet this geometrical requirement numerical experiments on the periodic homogenization of two phase complex cells demonstrate the accuracy and simplicity of the x fem c 2003 elsevier b v all rights reserved

maximum likelihood computations with repeated measures application of the em algorithm abstract the purpose of this article is to consider the use of the em algorithm dempster laird and rubin 1977 for both maximum likelihood ml and restricted maximum likelihood reml estimation in a general repeated measures setting using a multivariate normal data model with linear mean and covariance structure anderson 1973 several models and methods of analysis have been proposed in recent years for repeated measures data ware 1985 presented an overview because the em algorithm is a general purpose iterative method for computing ml estimates with incomplete data it has often been used in this particular setting dempster et al 1977 andrade and helms 1984 jennrich and schluchter 1985 there are two apparently different approaches to using the em algorithm in this setting in one application each experimental unit is observed under a standard protocol specifying measurements at each of n occasions or under n conditions and incompleteness implies that the number of measurements actua

problems on triangular norms and related operators abstract a number of open problems on triangular norms and related operators was posed during the 24th linz seminar on fuzzy set theory triangular norms and related operators in many valued logics held in february 2003 they are collected here together with some other open problems in this context and with some problems which were posed earlier and have been solved in the meantime

reproducing kernel triangular b spline based fem for solving pdes abstract we propose a reproducing kernel triangular b spline based finite element method fem as an improvement to the conventional triangular b spline element for solving partial differential equations pdes in the latter unexpected errors can occur throughout the analysis domain mainly due to the excessive flexibilities in defining the b spline the performance therefore becomes unstable and cannot be controlled in a desirable way to address this issue the proposed improvement adopts the reproducing kernel approximation in the calculation of b spline kernel function three types of pde problems are tested to validate the present element and compare against the conventional triangular b spline it has been shown that the improved triangular b spline satisfies the partition of unity condition even for extreme conditions including corners and holes

constrained maximum likelihood estimation of two level covariance structure model via em type algorithms in this paper the constrained maximum likelihood estimation of a two level covariance structure model with unbalanced designs is considered the two level model is reformulated as a single level model by treating the group level latent random vectors as hypothetical missing data then the popular em algorithm is extended to obtain the constrained maximum likelihood estimates for general nonlinear constraints the multiplier method is used at them step to find the constrained minimum of the conditional expectation an accelerated em gradient procedure is derived to handle linear constraints the empirical performance of the proposed em type algorithms is illustrated by some artifical and real examples

the ecme algorithm a simple extension of em and ecm with faster monotone convergence a generalisation of the ecm algorithm meng rubin 1993 which is itselfan extension of the em algorithm dempster laird rubin 1977 can be obtained by replacing some cm steps of ecm which maximise the constrained expected complete data loglikelihood function with steps that maximise the correspondingly constrained actual likelihood function this algorithm which we call ecme algorithm for expectation conditional maximisation either shares with both em and ecm their stable monotone convergence and basic simplicity of implementation relative to competing faster converging methods moreover ecme can have a substantially faster convergence rate than either em or ecm measured using either the number of iterations or actual computer time

isogeometric analysis of the cahn hilliard phase field model abstract the cahn hilliard equation involves fourth order spatial derivatives finite element solutions are not common because primal variational formulations of fourth order operators are only well defined and integrable if the finite element basis functions are piecewise smooth and globally c 1 continuous there are a very limited number of two dimensional finite elements possessing c 1 continuity applicable to complex geometries but none in three dimensions we propose isogeometric analysis as a technology that possesses a unique combination of attributes for complex problems involving higher order differential operators namely higher order accuracy robustness two and three dimensional geometric flexibility compact support and most importantly the possibility of c 1 and higher order continuity a nurbs based variational formulation for the cahn hilliard equation was tested on two and three dimensional problems we present steady state solutions in two dimensions and for the first time in three dimensions to achieve these results an adaptive time stepping method is introduced we also present a technique for desensitizing calculations to dependence on mesh refinement this enables the calculation of topologically correct solutions on coarse meshes opening the way to practical engineering applications of phase field methodology

