an efficient semiparametric estimator for binary response models this paper proposes an estimator for discrete choice models that makes no assumption concerning the functional form of the choice probability function where this function can be characterized by an index the estimator is shown to be consistent asymptotically normally distributed and to achieve the semiparametric efficiency bound monte carlo evidence indicates that there may be only modest efficiency losses relative to maximum likelihood estimation when the distribution of the disturbances is known and that the small sample behavior of the estimator in other cases is good

a new skewed link model for dichotomous quantal response data abstract the logit probit and student t links are widely used in modeling dichotomous quantal response data most of the commonly used link functions are symmetric except the complementary log log link however in some applications the overall fit can be significantly improved by the use of an asymmetric link in this article we propose a new skewed link model for analyzing binary response data with covariates introducing a skewed distribution for the underlying latent variable we develop a class of asymmetric link models for binary response data using a bayesian approach we first characterize the propriety of the posterior distributions using standard improper priors we further propose informative priors using historical data from a similar previous study we examine the proposed method through a large scale simulation study and use data from a prostate cancer study to demonstrate the use of historical data in bayesian model fitting and comparison of skewed link models

inference for mixtures of finite polya tree models mixtures of polya tree models provide a flexible alternative when a parametric model may only hold approximately i provide computational strategies for obtaining full semiparametric inference for mixtures of finite polya tree models given a standard parameterization including models that would be troublesome to fit using dirichlet process mixtures recommendations are put forth on choosing the level of a finite polya tree and model comparison is discussed several examples demonstrate the utility of finite polya tree modeling including data fit to generalized linear mixed models and several survival models

parametric links for binary choice models a fisherian bayesian colloquy abstract the familiar logit and probit models provide convenient settings for many binary response applications but a larger class of link functions may be occasionally desirable two parametric families of link functions are investigated the gosset link based on the student t latent variable model with the degrees of freedom parameter controlling the tail behavior and the pregibon link based on the generalized tukey family with two shape parameters controlling skewness and tail behavior both bayesian and maximum likelihood methods for estimation and inference are explored compared and contrasted in applications like the propensity score matching problem discussed below where it is critical to have accurate estimates of the conditional probabilities we find that misspecification of the link function can create serious bias bayesian point estimation via mcmc performs quite competitively with mle methods however nominal coverage of bayes credible regions is somewhat more problematic

estimating normal means with a dirichlet process prior abstract in this article the dirichlet process prior is used to provide a nonparametric bayesian estimate of a vector of normal means in the past there have been computational difficulties with this model this article solves the computational difficulties by developing a gibbs sampler algorithm the estimator developed in this article is then compared to parametric empirical bayes estimators peb and nonparametric empirical bayes estimators npeb in a monte carlo study the monte carlo study demonstrates that in some conditions the peb is better than the npeb and in other conditions the npeb is better than the peb the monte carlo study also shows that the estimator developed in this article produces estimates that are about as good as the peb when the peb is better and produces estimates that are as good as the npeb estimator when that method is better

ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

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

on the consistency of bayes estimates on etudie les proprietes de frequence des regles de bayes avec une attention particuliere a la consistence

an adaptive support vector regression based on a new sequence of unified orthogonal polynomials in practical engineering small scale data sets are usually sparse and contaminated by noise in this paper we propose a new sequence of orthogonal polynomials varying with their coefficient unified chebyshev polynomials ucp which has two important properties namely orthogonality and adaptivity based on these new polynomials a new kernel function the unified chebyshev kernel uck is constructed which has been proven to be a valid svm kernel to find the optimal polynomial coefficient and the optimal kernel we propose an adaptive algorithm based on the evaluation criterion for adaptive ability of uck to evaluate the performance of the new method we applied it to learning some benchmark data sets for regression and compared it with other three algorithms the experiment results show that the proposed adaptive algorithm has excellent generalization performance and prediction accuracy and does not cost more time compared with other svms therefore this method is suitable for practical engineering application

a boltzmann based estimation of distribution algorithm this paper introduces a new approach for estimation of distribution algorithms called the boltzmann univariate marginal distribution algorithm bumda it uses a normal gaussian model to approximate the boltzmann distribution hence formulae for computing the mean and variance parameters of the gaussian model are derived from the analytical minimization of the kullback leibler divergence the resulting formulae explicitly introduces information about the fitness landscape for the gaussian parameters computation in consequence the gaussian distribution obtains a better bias to sample intensively the most promising regions than simply using the maximum likelihood estimator of the selected set in addition the bumda formulae needs only one user parameter accordingly to the experimental results the bumda excels in its niche of application we provide theoretical graphical and statistical analysis to show the bumda performance contrasted with state of the art edas

