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

on finding the rectangular duals of planar triangular graphs this paper presents a new linear time algorithm for finding rectangular duals of planar triangular graphs the algorithm is conceptually simpler than the previously known algorithm the coordinates of the rectangular dual constructed by the new algorithm are integers and carry clear combinatorial meaning

estimation of adjusted rate differences using additive negative binomial regression rate differences are an important effect measure in biostatistics and provide an alternative perspective to rate ratios when the data are event counts observed during an exposure period adjusted rate differences may be estimated using an identity link poisson generalised linear model also known as additive poisson regression a problem with this approach is that the assumption of equality of mean and variance rarely holds in real data which often show overdispersion an additive negative binomial model is the natural alternative to account for this however standard model fitting methods are often unable to cope with the constrained parameter space arising from the non negativity restrictions of the additive model in this paper we propose a novel solution to this problem using a variant of the expectation conditional maximisation either algorithm our method provides a reliable way to fit an additive negative binomial regression model and also permits flexible generalisations using semi parametric regression functions we illustrate the method using a placebo controlled clinical trial of fenofibrate treatment in patients with type ii diabetes where the outcome is the number of laser therapy courses administered to treat diabetic retinopathy an r package is available that implements the proposed method copyright 2016 john wiley sons ltd

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

curvature characteristics and congruence of the thumb carpometacarpal joint differences between female and male joints abstract three dimensional geometric models of the articular surfaces of the thumb carpometacarpal cmc joint were constructed using precise data obtained from stereophotogrammetry spg it was demonstrated that by using a least squares surface fitting technique the spg data on the surface can accurately be described by a single parametric biquintic spline function from this mathematical description curvature maps of the surfaces were calculated for 13 cmc joints eight females average 64 yr old five males average 70 yr old the surface geometry of each joint was analyzed comparisons were made between trapezial and metacarpal surfaces of the joint and differences determined between males and females with regard to joint surface areas the female trapezium is significantly smaller than that of the metacarpal the shape of the female trapezial surface is also fundamentally different from of males no gender related difference exists regarding the shape of the metacarpal surface congruence of the two opposing articular surfaces was defined by their relative principal curvatures from these definitions congruence in the radioulnar and dorsovolar anatomic directions as well as the global congruence of the joint were calculated most cmc joints were found to be more congruent along the radioulnar direction than the dorsovolar direction and globally female joints were found to be less congruent than male joints the concept of joint congruence has played a central role in a number of hypotheses relating to the etiology of cmc joint osteoarthritis oa although conflicting hypotheses do exist the precise quantitative findings of this study may lead to an improved understanding of cmc joint oa and perhaps explain its prevalence in the female population over 55

bilinear mixed effects models for dyadic data this article discusses the use of a symmetric multiplicative interaction effect to capture certain types of third order dependence patterns often present in social networks and other dyadic datasets such an effect along with standard linear fixed and random effects is incorporated into a generalized linear model and a markov chain monte carlo algorithm is provided for bayesian estimation and inference in an example analysis of international relations data accounting for such patterns improves model fit and predictive performance

bayesian computation via the gibbs sampler and related markov chain monte carlo methods the use of the gibbs sampler for bayesian computation is reviewed and illustrated in the context of some canonical examples other markov chain monte carlo simulation methods are also briefly described and comments are made on the advantages of sample based approaches for bayesian inference summaries

markov chain monte carlo 10 years and still running although markov chain monte carlo mcmc techniques can be traced back to the early 1950s and are almost contemporary with independent monte carlo methods the use of these techniques has only really taken off in the past 10 years at least in mainstream statistics with the work of gelfand and smith 1990 and the rediscovery of metropolis s and hastings s papers the impact on the discipline is deep and durable because these methods have opened new horizons in the scale of the problems that one can deal with thus enhancing the position of statistics in most applied fields the mcmc revolution has in particular boosted bayesian statistics to new heights by providing a virtually universal tool for dealing with integration and optimization problems this can be seen in for instance the explosion of papers dealing with complex models hierarchical modelings nonparametric bayesian estimation and spatial statistics this trend has also created new synergies with mathematicians and probabilists as well as econometricians engineers ecologists astronomers and others for theoretical requests and practical implications of mcmc techniques it is impossible to provide here a complete perspective on mcmc methods and applications for this as well as for other references we refer the reader to the books by gilks richardson and spiegelhalter 1995 and robert and casella 1999 here we focus on four particular aspects of mcmc algorithms theoretical foundations practical implementation bayesian inference and prospects the web provides many relevant sites including the mcmc preprint server http www statslab cam ac uk r mcmc which offers a most useful window to the current research on mcmc wilson s site on perfect simulation http dimacs rutgers edu dbwilson exact h which keeps track of papers and applets on this topic and a site on convergence control techniques http www ensae fr crest statistique robert mcdiag even more recent developments allow for on line computations through applets like breyer s http www maths lancs ac uk breyer java html which impressively illustrates the behavior of different samplers for simple problems note also that the bugs and coda software are freely available at http www mrc bsu cam ac uk bu

