growing radial basis neural networks merging supervised and unsupervised learning with network growth techniques this paper proposes a framework for constructing and training radial basis function rbf neural networks the proposed growing radial basis function grbf network begins with a small number of prototypes which determine the locations of radial basis functions in the process of training the grbf network gross by splitting one of the prototypes at each growing cycle two splitting criteria are proposed to determine which prototype to split in each growing cycle the proposed hybrid learning scheme provides a framework for incorporating existing algorithms in the training of grbf networks these include unsupervised algorithms for clustering and learning vector quantization as well as learning algorithms for training single layer linear neural networks a supervised learning scheme based on the minimization of the localized class conditional variance is also proposed and tested grbf neural networks are evaluated and tested on a variety of data sets with very satisfactory results

existence of solutions to k n k 2 boundary value problems we provide very general existence criteria to solutions for a class of higher order boundary value problems our results supplement as well as improve several recent results established in the literature

analysis of rank measures of association for ordinal data from longitudinal studies abstract consideration is given to longitudinal data settings in which an ordinal response variable is observed at two or more visits for each subject in two or more ordered groups with at least moderately large sample sizes e g overall n 40 rank measures of association between group and response are constructed at each time and the covariance matrix of these measures is also estimated variation among the rank measures of association is then analyzed through weighted least squares methods with weights based on the estimated covariance matrix such methods permit evaluation of group visit interaction as well as other effects of interest extensions of this type of analysis to situations with stratification or concomitant variables or missing data are also considered examples are provided for illustrative purposes

deterministic neural classification this letter presents a minimum classification error learning formulation for a single layer feedforward network slfn by approximating the nonlinear counting step function using a quadratic function the classification error rate is shown to be deterministically solvable essentially the derived solution is related to an existing weighted least squares method with class specific weights set according to the size of data set by considering the class specific weights as adjustable parameters the learning formulation extends the classification robustness of the slfn without sacrificing its intrinsic advantage of being a closed form algorithm while the method is applicable to other linear formulations our empirical results indicate slfn s effectiveness on classification generalization

existence of positive solutions for non positive higher order bvps abstract we shall provide conditions on non positive function f t u 1 u n 1 so that the boundary value problem has at least one positive solution then we shall apply this result to establish several existence theorems which guarantee the multiple positive solutions

homogeneous linear predictor models for contingency tables maximum likelihood ml inference for the class of homogeneous linear predictor hlp models for contingency tables is described hlp models constrain the expected table counts m through l m x where the link l is allowed to be a many to one nonlinear function generalized log linear association trend marginal cumulative probit and conditional marginal homogeneity models are given as specific examples ml fit results which include point estimates goodness of fit statistics and asymptotic based approximate distributions are described and compared for equivalent hlp models the results are valid for a wide variety of sampling plans including combinations of product multinomial and poisson sampling an important practical implication of this article is that the implementation of ml fitting and theory is straightforward and an attractive alternative to weighted least squares estimation for hlp models

the green s function for k n k conjugate boundary value problems and its applications abstract a new integral representation of the green s function for k n k conjugate boundary value problems is obtained its applications are also given

local model network identification with gaussian processes a bayesian gaussian process gp modeling approach has recently been introduced to model based control strategies the estimate of the variance of the predicted output is the most useful advantage of gps in comparison to neural networks nns and fuzzy models however the gp model is computationally demanding and nontransparent to reduce the computation load and increase transparency a local linear gp model network is proposed in this paper the proposed methodology combines the local model network principle with the gp prior approach a novel algorithm for structure determination and optimization is introduced which is widely applicable to the training of local model networks the modeling procedure of the local linear gp lgp model network is demonstrated on an example of a nonlinear laboratory scale process rig

existence of positive solutions for n 2 order p laplacian bvp under some suitable assumptions we show that the n 2 order non linear boundary value problems bvp 1 e 1 f p u n t f t u t u 1 t u n 1 t bc 1 u i 0 0 i 0 1 2 n 3 u n 1 1 0u n 2 0 email protected n 1 h u n 1 0 email protected 1u n 1 x u n 1 email protected 1u n x and bvp 2 e 2 f p u n t f t u t u 1 t u n 1 t bc 2 u i 0 0 i 0 1 2 n 3 u n 1 0 0u n 2 1 email protected n 1 h u n 1 0 email protected 1u n 1 x u n 1 email protected 1u n x have at least two positive solutions in c n 0 1