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

generalized logistic models abstract a class of models indexed by two shape parameters is introduced both to extend the scope of the standard logistic model to asymmetric probability curves and improve the fit in the noncentral probability regions one parameter subclasses can be used to examine symmetric or asymmetric deviations from the logistic model the delta algorithm is adapted to obtain maximum likelihood estimates of the parameters a review is made of other proposed generalizations the standard linear logistic model is widely used for modeling the dependence of binary data on explanatory variables its success is due to its broad applicability simplicity of form and ease of interpretation this model works well for many common applications however it assumes that the expected probability curve is skew symmetric about and that the shape of is the cumulative distribution function of the logistic distribution symmetric data with a shallower or steeper slope of ascent may not be fitted well by this model

markov chains for exploring posterior distributions several markov chain methods are available for sampling from a posterior distribution two important examples are the gibbs sampler and the metropolis algorithm in addition several strategies are available for constructing hybrid algorithms this paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues on the theoretical side results from the theory of general state space markov chains can be used to obtain convergence rates laws of large numbers and central limit theorems for estimates obtained from markov chain methods these theoretical results can be used to guide the construction of more efficient algorithms for the practical use of markov chain methods standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation

a bayesian approach to robust binary nonparametric regression abstract this article presents a bayesian approach to binary nonparametric regression that assumes that the argument of the link is an additive function of the explanatory variables and their multiplicative interactions the article makes the following contributions first a comprehensive approach is presented in which the function estimates are smoothing splines with the smoothing parameters integrated out and the estimates are made robust to outliers second the approach can handle a wide range of link functions third efficient state space based algorithms are used to carry out the computations fourth an extensive set of simulations is carried out which show that the bayesian estimator works well and compares favorably to two estimators that have recently been proposed and used in practice

modeling dose and local control in radiotherapy abstract we discuss models for predicting local control prevention of tumor recurrence after therapeutic radiation in cancer patients the probability of control is first formulated from theoretical precepts biophysical principles dictate that the three factors in therapy that most universally influence outcome are total dose number of sessions in which the dose is administered and total time under treatment we show that these principles also suggest the scale or link function on which local control probability for a tumor of given size is a linear function of these predictors the probabilities are given clinical relevance by assigning a mixing distribution to tumor size effective size the number of actively dividing cells in a tumor is an unmeasurable but of course quite influential quantity we show in this case that a gamma distribution on tumor size induces linearity on a subset of the class of links first proposed by burr next we discuss methods of modeling control by a finite follow up

simultaneous feature selection and gaussian mixture model estimation for supervised classification problems abstract a new expectation maximization em algorithm for time critical supervised classification tasks in remote sensing is proposed compared to standard em and other approaches it has the following advantages 1 no knowledge about the class distributions is needed 2 the number of components is estimated 3 it does not require careful initialization 4 singular estimates are avoided due to the ability of pruning components 5 the best discriminating features are identified simultaneously 6 the features are identified by incorporating mahalanobis distances three experiments are carried out in order to demonstrate the relevance of the method the main findings are the following 1 feature selection is very important in terms of prediction quality of models 2 in the experiments the proposed method estimates better models than other state of the art methods 3 the incorporation of mahalanobis distances is very valuable for the identification of relevant features 4 the proposed method is more robust than the compared methods 5 in case of complex data distributions the new approach is able to provide better results