illustration of bayesian inference in normal data models using gibbs sampling abstract the use of the gibbs sampler as a method for calculating bayesian marginal posterior and predictive densities is reviewed and illustrated with a range of normal data models including variance components unordered and ordered means hierarchical growth curves and missing data in a crossover trial in all cases the approach is straightforward to specify distributionally and to implement computationally with output readily adapted for required inference summaries

maximum likelihood estimation via the ecm algorithm a general framework two major reasons for the popularity of the em algorithm are that its maximum step involves only complete data maximum likelihood estimation which is often computationally simple and that its convergence is stable with each iteration increasing the likelihood when the associated complete data maximum likelihood estimation itself is complicated em is less attractive because the m step is computationally unattractive in many cases however complete data maximum likelihood estimation is relatively simple when conditional on some function of the parameters being estimated

penalized maximum likelihood image reconstruction using space alternating generalized em algorithms most expectation maximization em type algorithms for penalized maximum likelihood image reconstruction converge slowly particularly when one incorporates additive background effects such as scatter random coincidences dark current or cosmic radiation in addition regularizing smoothness penalties or priors introduce parameter coupling rendering intractable the m steps of most em type algorithms this paper presents space alternating generalized em sage algorithms for image reconstruction which update the parameters sequentially using a sequence of small hidden data spaces rather than simultaneously using one large complete data space the sequential update decouples the m step so the maximization can typically be performed analytically we introduce new hidden data spaces that are less informative than the conventional complete data space for poisson data and that yield significant improvements in convergence rate this acceleration is due to statistical considerations not numerical overrelaxation methods so monotonic increases in the objective function are guaranteed we provide a general global convergence proof for sage methods with nonnegativity constraints

a particle algorithm for sequential bayesian parameter estimation and model selection we describe a particle algorithm for the sequential bayesian estimation of unknown static parameters the algorithm combines sequential importance sampling sis and markov chain monte carlo mcmc to achieve computational efficiency and stability in its most general form the algorithm has three components i sis ii a rejuvenation test and iii mcmc measurements are processed sequentially with an artificial time line if there is no natural one associated with the measurements by sis which is computationally inexpensive after each measurement is processed the rejuvenation test checks whether the resulting sis particles have to be rejuvenated when indicated by the test the particles are completely rejuvenated by mcmc which removes errors that accumulate from sis due to the finite number of particles thus ensuring stability whenever possible the sis particles can be used to advantage in the mcmc there is flexibility in the choice of the rejuvenation test as well as the mcmc method with potential to increase the usefulness of the algorithm in particular by using reversible jump mcnic with multiple models the algorithm can perform simultaneous model selection and parameter estimation in this paper we use a rejuvenation test based on a kullback leibler distance that is easy to compute and our choice of mcnic is independent metropolis hastings with a gaussian proposal density with these choices we illustrate the use of the algorithm in two signal processing applications passive source localization with angle of arrival and simultaneous weak signal detection and parameter estimation involving both simulated and real data the results demonstrate the algorithm s stability its built in protection against model overfitting and tolerance to model mismatch

large sample joint posterior approximations when full conditionals are approximately normal modern bayesian statistical methods such as gibbs and metropolis hastings sampling were developed to liberate statisticians from the necessity of making large sample assumptions and to facilitate the numerical approximation of problems that had previously been analytically intractable counter to this trend we develop a method for constructing asymptotic joint posterior approximations based on models with k blocks of parameters and where the corresponding properly normalized full conditionals are themselves asymptotically normal we illustrate these techniques by applying them to particular linear and generalized linear mixed models glmms we also consider the relevance of different parameterizations with regard to our asymptotics recent work has indicated that gibbs samplers based on so called centering parameterizations result in better convergence properties for the resulting markov chains our results for the one way random effects model shed some light on this issue for this example we also