markov chain monte carlo convergence diagnostics a comparative review abstract a critical issue for users of markov chain monte carlo mcmc methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest research into methods of computing theoretical convergence bounds holds promise for the future but to date has yielded relatively little of practical use in applied work consequently most mcmc users address the convergence problem by applying diagnostic tools to the output produced by running their samplers after giving a brief overview of the area we provide an expository review of 13 convergence diagnostics describing the theoretical basis and practical implementation of each we then compare their performance in two simple models and conclude that all of the methods can fail to detect the sorts of convergence failure that they were designed to identify we thus recommend a combination of strategies aimed at evaluating and accelerating mcmc sampler convergence including ap

automatic smoothing of regression functions in generalized linear models abstract we consider the penalized likelihood method for estimating nonparametric regression functions in generalized linear models nelder and wedderburn 1972 and present a generalized cross validation procedure for empirically assessing an appropriate amount of smoothing in these estimates asymptotic arguments and numerical simulations are used to show that the generalized cross validatory procedure preforms well from the point of view of a weighted mean squared error criterion the methodology adds to the battery of graphical tools for model building and checking within the generalized linear model framework included are two examples motivated by medical and horticultural applications

association marginal modeling of multivariate categorical responses a maximum likelihood approach abstract generalized log linear models can be used to describe the association structure and or the marginal distributions of multivariate categorical responses we simultaneously model the association structure and marginal distributions using association marginal am models which are specially formulated generalized log linear models that combine two models an association a model which describes the association among all the responses and a marginal m model which describes the marginal distributions of the responses because the model s composite link function is not required to be invertible a large class of models can be entertained and model specification is typically straightforward we propose a mixed freedom constraint parameterization that exploits the special structure of an am model using this parameterization maximum likelihood fitting is straightforward and typically feasible for large sparse tables when a parsimonious association model is used the size of the fitting proble

local existence of multiple positive solutions to a singular cantilever beam equation abstract by constructing suitable cone and control functions we prove some local existence theorems of positive solutions for a singular fourth order two point boundary value problem in mechanics the problem is called cantilever beam equation furthermore we improve a famous method appeared in the studies of singular boundary value problems the approximation theorem of completely continuous operators and the guo krasnosel skii fixed point theorem of cone expansion compression type play important parts in this work

modeling and inference for an ordinal effect size measure an ordinal measure of effect size is a simple and useful way to describe the difference between two ordered categorical distributions this measure summarizes the probability that an outcome from one distribution falls above an outcome from the other adjusted for ties we develop and compare confidence interval methods for the measure simulation studies show that with independent multinomial samples confidence intervals based on inverting the score test and a pseudo score type test perform well this score method also seems to work well with fully ranked data but for dependent samples a simple wald interval on the logit scale can be better with small samples we also explore how the ordinal effect size measure relates to an effect measure commonly used for normal distributions and we consider a logit model for describing how it depends on explanatory variables the methods are illustrated for a study comparing treatments for shoulder tip pain

computation with infinite neural networks for neural networks with a wide class of weight priors it can be shown that in the limit of an infinite number of hidden units the prior over functions tends to a gaussian process in this article analytic forms are derived for the covariance function of the gaussian processes corresponding to networks with sigmoidal and gaussian hidden units this allows predictions to be made efficiently using networks with an infinite number of hidden units and shows somewhat paradoxically that it may be easier to carry out bayesian prediction with infinite networks rather than finite ones

estimations of error bounds for neural network function approximators neural networks are being increasingly used for problems involving function approximation however a key limitation of neural methods is the lack of a measure of how much confidence can be placed in output estimates in the last few years many authors have addressed this shortcoming from various angles focusing primarily on predicting output bounds as a function of the trained network s characteristics typically as defined by the hessian matrix in this paper the problem of the effect of errors or noise in the presented input vector is examined and a method based on perturbation analysis of determining output bounds from the error in the input vector and the imperfections in the weight values after training is also presented and demonstrated