unbalanced repeated measures models with structured covariance matrices the question of how to analyze unbalanced or incomplete repeated measures data is a common problem facing analysts we address this problem through maximum likelihood analysis using a general linear model for expected responses and arbitrary structural models for the within subject covariances models that can be fit include standard univariate and multivariate models with incomplete data random effects models and models with time series and factor analytic error structures we describe newton raphson and fisher scoring algorithms for computing maximum likelihood estimates and generalized em algorithms for computing restricted and unrestricted maximum likelihood estimates an example fitting several models to a set of growth data is included

maximum likelihood estimation of nonlinear structural equation models the existing maximum likelihood theory and its computer software in structural equation modeling are established based on linear relationships among manifest variables and latent variables however models with nonlinear relationships are often encountered in social and behavioral sciences in this article an em type algorithm is developed for maximum likelihood estimation of a general nonlinear structural equation model to avoid computation of the complicated multiple integrals involved the e step is completed by a metropolis hastings algorithm it is shown that the m step can be completed efficiently by simple conditional maximization standard errors of the maximum likelihood estimates are obtained via louis s formula the methodology is illustrated with results from a simulation study and two real examples

conjugate gradient acceleration of the em algorithm the em algorithm is a very popular and widely applicable algorithm for the computation of maximum likelihood estimates although its implementation is generally simple the em algorithm often exhibits slow convergence and is costly in some areas of application past attempts to accelerate the em algorithm have most commonly been based on some form of aitken acceleration here we propose an alternative method based on conjugate gradients the key as we show is that the em step can be viewed approximately at least as a generalized gradient making it natural to apply generalized conjugate gradient methods in an attempt to accelerate the em algorithm the proposed method is relatively simple to implement and can handle problems with a large number of parameters an important feature of most em algorithms to demonstrate the effectiveness of the proposed acceleration method we consider its application to several problems in each of the following areas estimation of a covariance matrix from incomplete mu

on the rate of convergence of the ecme algorithm for multiple regression models with t distributed errors although much work has been done on comparing and contrasting the em and ecme algorithms in terms of their rates of convergence it is not clear what mechanism underlies each and furthermore what factors may determine and influence their rates of convergence in this paper we examine the convergence rates and properties of these two popular optimisation algorithms as used in computing the maximum likelihood estimates from regression models with t distributed errors by approaching this computing problem through the use of two data augmentation schemes as well as variations of these well known algorithms we offer a more composite view on the performance of each

construction of polygonal interpolants a maximum entropy approach in this paper we establish a link between maximizing information theoretic entropy and the construction of polygonal interpolants the determination of shape functions on n gons n 3 leads to a non unique under determined system of linear equations the barycentric co ordinates i which form a partition of unity are associated with discrete probability measures and the linear reproducing conditions are the counterpart of the expectations of a linear function the i are computed by maximizing the uncertainty h 1 2 n i log i subject to the above constraints the description is expository in nature and the numerical results via the maximum entropy maxent formulation are compared to those obtained from a few distinct polygonal interpolants the maximum entropy formulation leads to a feasible solution for i in any convex or non convex polygon this study is an instance of the application of the maximum entropy principle wherein least biased inference is made on the basis of incomplete information copyright 2004 john wiley sons ltd