a priori optimization for the probabilistic maximum independent set problem we first propose a formal definition for the concept of probabilistic combinatorial optimization problem under the a priori method next we study the complexity of optimally solving probabilistic maximum independent set problem under several a priori optimization strategies as well as the complexity of approximating optimal solutions for the different strategies studied we present results about the restriction of probabilistic independent set on bipartite graphs

effects of variation on extensor elements and operative procedures in patellofemoral disorders the influence of both insertion and strength elasticity of each extensor in patellofemoral disorders was fully investigated through a two dimensional mathematical model analysis in a horizontal plane in combination with experimental design theory for analyzing mutually correlated influences in the model patellofemoral joint profiles projected on a horizontal plane have been expressed as spline functions each muscle of the quadriceps has been represented as a string pulled by the respective force fascias and tendons have been represented by springs nonlinear equations have been constructed to represent the forces involved and then solved by numerical iteration an analysis of variance was performed on the data derived from a series of simulations obtaining the following results the strength of most extensors has been shown to have an influence on the increase in lateral contact force but not patellar translation the tibial tubercle position has significant influence on both patellar translation and lateral contact force the quadriceps insertion on the femur has no influence on patellar translation the insertion of each extensor on the patella has been shown to have a strong effect on patellar translation but not on contact force

a best possible heuristic for the k center problem in this paper we present a 2 approximation algorithm for the k center problem with triangle inequality this result is best possible since for any 2 the existence of approximation algorithm would imply that p np it should be noted that no approximation algorithm for any constant has been reported to date linear programming duality theory provides interesting insight to the problem and enables us to derive in o e log e time a solution with value no more than twice the k center optimal value a by product of the analysis is an o e algorithm that identifies a dominating set in g2 the square of a graph g the size of which is no larger than the size of the minimum dominating set in the graph g the key combinatorial object used is called a strong stable set and we prove the np completeness of the corresponding decision problem

the accuracy of joint surface models constructed from data obtained with an electromagnetic tracking device electromagnetic tracking devices are widely used in biomechanics in this article a method is evaluated to construct models of articular surfaces using an electromagnetic tracking device first the accuracy of the space tracker was examined and optimised then from several joint surfaces random points were measured and eighth degree polynomials were fitted to these measurements to check if the fit converged well plots of cross sections of the model with corresponding data points were examined the accuracy of the models was determined by comparing them with computed tomography data and by reproducibility tests all the fits converged well to the data the root mean square rms error of the models varied from 0 07 to 0 18mm and was proportional to the size and complexity of the surface this was mainly due to systematic errors made by the space tracker which were also proportional to the size and complexity of the surface

modeling through group invariance an interesting example with potential applications a particular linear group symmetry model called the dyadic symmetry model is studied in some detail statistical procedures analogous to multivariate analysis of variance are introduced this model may be suitable for various kinds of data collected on pairs of sampling units examples include complete diallel cross experiments in genetics and social relations analysis in psychology for which ad hoc methods of analysis have been developed independently in those disciplines our approach is based entirely on formal data structure following the principle of group symmetry and hence its applicability is not restricted to any specific substantive areas this paper illustrates the benefits that can be derived from the exploration of mathematical meanings in the development of statistical methods

convergence of slice sampler markov chains we analyse theoretical properties of the slice sampler we find that the algorithm has extremely robust geometric ergodicity properties for the case of just one auxiliary variable we demonstrate that the algorithm is stochastically monotone and we deduce analytic bounds on the total variation distance from stationarity of the method by using foster lyapunov drift condition methodology

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

solving np hard problems on graphs that are almost trees and an application to facility location problems description d une technique generale pour resoudre certains problemes de graphes np durs en un temps qui est exponentiel dans un parametre k defini comme le maximum sur tous les composants c non separables du graphe d un nombre de bords qui peut etre ajoute a l arbre pour produire c on donne un algorithme de temps de complexite o e 6r rh 27