multivariate logistic models summary when data composed of several categorical responses together with categorical or continuous predictors are observed the multivariate logistic transform introduced by mccullagh and nelder can be used to define a class of regression models that is in many applications particularly suitable for relating the joint distribution of the responses to predictors in this paper we give a general definition of this class of models and study their properties a computational scheme for performing maximum likelihood estimation for data sets of moderate size is described and a system of model formulae that succinctly define particular models is introduced applications of these models to longitudinal problems are illustrated by numerical examples

multinomial poisson homogeneous models for contingency tables a unified approach to maximum likelihood inference for a broad new class of contingency table models is presented the model class comprises multinomial poisson homogeneous mph models which can be characterized by an independent sampling plan and a system of homogeneous constraints h m 0 where m is the vector of expected table counts maximum likelihood ml fitting and large sample inference for mph models are described the mph models are partitioned into well defined equivalence classes and explicit comparisons of the large sample behaviors of ml estimators of equivalent models are given the equivalence theory not only unifies a large collection of previously known results it also leads to useful generalizations and many new results the practical computational implication is that ml fit results for any particular mph model can be obtained directly from the ml fit results for any conveniently chosen equivalent model issues of hypothesis testability and parameter estimability are also addressed to illustrate an example based on statistics journal citation patterns is given for which the data can be used to test the hypothesis that a certain model holds but they cannot be used to estimate any of that model s parameters

existence of positive solutions for an n 2 order nonlinear bvp under some suitable assumptions we shall show that the n 2 order nonlinear boundary value problem bvp e f p u n t f t u t u 1 t u n 1 t bc u i 0 0 i 0 1 2 n 3 u n 2 0 email protected n 2 1 u n 1 1 email protected n 1 0 u n 0 email protected n d u n 1 email protected n d has at least three solutions in c n 0 1 n 2

a class of regression models for multivariate categorical responses summary when data composed of several categorical responses together with categorical or continuous predictors are observed it is often useful to relate the response probabilities to the predictors via a generalised linear model with a composite link function this paper discusses a class of link functions that lie between the two extremes of the multivariate logistic transform of mccullagh nelder 1989 and the log linear decomposition of contingency table analysis the models derived from these link functions are shown to inherit various desirable properties of both the multivariate logistic regression models and the log linear regression models a computational scheme for implementing these models is derived and they are demonstrated to be computationally more tractable than the multivariate logistic regression models their application is illustrated in a numerical example

polynomial based radial basis function neural networks p rbf nns realized with the aid of particle swarm optimization in this study we design polynomial based radial basis function neural networks p rbf nns based on a fuzzy inference mechanism the essential design parameters including learning rate momentum coefficient and fuzzification coefficient of the underlying clustering method are optimized by means of the particle swarm optimization the proposed p rbf nns dwell upon structural findings about training data that are expressed in terms of a partition matrix resulting from fuzzy clustering in this case being the fuzzy c means fcm the network is of functional nature as the weights between the hidden layer and the output are some polynomials the use of the polynomial weights becomes essential in capturing the nonlinear nature of data encountered in regression or classification problems from the perspective of linguistic interpretation the proposed network can be expressed as a collection of if then fuzzy rules the architecture of the networks discussed here embraces three functional modules reflecting the three phases of input output mapping realized in rule based architectures namely condition formation conclusion creation and aggregation the proposed classifier is applied to some synthetic and machine learning datasets and its results are compared with those reported in the previous studies

on eigenvalue intervals and twin eigenfunctions of higher order boundary value problems abstract in this paper we shall consider the boundary value problem y n q t y y 1 y n 2 p t y y 1 y n 2 n 2 t 1 1 y i 0 0 0 i n 3 y n 2 0 y n 1 0 0 yy n 2 1 y n 1 1 0 where 0 and are constants satisfying 0 0 0 and 0 intervals of are determined to ensure the existence of a positive solution of the boundary value problem for 1 we shall also offer criteria for the existence of two positive solutions of the boundary value problem in addition upper and lower bounds for these positive solutions are obtained for special cases several examples are included to dwell upon the importance of the results obtained

a novel radial basis function neural network for discriminant analysis a novel radial basis function neural network for discriminant analysis is presented in this paper in contrast to many other researches this work focuses on the exploitation of the weight structure of radial basis function neural networks using the bayesian method it is expected that the performance of a radial basis function neural network with a well explored weight structure can be improved as the weight structure of a radial basis function neural network is commonly unknown the bayesian method is therefore used in this paper to study this a priori structure two weight structures are investigated in this study i e a single gaussian structure and a two gaussian structure an expectation maximization learning algorithm is used to estimate the weights the simulation results showed that the proposed radial basis function neural network with a weight structure of two gaussians outperformed the other algorithms