finite element analysis on implicitly defined domains an accurate representation based on arbitrary parametric surfaces in this paper we present some novel results and ideas for robust and accurate implicit representation of geometric surfaces in finite element analysis the novel contributions of this paper are threefold 1 describe and validate a method to represent arbitrary parametric surfaces implicitly 2 represent arbitrary solids implicitly including sharp features using level sets and boolean operations 3 impose arbitrary dirichlet and neumann boundary conditions on the resulting implicitly defined boundaries the methods proposed do not require local refinement of the finite element mesh in regions of high curvature ensure the independence of the domain s volume on the mesh do not rely on boundary regularization and are well suited to methods based on fixed grids such as the extended finite element method xfem numerical examples are presented to demonstrate the robustness and effectiveness of the proposed approach and show that it is possible to achieve optimal convergence rates using a fully implicit representation of object boundaries this approach is one step in the desired direction of tying numerical simulations to computer aided design cad similarly to the isogeometric analysis paradigm

analysis suitable t splines are dual compatible abstract in this paper we define dual compatible dc t splines and we prove that analysis suitable as t splines are dual compatible we show that the classical construction of a dual basis for tensor product t splines easily generalizes to dc t spline spaces and we discuss in the last section of the paper how it paves the way to a mathematical theory of as t splines

operations and evaluation measures for learning possibilistic graphical models one focus of research in graphical models is how to learn them from a dataset of sample cases this learning task can pose unpleasant problems if the dataset to learn from contains imprecise information in the form of sets of alternatives instead of precise values in this paper we study an approach to cope with these problems which is not based on probability theory as the more common approaches like e g expectation maximization but uses possibility theory as the underlying calculus of a graphical model since the search methods employed in a learning algorithm are relatively independent of the underlying uncertainty or imprecision calculus we focus on evaluation measures or scoring functions

association pattern discovery via theme dictionary models summary discovering patterns from a set of text or more generally categorical data is an important problem in many disciplines such as biomedical research linguistics artificial intelligence and sociology we consider here the well known market basket problem that is often discussed in the data mining community and is also quite ubiquitous in biomedical research the data under consideration are a set of baskets where each basket contains a list of items our goal is to discover themes which are defined as subsets of items that tend to co occur in a basket we describe a generative model i e the theme dictionary model for such data structures and describe two likelihood based methods to infer themes that are hidden in a collection of baskets we also propose a novel sequential monte carlo method to overcome computational challenges using both simulation studies and real applications we demonstrate that the new approach proposed is significantly more powerful than existing methods such as association rule mining and topic modelling in detecting weak and subtle interactions in the data

acceleration of the em algorithm by using quasi newton methods the em algorithm is a popular method for maximum likelihood estimation its simplicity in many applications and desirable convergence properties make it very attractive its sometimes slow convergence however has prompted researchers to propose methods to accelerate it we review these methods classifying them into three groups pure hybrid and em type accelerators we propose a new pure and a new hybrid accelerator both based on quasi newton methods and numerically compare these and two other quasi newton accelerators for this we use examples in each of three areas poisson mixtures the estimation of covariance from incomplete data and multivariate normal mixtures in these comparisons the new hybrid accelerator was fastest on most of the examples and often dramatically so in some cases it accelerated the em algorithm by factors of over 100 the new pure accelerator is very simple to implement and competed well with the other accelerators it accelerated the em algorithm in some cases by factors of over 50 to obtain standard errors we propose to approximate the inverse of the observed information matrix by using auxiliary output from the new hybrid accelerator a numerical evaluation of these approximations indicates that they may be useful at least for exploratory purposes

from nurbs to nurps geometries abstract quadratic powell sabin splines and their rational extension the so called nurps surfaces are an interesting alternative for classical tensor product nurbs in the context of isogeometric analysis because they allow the use of local refinements while retaining a b spline like representation and exact description of conic sections in this paper we present a simple and effective strategy to convert a given planar geometry defined by a quadratic nurbs representation into a nurps representation suitable for the analysis