on the global and componentwise rates of convergence of the em algorithm abstract the em algorithm is a very general and popular iterative algorithm in statistics for finding maximum likelihood estimates in the presence of incomplete data in the paper that defined and popularized em dempster laird and rubin 1977 showed that its global rate of convergence is governed by the largest eigenvalue of the matrix of fractions of missing information due to incomplete data it was also mentioned that componentwise rates of convergence can differ from each other when the fractions of information loss vary across different components of a parameter vector in this article using the well known diagonability theorem we present a general description on how and when the componentwise rates differ as well as their relationships with the global rate we also provide an example a standard contaminated normal model to show that such phenomena are not necessarily pathological but can occur in useful statistical models

robust statistical modeling using the t distribution abstract the t distribution provides a useful extension of the normal for statistical modeling of data sets involving errors with longer than normal tails an analytical strategy based on maximum likelihood for a general model with multivariate t errors is suggested and applied to a variety of problems including linear and nonlinear regression robust estimation of the mean and covariance matrix with missing data unbalanced multivariate repeated measures data multivariate modeling of pedigree data and multivariate nonlinear regression the degrees of freedom parameter of the t distribution provides a convenient dimension for achieving robust statistical inference with moderate increases in computational complexity for many models estimation of precision from asymptotic theory and the bootstrap is discussed and graphical methods for checking the appropriateness of the t distribution are presented

fast em type implementations for mixed effects models the mixed effects model in its various forms is a common model in applied statistics a useful strategy for fitting this model implements em type algorithms by treating the random effects as missing data such implementations however can be painfully slow when the variances of the random effects are small relative to the residual variance in this paper we apply the working parameter approach to derive alternative em type implementations for fitting mixed effects models which we show empirically can be hundreds of times faster than the common em type implementations in our limited simulations they also compare well with the routines in s plus and stata in terms of both speed and reliability the central idea of the working parameter approach is to search for efficient data augmentation schemes for implementing the em algorithm by minimizing the augmented information over the working parameter and in the mixed effects setting this leads to a transfer of the mixed effects variances into the regression slope parameters we also describe a variation for computing the restricted maximum likelihood estimate and an adaptive algorithm that takes advantage of both the standard and the alternative em type implementations

a new approach for surface fitting method of articular joint surfaces the application of joint contact mechanics requires a precise configuration of the joint surfaces b spline and nurbs have been widely used to model joint surfaces but because these formulations use a structured data set provided by a rectangular net first then a grid there is a limit to the accuracy of the models they can produce however new imaging systems such as 3d laser scanners can provide more realistic unstructured data sets what is needed is a method to manipulate the unstructured data we created a parametric polynomial function and applied it to unstructured data sets obtained by scanning joint surfaces we applied our polynomial model to unstructured data sets from an artificial joint and confirmed that our polynomial produced a smoother and more accurate model than the conventional b spline method next we applied it to a diarthrodial joint surface containing many ripples and found that our function s noise filtering characteristics smoothed out existing ripples since no formulation was found to be optimal for all applications we used two formulations to model surfaces with ripples first we used our polynomial to describe the global shape of the objective surface minute undulations were then specifically approximated with a fourier series function finally both approximated surfaces were superimposed to reproduce the original surface in a complete fashion

minorization conditions and convergence rates for markov chain monte carlo abstract general methods are provided for analyzing the convergence of discrete time general state space markov chains such as those used in stochastic simulation algorithms including the gibbs sampler the methods provide rigorous a priori bounds on how long these simulations should be run to give satisfactory results results are applied to two models of the gibbs sampler a bivariate normal model and a hierarchical poisson model with gamma conditionals the methods use the notion of minorization conditions for markov chains

an imputation regularized optimization algorithm for high dimensional missing data problems and beyond missing data are frequently encountered in high dimensional problems but they are usually difficult to deal with by using standard algorithms such as the expectation maximization algorithm and its variants to tackle this difficulty some problem specific algorithms have been developed in the literature but there still lacks a general algorithm this work is to fill the gap we propose a general algorithm for high dimensional missing data problems the algorithm works by iterating between an imputation step and a regularized optimization step at the imputation step the missing data are imputed conditionally on the observed data and the current estimates of parameters and at the regularized optimization step a consistent estimate is found via the regularization approach for the minimizer of a kullback leibler divergence defined on the pseudocomplete data for high dimensional problems the consistent estimate can be found under sparsity constraints the consistency of the averaged estimate for the true parameter can be established under quite general conditions the algorithm is illustrated by using high dimensional gaussian graphical models high dimensional variable selection and a random coefficient model