classification of faces in man and machine we attempt to shed light on the algorithms humans use to classify images of human faces according to their gender for this a novel methodology combining human psychophysics and machine learning is introduced we proceed as follows first we apply principal component analysis pca on the pixel information of the face stimuli we then obtain a data set composed of these pca eigenvectors combined with the subjects gender estimates of the corresponding stimuli second we model the gender classification process on this data set using a separating hyperplane sh between both classes this sh is computed using algorithms from machine learning the support vector machine svm the relevance vector machine the prototype classifier and the k means classifier the classification behavior of humans and machines is then analyzed in three steps first the classification errors of humans and machines are compared for the various classifiers and we also assess how well machines can recreate the subjects internal decision boundary by studying the training errors of the machines second we study the correlations between the rank order of the subjects responses to each stimulus the gender estimate with its reaction time and confidence rating and the rank order of the distance of these stimuli to the sh finally we attempt to compare the metric of the representations used by humans and machines for classification by relating the subjects gender estimate of each stimulus and the distance of this stimulus to the sh while we show that the classification error alone is not a sufficient selection criterion between the different algorithms humans might use to classify face stimuli the distance of these stimuli to the sh is shown to capture essentials of the internal decision space of humans furthermore algorithms such as the prototype classifier using stimuli in the center of the classes are shown to be less adapted to model human classification behavior than algorithms such as the svm based on stimuli close to the boundary between the classes

approximation of nonlinear systems with radial basis function neural networks a technique for approximating a continuous function of n variables with a radial basis function rbf neural network is presented the method uses an n dimensional raised cosine type of rbf that is smooth yet has compact support the rbf network coefficients are low order polynomial functions of the input a simple computational procedure is presented which significantly reduces the network training and evaluation time storage space is also reduced by allowing for a nonuniform grid of points about which the rbfs are centered the network output is shown to be continuous and have a continuous first derivative when the network is used to approximate a nonlinear dynamic system the resulting system is bounded input bounded output stable for the special case of a linear system the rbf network representation is exact on the domain over which it is defined and it is optimal in terms of the number of distinct storage parameters required several examples are presented which illustrate the effectiveness of this technique

simultaneous clustering and classification over cluster structure representation two main tasks in pattern recognition area are clustering and classification owing to their different goals traditionally these two tasks are treated separately however when label information is available such separate treatment can not fully explore data information first classification is not favored by the data cluster structure second clustering is not guided by valuable label information third the relationship of clusters and classes is not revealed contrary to this separate learning treatment simultaneous learning clustering and classification could benefit each other and overcomes these problems recently a simultaneous learning framework scc was proposed through modeling p class cluster classification and clustering mechanism in scc depend only on cluster centroids however it produces severely nonlinear objective thus has to use a heuristic searching method modified particle swarm optimization to find the optimal solution but it is very slow further modeling p class cluster makes scc hard to incorporate semi supervised settings in this paper we propose an alternative framework sc 3sr for simultaneous learning besides a classifier derived on the original data another classifier on the newly formed cluster structure representation is derived as well through this classifier the clustering learning is guided by the label and classification learning is also favored by cluster structure of data the final objective is continuously differentiable for which some principled optimization algorithms with convergence guaranteed exist as a result our algorithm is much faster than scc further we generalize this framework to semisupervised situation with the idea of manifold regularization and propose semisc 3sr algorithm our experiments demonstrate the effectiveness of both sc 3sr and semisc 3sr

the fisher information matrix for log linear models arguing conditionally on observed explanatory variable summary for poisson or multinomial contingency table data the conditional distribution is product multinomial when conditioning on observed values of explanatory variables birch 1963 showed that under the restriction formed by keeping the marginal totals of one margin fixed at their observed values the poisson multinomial and product multinomial likelihoods are proportional and give the same estimates for common parameters in the log linear model here the inverses of the fisher information matrices are shown to be identical over common parameters so that the asymptotic covariance matrices of the estimates correspond