new hermite orthogonal polynomial kernel and combined kernels in support vector machine classifier support vector machine is a desired method for classification of different types of data but the main obstacle to using this method is the considerable reduction of classification speed upon increase in the size of problem in this paper a new kernel function is proposed for svm which is derived from hermite orthogonal polynomials this function improves classification accuracy as well as reduction in the number of support vectors and increases the classification speed the overall kernel performance has been evaluated on real world data sets from uci repository by the ten fold cross validation method the combinations of hermite function with common kernels are proposed in this paper experimental results reveal that the hermite chebyshev kernel which is obtained from combination of hermite and chebyshev kernel has the best performance in the number of support vectors and hermite gussian kernel that is produced from combination hermite and gussian kernel has the first rank in the error rate among all experimental kernels on the other hand the hermite proposed method has the least number of support vectors and best performance in the error rate in comparison with common kernels and lowest required time among all kernels a new kernel function has been proposed by using hermite orthogonal polynomial new combined kernels resulted by combining hermite and common kernels have been proposed the proposed methods have been compared with three common kernels on real and synthetic data sets hermite kernel function has the lowest required time for classification the proposed methods yield better error rate and they have the best support vectors reduction significantly

feature selection based on the approximation of class densities by finite mixtures of special type abstract a new method of feature selection based on the approximation of class conditional densities by a mixture of parameterized densities of a special type suitable especially for multimodal data is presented no search procedure is needed when using the proposed method its performance is tested both on real simulated data

distribution free maximum likelihood estimator of the binary choice model1 is a given function of the exogenous variables z and unknown parameters 9 representing the systematic component of the utility difference and f is the distribution function of the random component of the utility difference this paper describes a method of estimating the parameters 9 without assuming any functional form for the distribution function f and proves that this estimator is consistent f is also consistently estimated the method uses maximum likelihood estimation in which the likelihood is maximized not only over the parameter 9 but also over a space which contains all distribution functions

a novel lyapunov function for a non weighted l2 gain of asynchronously switched linear systems abstract in this paper a novel lyapunov function is proposed to study switched linear systems with a switching delay between activation of system modes and activation of candidate controller modes the novelty consists in continuity of the lyapunov function at the switching instants and discontinuity when the system modes and controller modes are matched this structure is exploited to construct a time varying lyapunov function that is non increasing at time instants of discontinuity stability criteria based on the novel lyapunov function are developed to guarantee global asymptotic stability in the noiseless case most importantly when exogenous disturbances are considered the proposed lyapunov function can be used to guarantee a finite non weighted l 2 gain for asynchronously switched systems for which lyapunov functions proposed in literature are inconclusive a numerical example illustrates the effectiveness of the proposed method

a semi parametric bayesian approach to generalized linear mixed models summary the linear mixed e ects model with normal errors is a popular model for the analysis of repeated measures and longitudinal data the generalized linear model is useful for data that have non normal errors but where the errors are uncorrelated a descendant of these two models generates a model for correlated data with non normal errors called the generalized linear mixed model glmm frequentist attempts to fit these models generally rely on approximate results and inference relies on asymptotic assumptions recent advances in computing technology have made bayesian approaches to this class of models computationally feasible markov chain monte carlo methods can be used to obtain exact inference for these models as demonstrated by zeger and karim 6 in the linear or generalized linear mixed model the random e ects are typically taken to have a fully parametric distribution such as the normal distribution in this paper we extend the glmm by allowing the random e ects to have a non parametric prior distribution we do this using a dirichlet process prior for the general distribution of the random e ects the approach easily extends to more general population models we perform computations for the models using the gibbs sampler 1998 john wiley sons ltd

unsupervised learning of finite mixture models this paper proposes an unsupervised algorithm for learning a finite mixture model from multivariate data the adjective unsupervised is justified by two properties of the algorithm 1 it is capable of selecting the number of components and 2 unlike the standard expectation maximization em algorithm it does not require careful initialization the proposed method also avoids another drawback of em for mixture fitting the possibility of convergence toward a singular estimate at the boundary of the parameter space the novelty of our approach is that we do not use a model selection criterion to choose one among a set of preestimated candidate models instead we seamlessly integrate estimation and model selection in a single algorithm our technique can be applied to any type of parametric mixture model for which it is possible to write an em algorithm in this paper we illustrate it with experiments involving gaussian mixtures these experiments testify for the good performance of our approach

generalized linear models with unknown link functions function by incorporating it as an unknown in the model since the link function is usually taken to be strictly increasing by a strictly increasing transformation of its range to the unit interval we can model it as a strictly increasing cumulative distribution function the transformation results in a domain which is 0 1 we model the cumulative distribution function as a mixture of beta cumulative distribution functions noting that the latter family is dense within the collection of all continuous densities on 0 1 for the fitting of the model we take a bayesian approach encouraging vague priors to focus upon the likelihood we discuss choices of such priors as well as the integrability of the resultant posteriors implementation of the bayesian approach is carried out using sampling based methods in particular a tailored metropolis within gibbs algorithm an illustrative example utilising data involving wave damage to cargo ships is provided