optimal scaling of discrete approximations to langevin diffusions we consider the optimal scaling problem for proposal distributions in hastings metropolis algorithms derived from langevin diffusions we prove an asymptotic diffusion limit theorem and show that the relative efficiency of the algorithm can be characterized by its overall acceptance rate independently of the target distribution the asymptotically optimal acceptance rate is 0 574 we show that as a function of dimension n the complexity of the algorithm is o n1 3 which compares favourably with the o n complexity of random walk metropolis algorithms we illustrate this comparison with some example simulations

reversible jump birth and death and more general continuous time markov chain monte carlo samplers reversible jump methods are the most commonly used markov chain monte carlo tool for exploring variable dimension statistical models recently however an alternative approach based on birth and death processes has been proposed by stephens for mixtures of distributions we show that the birth and death setting can be generalized to include other types of continuous time jumps like split and combine moves in the spirit of richardson and green we illustrate these extensions both for mixtures of distributions and for hidden markov models we demonstrate the strong similarity of reversible jump and continuous time methodologies by showing that on appropriate rescaling of time the reversible jump chain converges to a limiting continuous time birth and death process a numerical comparison in the setting of mixtures of distributions highlights this similarity

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

regular edge labeling of 4 connected plane graphs and its applications in graph drawing problems abstract in this paper we extend the concept of the regular edge labeling for general plane graphs and for triconnected triangulated plane graphs to 4 connected triangulated plane graphs we present two different linear time algorithms for constructing such a labeling by using regular edge labeling we present a new linear time algorithm for constructing rectangular dual of planar graphs our algorithm is simpler than previously known algorithms the coordinates of the rectangular dual constructed by our algorithm are integers while the one constructed by known algorithms are real numbers our second regular edge labeling algorithm is based on canonical ordering of 4 connected triangulated plane graphs by using this technique we present a new algorithm for constructing visibility representation of 4 connected planar graphs our algorithm reduces the size of the representation by a factor of 2 for such graphs

algorithms for computing a parameterized st orientation st orientations st numberings or bipolar orientations of undirected graphs are central to many graph algorithms and applications several algorithms have been proposed in the past to compute an st orientation of a biconnected graph in this paper we present new algorithms that compute such orientations with certain parameterized characteristics in the final st oriented graph such as the length of the longest path this work has many applications including graph drawing and network routing where the length of the longest path is vital in deciding certain features of the final solution this work applies to other difficult problems as well such as graph coloring and of course longest path we present extended theoretical and experimental results which show that our technique is efficient and performs well in practice

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

a widely applicable extension of the random effects two way layout its definition and statistical analysis based on group invariance a type of data layout that may be considered as an extension of the two way random effects analysis of variance is characterized and modeled based on group invariance the data layout seems to be suitable for several scenarios in psychometrics including the one in which multiple measurements are taken on each of a set of variables and the measurements can be divided into exchangeable subsets the algebraic structure of the model is studied which leads to results that are applicable to such problems as estimating correlation matrix corrected for attenuation and testing symmetry hypotheses

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

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

three dimensional mathematical model analysis of the patellofemoral joint this paper is concerned with a mathematical model analysis of the patellofemoral joint in the human knee taking into account the articular surface geometry and mechanical properties of the ligament it was made by the application of a computer aided design theory previously studied and it was possible to express the articular surface geometries in a mathematical formulation and hence elucidate the joint movement mechanics this method was then applied to a three dimensional geometrical model of the patellofemoral joint for the modelling of tendofemoral contact at large angles of knee flexion the geodestic line theory was adopted applying the newton raphson method and the runge kutta gil method to the model variables such as patellar attitudes patellofemoral contact force and tensile force of the patellar ligament for various knee flexion angles were computed applying the hertzian elastic theory contact stress was also computed these results showed good agreement with the previously reported experimental results as an application for the model some parameter analyses were performed in terms of the contact stress variations and compared with those of the normal knee the simulation results indicated that both the q angle increase and decrease increased contact stress the patella alta showed undulating variations of stress while the patella infera showed little change of stress and the tibial tuberositas elevation showed 20 30 reduction of stress