generalized b splines as a tool in isogeometric analysis the concept of isogeometric analysis has been proposed in 13 where nurbs are considered as basis of the analysis thanks to their ability to construct an exact geometric model in several practical applications and to their popularity in commercial cad systems in this paper we propose an alternative to the rational model presenting an isogeometric analysis approach based on generalized b splines geometric models exactly represented by generalized b splines include those generated by nurbs moreover generalized b splines possess all fundamental properties of algebraic b splines and nurbs including classical refinement processes as h p k refinements finally since generalized b splines are not confined to rational functions they behave completely similar to algebraic b splines with respect to differentiation and integration this seems to be of interest in the treatment of some relevant problems

space alternating generalized expectation maximization algorithm the expectation maximization em method can facilitate maximizing likelihood functions that arise in statistical estimation problems in the classical em paradigm one iteratively maximizes the conditional log likelihood of a single unobservable complete data space rather than maximizing the intractable likelihood function for the measured or incomplete data em algorithms update all parameters simultaneously which has two drawbacks 1 slow convergence and 2 difficult maximization steps due to coupling when smoothness penalties are used the paper describes the space alternating generalized em sage method which updates the parameters sequentially by alternating between several small hidden data spaces defined by the algorithm designer the authors prove that the sequence of estimates monotonically increases the penalized likelihood objective derive asymptotic convergence rates and provide sufficient conditions for monotone convergence in norm two signal processing applications illustrate the method estimation of superimposed signals in gaussian noise and image reconstruction from poisson measurements in both applications the sage algorithms easily accommodate smoothness penalties and converge faster than the em algorithms

em algorithms for ml factor analysis the details of em algorithms for maximum likelihood factor analysis are presented for both the exploratory and confirmatory models the algorithm is essentially the same for both cases and involves only simple least squares regression operations the largest matrix inversion required is for aq q symmetric matrix whereq is the matrix of factors the example that is used demonstrates that the likelihood for the factor analysis model may have multiple modes that are not simply rotations of each other such behavior should concern users of maximum likelihood factor analysis and certainly should cast doubt on the general utility of second derivatives of the log likelihood as measures of precision of estimation

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

an em algorithm for fitting two level structural equation models maximum likelihood is an important approach to analysis of two level structural equation models different algorithms for this purpose have been available in the literature in this paper we present a new formulation of two level structural equation models and develop an em algorithm for fitting this formulation this new formulation covers a variety of two level structural equation models as a result the proposed em algorithm is widely applicable in practice a practical example illustrates the performance of the em algorithm and the maximum likelihood statistic

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

estimation for general birth death processes birth death processes bdps are continuous time markov chains that track the number of particles in a system over time while widely used in population biology genetics and ecology statistical inference of the instantaneous particle birth and death rates remains largely limited to restrictive linear bdps in which per particle birth and death rates are constant researchers often observe the number of particles at discrete times necessitating data augmentation procedures such as expectation maximization em to find maximum likelihood estimates mles for bdps on finite state spaces there are powerful matrix methods for computing the conditional expectations needed for the e step of the em algorithm for bdps on infinite state spaces closed form solutions for the e step are available for some linear models but most previous work has resorted to time consuming simulation remarkably we show that the e step conditional expectations can be expressed as convolutions of computable transition probabi

majorization minimization algorithms in signal processing communications and machine learning this paper gives an overview of the majorization minimization mm algorithmic framework which can provide guidance in deriving problem driven algorithms with low computational cost a general introduction of mm is presented including a description of the basic principle and its convergence results the extensions acceleration schemes and connection to other algorithmic frameworks are also covered to bridge the gap between theory and practice upperbounds for a large number of basic functions derived based on the taylor expansion convexity and special inequalities are provided as ingredients for constructing surrogate functions with the pre requisites established the way of applying mm to solving specific problems is elaborated by a wide range of applications in signal processing communications and machine learning