a comparison of gcv and gml for choosing the smoothing parameter in the generalized spline smoothing problem the partially improper prior behind the smoothing spline model is used to obtain a generalization of the maximum likelihood gml estimate for the smoothing parameter then this estimate is compared with the generalized cross validation gcv estimate both analytically and by monte carlo methods the comparison is based on a predictive mean square error criteria it is shown that if the true unknown function being estimated is smooth in a sense to be defined then the gml estimate undersmooths relative to the gcv estimate and the predictive mean square error using the gml estimate goes to zero at a slower rate than the mean square error using the gcv estimate if the true function is rough then the gcv and gml estimates have asymptotically similar behavior a monte carlo experiment was designed to see if the asymptotic results in the smooth case were evident in small sample sizes mixed results were obtained for n 32 gcv was somewhat better than gml for n 64 and gcv was decidedly superior for n 128 in the n 32 case gcv was better for smaller sigma 2 and the comparison close for larger sigma 2 the theoretical results are shown to extend to the generalized spline smoothing model which includes the estimate of functions given noisy values of various integrals of them

maximum likelihood estimation in log linear models we study maximum likelihood estimation in log linear models under conditional poisson sampling schemes we derive necessary and sufficient conditions for existence of the maximum likelihood estimator mle of the model parameters and investigate estimability of the natural and mean value parameters under a nonexistent mle our conditions focus on the role of sampling zeros in the observed table we situate our results within the framework of extended exponential families and we exploit the geometric properties of log linear models we propose algorithms for extended maximum likelihood estimation that improve and correct the existing algorithms for log linear model analysis

testing conditional independence in sets of i j tables by means of moment and correlation score tests with application to hpv vaccine a new testing approach is described for improving statistical tests of independence in sets of tables stratified on one or more relevant factors in case of categorical nominal or ordinal variables common tests of independence that exploit the ordinality of one of the variables use a restricted alternative approach a different relaxed null method is presented specifically the m moment score tests and the correlation tests are introduced using multinomial poisson homogeneous modeling theory it is shown that these tests are computationally and conceptually simple and simulation results suggest that they can perform better than other common tests of conditional independence to illustrate the proposed tests are used to better understand the human papillomavirus type specific infection by exploring the intention to vaccinate copyright 2016 john wiley sons ltd

maximum likelihood methods for a generalized class of log linear models we discuss maximum likelihood methods for fitting a broad class of multivariate categorical response data models in particular we derive the large sample distributions for maximum likelihood estimators of parameters of product multinomial generalized log linear models the large sample behavior of other relevant likelihood based statistics such as goodness of fit statistics and adjusted residuals is also described the asymptotic results are derived within the framework of the constraint specification rather than the more common freedom specification of the model we also outline an improved fitting algorithm for computing parameter maximum likelihood estimates and other relevant statistics the broad class of multivariate categorical response data models which are referred to as generalized log linear models can imply structure on several response configuration distributions e g joint and marginal distributions these models which include as special cases log linear logit and cumulative logit models enjoy a wide breadth of application including longitudinal rater agreement and crossover data analyses

positive solutions to semipositone k n k conjugate eigenvalue problems abstract in this paper we consider the existence of positive solutions to the following semipositone k n k conjugate eigenvalue problems scep 1 n k u n t f t u t 0 t 1 u i 0 0 0 i k 1 u j 1 0 0 j n k 1 where n 2 1 k n 1 and 0 is positive parameter the nonlinear function f may change sign for 0 t 1 i e we allow that the nonlinear term f is both semipositone and lower unbounded without making any monotone type assumptions by using the fixed point index theory we derive an explicit interval of such that for any in this interval the existence of at least one positive solution to the boundary value problem is guaranteed and the existence of at least two solutions for in an appropriate interval is also discussed

simultaneously modeling joint and marginal distributions of multivariate categorical responses abstract we discuss model fitting methods for analyzing simultaneously the joint and marginal distributions of multivariate categorical responses the models are members of a broad class of generalized logit and loglinear models we fit them by improving a maximum likelihood algorithm that uses lagrange s method of undetermined multipliers and a newton raphson iterative scheme we also discuss goodness of fit tests and adjusted residuals and give asymptotic distributions of model parameter estimators for this class of models inferences are equivalent for poisson and multinomial sampling assumptions simultaneous models for joint and marginal distributions may be useful in a variety of applications including studies dealing with longitudinal data multiple indicators in opinion research cross over designs social mobility and inter rater agreement the models are illustrated for one such application using data from a recent general social survey regarding opinions about various types of government s