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

the collapsed gibbs sampler in bayesian computations with applications to a gene regulation problem abstract this article describes a method of grouping and collapsing in using the gibbs sampler and proves from an operator theory viewpoint that the method is in general beneficial the norms of the forward operators associated with the corresponding nonreversible markov chains are used to discriminate among different simulation schemes when applied to bayesian missing data problems the idea of collapsing suggests skipping the steps of sampling parameter s values in standard data augmentation by doing this we obtain a predictive update version of the gibbs sampler a procedure of calculating the posterior odds ratio via the collapsed gibbs sampler when incomplete observations are involved is presented as an illustration of possible applications three examples along with a bayesian treatment for identifying common protein binding sites in unaligned dna sequences are provided

analysis of structural equation model with ignorable missing continuous and polytomous data the main purpose of this article is to develop a bayesian approach for structural equation models with ignorable missing continuous and polytomous data joint bayesian estimates of thresholds structural parameters and latent factor scores are obtained simultaneously the idea of data augmentation is used to solve the computational difficulties involved in the posterior analysis in addition to the real missing data latent variables and latent continuous measurements underlying the polytomous data are treated as hypothetical missing data an algorithm that embeds the metropolis hastings algorithm within the gibbs sampler is implemented to produce the bayesian estimates a goodness of fit statistic for testing the posited model is presented it is shown that the proposed approach is not sensitive to prior distributions and can handle situations with a large number of missing patterns whose underlying sample sizes may be small computational efficiency of the proposed procedure is illustrated by simulation studies and a real example

compact visibility representation of 4 connected plane graphs the visibility representation vr for short is a classical representation of plane graphs the vr has various applications and has been extensively studied in the literature a main focus of the study is to minimize the size of the vr it is known that there exists a plane graph g with n vertices where any vr of g requires a size at least 2n3 x 4n3 3 for upper bounds it is known that every plane graph has a vr with size at most 23n x 2n 5 and a vr with size at most n 1 x 43n it has been an open problem to find a vr with both height and width simultaneously bounded away from the trivial upper bounds namely of size c hnxc wn with c h 1 and c w 2 in this paper we provide the first vr construction for a non trivial graph class that simultaneously bounds both the height and the width we prove that every 4 connected plane graph has a vr with height 3n4 2 n 4 and width 3n2 our vr algorithm is based on an st orientation of 4 connected plane graphs with special properties the area of the vr presented in this paper is larger than the area of some of the previous results for this graph class however bounding one dimension of the vr only requires finding a good st orientation or a good dual s t orientation of g on the other hand bounding both dimensions of the vr requires finding a good st orientation and a good dual s t orientation of g at the same time and hence is far more challenging since the st orientation is a very useful concept in other applications this result may be of independent interest reducing the height the width respectively of the vr is the same as reducing the length of the longest path in an st orientation of g dual st orientation respectively we show that it s np complete to find an st orientation of a 2 connected plane graph that minimizes the sum of the length of the longest path in the orientation and the length of the longest path in its dual orientation

antithetic coupling of two gibbs sampler chains two coupled gibbs sampler chains both with invariant probability density are run in parallel so that the chains are negatively correlated we define an asymptotically unbiased estimator of the expectation e f x which achieves significant variance reduction with respect to the usual gibbs sampler at comparable computational cost the variance of the estimator based on the new algorithm is always smaller than the variance of a single gibbs sampler chain if is attractive and f is monotone nondecreasing in all components of x for nonattractive targets our results are not complete the new antithetic algorithm outperforms the standard gibbs sampler when is a multivariate normal density or the ising model more generally nonrigorous arguments and numerical experiments support the usefulness of the antithetically coupled gibbs samplers also for other nonattractive models in our experiments the variance is reduced to at least a third and the efficiency also improves significantly

fitting parametrized polynomials with scattered surface data currently used joint surface models require the measurements to be structured according to a grid with the currently available tracking devices a large quantity of unstructured surface points can be measured in a relatively short time in this paper a method is presented to fit polynomial functions to three dimensional unstructured data points to test the method spherical cylindrical parabolic hyperbolic exponential logarithmic and sellar surfaces with different undulations were used the resulting polynomials were compared with the original shapes the results show that even complex joint surfaces can be modelled with polynomial functions in addition the influence of noise and the number of data points was also analyzed from a surface diam 20 mm which is measured with a precision of 0 2 mm a model can be constructed with a precision of 0 02 mm

rates of convergence of the hastings and metropolis algorithms we apply recent results in markov chain theory to hastings and metropolis algorithms with either independent or symmetric candidate distributions and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution pi in the independence case in mathbb r k these indicate that geometric convergence essentially occurs if and only if the candidate density is bounded below by a multiple of pi in the symmetric case in mathbb r only we show geometric convergence essentially occurs if and only if pi has geometric tails we also evaluate recently developed computable bounds on the rates of convergence in this context examples show that these theoretical bounds can be inherently extremely conservative although when the chain is stochastically monotone the bounds may well be effective