a hybrid algorithm for computation of the nonparametric maximum likelihood estimator from censored data abstract we present a hybrid algorithm for nonparametric maximum likelihood estimation from censored data when the log likelihood is concave the hybrid algorithm uses a composite algorithmic mapping combining the expectation maximization em algorithm and the modified iterative convex minorant icm algorithm global convergence of the hybrid algorithm is proven the iterates generated by the hybrid algorithm are shown to converge to the nonparametric maximum likelihood estimator npmle unambiguously numerical simulations demonstrate that the hybrid algorithm converges more rapidly than either of the em or the naive icm algorithm for doubly censored data the speed of the hybrid algorithm makes it possible to accompany the npmle with bootstrap confidence bands

convexity conditions on t norms and their additive generators abstract let t be an archimedean continuous t norm and 0 1 2 fodor and ovchinnikov have studied a relation between the inequality t max x 0 min x 1 t x x and the convexity of the additive generator of t here we clarify this relation and answer open problems from previous studies

a fast improvement to the em algorithm on its own terms the em algorithm is a numerical technique for the evaluation of maximum likelihood estimates for parameters describing incomplete data models it is easy to apply in many problems and is stable but slow the algorithm fails to provide a consistent estimator of the standard errors of the maximum likelihood estimates unless the additional analysis required by the louis method is performed newton type or other gradient methods are faster and provide error estimates but tend to be unstable and require the analytical evaluation of likelihoods to derive expressions for the score function and at least approximations to the fisher information matrix the purpose of this paper is to expand on a result by fisher that permits a unification of em methodology and newton methods the evaluation of the individual observation by observation score functions of the incomplete data is a byproduct of the application of the e step of the em algorithm once these become available the fisher information matrix may be consistently estimated and the m step may be replaced by a fast newton type step

newton raphson and em algorithms for linear mixed effects models for repeated measures data abstract we develop an efficient and effective implementation of the newton raphson nr algorithm for estimating the parameters in mixed effects models for repeated measures data we formulate the derivatives for both maximum likelihood and restricted maximum likelihood estimation and propose improvements to the algorithm discussed by jennrich and schluchter 1986 to speed convergence and ensure a positive definite covariance matrix for the random effects at each iteration we use matrix decompositions to develop efficient and computationally stable implementations of both the nr algorithm and an em algorithm laird and ware 1982 for this model we compare the two methods em vs nr in terms of computational order and performance on two sample data sets and conclude that in most situations a well implemented nr algorithm is preferable to the em algorithm or em algorithm with aitken s acceleration the term repeated measures refers to experimental designs where there are several individuals and several

a weakening of schur concavity for copulas the class of copulas satisfying a new property called weak schur concavity is introduced and studied and the relationships of this property with other known notions of concavity are investigated

isogeometric analysis using t splines on two patch geometries we develop optimal approximation estimates for t splines in the case of geometries obtained by gluing two standard tensor product patches we derive results both for the t spline space in the parametric domain and the mapped t nurbs in the physical one a set of numerical tests in complete accordance with the theoretical developments is also presented

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

isogeometric analysis with powell sabin splines for advection diffusion reaction problems abstract this paper presents the use of powell sabin splines in the context of isogeometric analysis for the numerical solution of advection diffusion reaction equations powell sabin splines are piecewise quadratic c 1 functions defined on a given triangulation with a particular macro structure we discuss the galerkin discretization based on a normalized powell sabin b spline basis we focus on the accurate detection of internal and boundary layers and on local refinements we apply the approach to several test problems and we illustrate its effectiveness by a comparison with classical finite element and recent isogeometric analysis procedures

an application of mixture distributions in modelization of length of hospital stay length of hospital stay los is an important indicator of the hospital activity and management of health care the skewness exhibited by this variable poses problems in statistical modeling the aim of this work is to model the variable los within diagnosis related groups drg through finite mixtures of distributions a mixture of the union of gamma weibull and lognormal families is used in the model instead of a mixture of a unique distribution family some theoretical questions regarding the model such as the identifiability and study of asymptotic properties of ml estimators are analyzed the em algorithm is proposed for performing these estimators finally this new proposed model is illustrated by using data from different drgs