score and profile likelihood confidence intervals for contingency table parameters a straightforward approach to computing score and profile likelihood confidence intervals for contingency table parameters is described the computational approach herein avoids two main limitations of existing methods 1 compared with existing methods this paper s approach is applicable to a much broader class of parameters 2 unlike existing methods this paper s approach is not case specific and hence lends itself to a general yet very simple computational algorithm this paper describes the sliding quadratic computational algorithm and illustrates its use on examples that have not been previously considered in the literature a small scale simulation study highlights the advantage of using score and profile likelihood intervals rather than wald intervals

efficient relighting of rbf based illumination adjustable images an illumination adjustable image iai contains a large number of prerecorded images under various light directions relighting a scene under complicated lighting conditions can be achieved from the iai using the radial basis function rbf approach to represent an iai is proven to be more efficient than using the spherical harmonic approach however to represent high frequency lighting effects we need to use many rbfs hence the relighting speed could be very slow this brief investigates a partial reconstruction scheme for relighting an iai based on the locality of rbfs compared with the conventional rbf and spherical harmonics sh approaches the proposed scheme has a much faster relighting speed under the similar distortion performance

bayesian generalized kernel mixed models we propose a fully bayesian methodology for generalized kernel mixed models gkmms which are extensions of generalized linear mixed models in the feature space induced by a reproducing kernel we place a mixture of a point mass distribution and silverman s g prior on the regression vector of a generalized kernel model gkm this mixture prior allows a fraction of the components of the regression vector to be zero thus it serves for sparse modeling and is useful for bayesian computation in particular we exploit data augmentation methodology to develop a markov chain monte carlo mcmc algorithm in which the reversible jump method is used for model selection and a bayesian model averaging method is used for posterior prediction when the feature basis expansion in the reproducing kernel hilbert space is treated as a stochastic process this approach can be related to the karhunen loeve expansion of a gaussian process gp thus our sparse modeling framework leads to a flexible approximation method for gps

orthogonal least squares learning algorithm for radial basis function networks the radial basis function network offers a viable alternative to the two layer neural network in many applications of signal processing a common learning algorithm for radial basis function networks is based on first choosing randomly some data points as radial basis function centers and then using singular value decomposition to solve for the weights of the network such a procedure has several drawbacks and in particular an arbitrary selection of centers is clearly unsatisfactory the authors propose an alternative learning procedure based on the orthogonal least squares method the procedure chooses radial basis function centers one by one in a rational way until an adequate network has been constructed in the algorithm each selected center maximizes the increment to the explained variance or energy of the desired output and does not suffer numerical ill conditioning problems the orthogonal least squares learning strategy provides a simple and efficient means for fitting radial basis function networks this is illustrated using examples taken from two different signal processing applications

learning simultaneous adaptive clustering and classification via moea clustering learning and classification learning are two major tasks in pattern recognition the traditional hybrid clustering and classification algorithms handle them in a sequential way rather than a simultaneous way fortunately multiobjective optimization provides a way to solve this problem in this paper an algorithm that learns simultaneous clustering and classification adaptively via multiobjective evolutionary algorithm is proposed the main idea of this paper is to optimize two objective functions which represent fuzzy cluster connectedness and classification error rate to achieve the goal of simultaneous learning firstly we adopt a graph based representation scheme to encode so that it can generate a set of solutions with different number of clusters in a single run then the relationship between clustering and classification is built via the bayesian theory during the optimization process the quality of clustering and classification is measured by the objective functions and the feedback drawn from both aspects is used to guide the mutation at last a set of nondominated solutions are generated from which the final pareto optimal solution is selected by using adjusted rand index the results on synthetic datasets and real life datasets demonstrate the rationality and effectiveness of the proposed algorithm furthermore we apply the proposed algorithm to image segmentation including texture images and synthetic aperture radar images the experimental results show the superiority of the proposed algorithm compared with other five algorithms highlightsa simultaneous adaptive clustering and classification learning via moea is proposed new clustering objective function is designed and two objective functions complement with each other the number of clusters can be determined adaptively during the learning process the drawback from clustering classification learning is used to guide the search we extend it to texture image and sar image segmentation to show its effectiveness