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

multiple shrinkage and subset selection in wavelets this paper discusses bayesian methods for multiple shrinkage estimation in wavelets wavelets are used in applications for data denoising via shrinkage of the coefficients towards zero and for data compression by shrinkage and setting small coefficients to zero we approach wavelet shrinkage by using bayesian hierarchical models assigning a positive prior probability to the wavelet coefficients being zero the resulting estimator for the wavelet coefficients is a multiple shrinkage estimator that exhibits a wide variety of nonlinear patterns we discuss fast computational implementations with a focus on easy to compute analytic approximations as well as importance sampling and markov chain monte carlo methods multiple shrinkage estimators prove to have excellent mean squared error performance in reconstructing standard test functions we demonstrate this in simulated test examples comparing various implementations of multiple shrinkage to commonly used shrinkage rules finally we illustrate our approach with an application to the so called glint data

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

bayesian robust multivariate linear regression with incomplete data abstract the multivariate t distribution and other normal independent multivariate distributions such as the multivariate slash distribution and the multivariate contaminated distribution are used for robust regression with complete or incomplete data most previous work focused on the method of maximum likelihood estimation for linear regression using normal independent distributions this article considers bayesian estimation of multivariate linear regression models using normal independent distributions with fully observed predictor variables and possible missing values from outcome variables a monotone data augmentation algorithm for posterior simulation of the parameters and missing data imputation is presented the posterior distributions of functions of the parameters can be obtained using monte carlo methods the monotone data augmentation algorithm can also be used for creating multiple imputations for incomplete data sets an illustrative example of using the multivariate t is also included

a bayesian restoration of an ion channel signal summary we present a bayesian method of ion channel analysis and apply it to a simulated data set an alternating renewal process prior is assigned to the signal and an autoregressive process is fitted to the noise after choosing model hyperconstants to yield uninformative priors on the parameters the joint posterior distribution is computed by using the reversible jump markov chain monte carlo method a novel form of simulated tempering is used to improve the mixing of the original sampler

filtering via simulation auxiliary particle filters this article analyses the recently suggested particle approach to filtering time series we suggest that the algorithm is not robust to outliers for two reasons the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution here we tackle the first of these problems

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

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

multivariate linear mixed models for multiple outcomes we propose a multivariate linear mixed mlmm for the analysis of multiple outcomes which generalizes the latent variable model of sammel and ryan the proposed model assumes a flexible correlation structure among the multiple outcomes and allows a global test of the impact of exposure across outcomes in contrast to the sammel ryan model the mlmm separates the mean and correlation parameters so that the mean estimation will remain reasonably robust even if the correlation is misspecified the model is applied to birth defects data where continuous data on the size of infants who were exposed to anticonvulsant medications in utero are compared to controls

distance k knowledge in self stabilizing algorithms many graph problems seem to require knowledge that extends beyond the immediate neighbors of a node the usual self stabilizing model only allows for nodes to make decisions based on the states of their immediate neighbors we provide a general transformation for constructing self stabilizing algorithms which utilize distance k knowledge our transformation has both a slowdown and space overhead in n o l o g k and might be thought of as a distance k resource allocation algorithm our main application is a polynomial time self stabilizing algorithm for finding maximal irredundant sets a problem which seems to require distance 4 information these results can be generalized to efficiently find maximal p sets for properties p which we call local monotonic our techniques extend results in a recent paper by gairing et al for achieving distance two information

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

efficient algorithms for center problems in cactus networks efficient algorithms for solving the center problems in weighted cactus networks are presented in particular we have proposed the following algorithms for the weighted cactus networks of size n an o nlogn time algorithm to solve the 1 center problem and an o nlog 3n time algorithm to solve the weighted continuous 2 center problem we have also provided improved solutions to the general p center problems in cactus networks the developed ideas are then applied to solve the obnoxious 1 center problem in weighted cactus networks