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

flexible link functions in nonparametric binary regression with gaussian process priors in many scientific fields it is a common practice to collect a sequence of 0 1 binary responses from a subject across time space or a collection of covariates researchers are interested in finding out how the expected binary outcome is related to covariates and aim at better prediction in the future 0 1 outcomes gaussian processes have been widely used to model nonlinear systems in particular to model the latent structure in a binary regression model allowing nonlinear functional relationship between covariates and the expectation of binary outcomes a critical issue in modeling binary response data is the appropriate choice of link functions commonly adopted link functions such as probit or logit links have fixed skewness and lack the flexibility to allow the data to determine the degree of the skewness to address this limitation we propose a flexible binary regression model which combines a generalized extreme value link function with a gaussian process prior on the latent structure bayesian computation is employed in model estimation posterior consistency of the resulting posterior distribution is demonstrated the flexibility and gains of the proposed model are illustrated through detailed simulation studies and two real data examples empirical results show that the proposed model outperforms a set of alternative models which only have either a gaussian process prior on the latent regression function or a dirichlet prior on the link function

moment conditions and bayesian non parametrics models phrased through moment conditions are central to much of modern inference here these moment conditions are embedded within a non parametric bayesian set up handling such a model is not probabilistically straightforward as the posterior has support on a manifold we solve the relevant issues building new probability and computational tools by using hausdorff measures to analyse them on real and simulated data these new methods which involve simulating on a manifold can be applied widely including providing bayesian analysis of quasi likelihoods linear and non linear regression missing data and hierarchical models

bayesian nonparametric estimation of the median part i computation of the estimates let x i i 1 ldots n be i i d sim f theta where f theta x f x theta for some f that has median equal to 0 f is assumed unknown or only partially known and the problem is to estimate theta priors are put on the pair f theta the priors on f concentrate all their mass on c d f s with median equal to 0 these priors include dirichlet type priors the marginal posterior distribution of theta given x 1 ldots x n is computed the mean of the posterior is taken as the estimate of theta

a novel formulation of orthogonal polynomial kernel functions for svm classifiers the gegenbauer family abstract orthogonal polynomial kernels have been recently introduced to enhance support vector machine classifiers by reducing their number of support vectors previous works have studied these kernels as isolated cases and discussed only particular aspects in this paper a novel formulation of orthogonal polynomial kernels that includes and improves previous proposals legendre chebyshev and hermite is presented two undesired effects that must be avoided in order to use orthogonal polynomial kernels are identified and resolved the annihilation and the explosion effects the proposed formulation is studied by means of introducing a new family of orthogonal polynomial kernels based on gegenbauer polynomials and comparing it against other kernels experimental results reveal that the gegenbauer family competes with the rbf kernel in accuracy while requiring fewer support vectors and overcomes other classical and orthogonal kernels

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

exploiting the relationships among several binary classifiers via data transformation the structural resemblance among several existing classifiers has motivated us to investigate their underlying relationships by exploring into the mapping solutions of these classifiers we found that they can be linked by simple feature data scaling in other words the key to these relationships lies upon how the replica of feature data are being scaled this finding leads us directly to an exploration of novel classifiers beyond existing settings based on an extensive empirical evaluation we show that the proposed formulation facilitates a tuning capability beyond existing settings for classifier generalization highlightsestablishment of relationship among several binary classifiers exploration of a random projection network for such classifier learning proposal of novel classifier which exploits the established relationship observe the performance of novel classifier on several performance measures