simultaneous confidence intervals using ordinal effect measures for ordered categorical outcomes when outcomes are ordered categorical a model using an ordinal effect size measure is a good alternative of the cumulative logit model to compare several independent group differences we present a method of constructing simultaneous confidence intervals for the ordinal effect size measures using the studentized range distribution with the score test statistic a simulation study shows that the proposed method performs well in terms of coverage probability and it seems better than the method using a bonferroni correction for wald type statistics and methods that account for the dependencies among pairwise ordinal effect size measures using the multivariate normal distribution or the multivariate t distribution for small samples

maximum likelihood methods for log linear models when expected frequencies are subject to linear constraints abstract hypotheses relating to log linear models may be defined in terms of constraints on the frequencies or on the logarithms of the frequencies a two step algorithm is developed to allow fitting models containing constraints of both types this algorithm is shown to yield maximum likelihood estimates of the log linear parameters three examples are presented to illustrate cases in which these models are of interest

pseudo score confidence intervals for parameters in discrete statistical models we propose pseudo score confidence intervals for parameters in models for discrete data the confidence interval is obtained by inverting a test that uses a pearson chi squared statistic to compare fitted values for the working model with fitted values of the model when a parameter of interest takes various fixed values for multinomial models the pseudo score method simplifies to the score method when the model is saturated and otherwise it is asymptotically equivalent to score and likelihood ratio test based inferences for cases in which ordinary score methods are impractical such as when the likelihood function is not an explicit function of model parameters the pseudo score method is feasible we illustrate the method for four such examples generalizations of the method are also presented for future research including inference for complex sampling designs using a quasilikelihood pearson statistic that compares fitted values for two models relative to the variance of the observations under the simpler model

maximum likelihood estimation of models for residual covariance in spatial regression we describe the maximum likelihood method for fitting the linear model when residuals are correlated and when the covariance among the residuals is determined by a parametric model containing unknown parameters observations are assumed to be gaussian we give conditions which ensure consistency and asymptotic normality of the estimators our main concern is with the analysis of spatial data and in this context we describe some simulation experiments to assess the small sample behaviour of estimators we also discuss an application of the spectral approximation to the likelihood for processes on a lattice

computing average shaped tissue probability templates this note presents a framework for generating tissue probability maps that represent the average shape of a number of subjects brain images the procedure is formulated as finding maximum a posteriori estimates within a probabilistic generative model estimating the parameters involves alternating between estimating the deformations that match tissue class images of individual subjects to template and updating the template according to the latest estimates of the deformations a multinomial matching criterion is used such that multiple tissue class images e g grey and white matter are registered simultaneously with the current template estimate in order to generalise the resulting template to a broader range of subjects a template blurriness prior is included within the model

bayesian classification with gaussian processes we consider the problem of assigning an input vector to one of m classes by predicting p c x for c 1 m for a two class problem the probability of class one given x is estimated by spl sigma y x where spl sigma y 1 1 e sup y a gaussian process prior is placed on y x and is combined with the training data to obtain predictions for new x points we provide a bayesian treatment integrating over uncertainty in y and in the parameters that control the gaussian process prior the necessary integration over y is carried out using laplace s approximation the method is generalized to multiclass problems m 2 using the softmax function we demonstrate the effectiveness of the method on a number of datasets

rbf neural network center selection based on fisher ratio class separability measure for classification applications the role of hidden layer neurons of a radial basis function rbf neural network can be interpreted as a function which maps input patterns from a nonlinear separable space to a linear separable space in the new space the responses of the hidden layer neurons form new feature vectors the discriminative power is then determined by rbf centers in the present study we propose to choose rbf centers based on fisher ratio class separability measure with the objective of achieving maximum discriminative power we implement this idea using a multistep procedure that combines fisher ratio an orthogonal transform and a forward selection search method our motivation of employing the orthogonal transform is to decouple the correlations among the responses of the hidden layer neurons so that the class separability provided by individual rbf neurons can be evaluated independently the strengths of our method are double fold first our method selects a parsimonious network architecture second this method selects centers that provide large class separation