leptokurtic and platykurtic class of robust symmetrical and asymmetrical time series models abstract in this study we examined the well known autoregressive time series model in which innovations follow the flexible class of two piece distributions based on the scale mixtures of normal tp smn family the mentioned class of distributions is a rich class of distributions family that covers the robust symmetric asymmetric light heavy tailed distributions a key feature of this study is using a new suitable hierarchical representation of the family to obtain the maximum likelihood estimates of the model parameters via an expectation maximization em type algorithm performances and usefulness of the proposed model and estimates are shown via simulation studies and a real dataset

covariance structure of the gibbs sampler with applications to the comparisons of estimators and augmentation schemes summary we study the covariance structure of a markov chain generated by the gibbs sampler with emphasis on data augmentation when applied to a bayesian missing data problem the gibbs sampler produces two natural approximations for the posterior distribution of the parameter vector the empirical distribution based on the sampled values of the parameter vector and a mixture of complete data posteriors we prove that rao blackwellization causes a one lag delay for the autocovariances among dependent samples obtained from data augmentation and consequently the mixture approximation produces estimates with smaller variances than the empirical approximation the covariance structure results are used to compare different augmentation schemes it is shown that collapsing and grouping random components in a gibbs sampler with two or three components usually result in more efficient sampling schemes

asymptotic convergence rate of the em algorithm for gaussian mixtures it is well known that the convergence rate of the expectation maximization em algorithm can be faster than those of convention first order iterative algorithms when the overlap in the given mixture is small but this argument has not been mathematically proved yet this article studies this problem asymptotically in the setting of gaussian mixtures under the theoretical framework of xu and jordan 1996 it has been proved that the asymptotic convergence rate of the em algorithm for gaussian mixtures locally around the true solution is o e0 5 e where e 0 is an arbitrarily small number o x means that it is a higher order infinitesimal as x 0 and e is a measure of the average overlap of gaussians in the mixture in other words the large sample local convergence rate for the em algorithm tends to be asymptotically superlinear when e tends to zero

algorithm to find a maximum 2 packing set in a cactus abstract in this paper we address the problem of finding a maximum 2 packing set in a cactus let g v g e g be an undirected connected graph then a subset s v g is a 2 packing set if for every pair of vertices u v s the shortest path between them is at least three edges long this type of sets results in a wide range of applications such as the study of molecules network modeling allocation of facilities and frequency assignment the cactus is a planar graph such that any edge belongs to at most one cycle hitherto to the best of the authors knowledge no algorithm finds a maximum 2 packing set in a cactus this problem is np hard in arbitrary graphs our approach to solving this problem was first finding a maximum 2 packing set in a unicyclic graph then we adapted this algorithm to run in a cactus the time complexity of the resulting algorithm is o n 2 where n v g

power analyses for correlations from clustered study designs power analysis constitutes an important component of modern clinical trials and research studies although a variety of methods and software packages are available almost all of them are focused on regression models with little attention paid to correlation analysis however the latter is arguably a simpler and more appropriate approach for modelling concurrent events especially in psychosocial research in this paper we discuss power and sample size estimation for correlation analysis arising from clustered study designs our approach is based on the asymptotic distribution of correlated pearson type estimates although this asymptotic distribution is easy to use in data analysis the presence of a large number of parameters creates a major problem for power analysis due to the lack of real data to estimate them by introducing a surrogacy type assumption we show that all nuisance parameters can be eliminated making it possible to perform power analysis based only on the parameters of interest simulation results suggest that power and sample size estimates obtained under the proposed approach are robust to this assumption copyright 2005 john wiley sons ltd

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

np completeness of st orientations for plane graphs an st orientation or bipolar orientation of a 2 connected graph g is an orientation of its edges to generate a directed acyclic graph with a single source s and a single sink t given a plane graph g and two exterior vertices s and t the problem of finding an optimum st orientation i e an st orientation in which the length of a longest st path is minimized was first proposed indirectly by rosenstiehl and tarjan in and then later directly by he and kao in in this paper we prove that given a 2 connected plane graph g two exterior vertices s t and a positive integer k the decision problem of whether g has an st orientation where the maximum length of an st path is k is np complete this solves a long standing open problem on the complexity of optimum st orientations for plane graphs as a by product we prove that the np completeness result holds for planar graphs as well

perfect slice samplers perfect sampling allows the exact simulation of random variables from the stationary measure of a markov chain by exploiting monotonicity properties of the slice sampler we show that a perfect version of the algorithm can be easily implemented at least when the target distribution is bounded various extensions including perfect product slice samplers and examples of applications are discussed