generalizing logistic regression by nonparametric mixing abstract logistic regression is a common technique for analyzing the effect of a covariate vector x on the number of successes y in m trials when y has a binomial distribution but at times either the logistic curve does not describe the probability of success p x adequately or m is larger than 1 and y is more variable than the binomial distribution allows overdispersion relative to the binomial distribution is possible if the m trials in a set or litter are positively correlated an important covariate is omitted or x is measured with error a simple way to accommodate departures from the logit link and overdispersion is to introduce a random intercept and thus permit a random propensity toward success when varies between individual binary trials according to a discrete or multimodal distribution p x has smooth steps and y has a binomial m p x distribution when the random is constant for a set of m binary trials and varies between sets of m trials according to a discrete or multimodal

unsupervised clustering and feature weighting based on generalized dirichlet mixture modeling abstract we propose a possibilistic approach for generalized dirichlet mixture parameter estimation data clustering and feature weighting the proposed algorithm called robust and unsupervised learning of finite generalized dirichlet mixture models rule gdm exploits a property of the generalized dirichlet distributions that transforms the data to make the features independent and follow beta distributions then it learns optimal relevance weights for each feature within each cluster this property makes rule gdm suitable for noisy and high dimensional feature spaces in addition rule gdm associates two types of memberships with each data sample the first one is the posterior probability and indicates how well a sample fits each estimated distribution the second membership represents the degree of typicality and is used to identify and discard noise points and outliers rule gdm minimizes one objective function which combines learning the two membership functions distribution parameters and the relevance weights for each feature within each distribution we also extend our algorithm to find the optimal number of clusters in an unsupervised and efficient way by exploiting some properties of the possibilistic membership function the performance of rule gdm is illustrated and compared to similar algorithms we use synthetic data to illustrate its robustness to noisy and high dimensional features we also compare our approach to other relevant algorithms using several standard data sets

minimally informative prior distributions for non parametric bayesian analysis summary we address the problem of how to conduct a minimally informative non parametric bayesian analysis the central question is how to devise a model so that the posterior distribution satisfies a few basic properties the concept of local mass provides the key to the development of the limiting dirichlet process model this model is then used to provide an engine for inference in the compound decision problem and for multiple comparisons inference in a one way analysis of variance setting our analysis in this setting may be viewed as a limit of the analyses that were developed by escobar and by gopalan and berry computations for the analysis are described and the predictive performance of the model is compared with that of mixture of dirichlet processes models

bayesian nonparametric estimation for incomplete data via successive substitution sampling in the problem of estimating an unknown distribution function f in the presence of censoring one can use a nonparametric estimator such as the kaplan meier estimator or one can consider parametric modeling there are many situations where physical reasons indicate that a certain parametric model holds approximately in these cases a nonparametric estimator may be very inefficient relative to a parametric estimator on the other hand if the parametric model is only a crude approximation to the actual model then the parametric estimator may perform poorly relative to the nonparametric estimator and may even be inconsistent the bayesian paradigm provides a reasonable framework for this problem in a bayesian approach one would try to put a prior distribution on f that gives most of its mass to small neighborhoods of the entire parametric family we show that certain priors based on the dirichlet process prior can be used to accomplish this for these priors the posterior distribution of f given the censored data appears to be analytically intractable we provide a method for approximating this posterior distribution through the use of a successive substitution sampling algorithm we also show convergence of the algorithm

marginal likelihood and bayes factors for dirichlet process mixture models we present a method for comparing semiparametric bayesian models constructed under the dirichlet process mixture dpm framework with alternative semiparameteric or parameteric bayesian models a distinctive feature of the method is that it can be applied to semiparametric models containing covariates and hierarchical prior structures and is apparently the first method of its kind formally the method is based on the marginal likelihood estimation approach of chib 1995 and requires estimation of the likelihood and posterior ordinates of the dpm model at a single high density point an interesting computation is involved in the estimation of the likelihood ordinate which is devised via collapsed sequential importance sampling extensive experiments with synthetic and real data involving semiparametric binary data regression models and hierarchical longitudinal mixed effects models are used to illustrate the implementation performance and applicability of the method

switching lpv control designs using multiple parameter dependent lyapunov functions in this paper we study the switching control of linear parameter varying lpv systems using multiple parameter dependent lyapunov functions to improve performance and enhance control design flexibility a family of lpv controllers is designed each suitable for a specific parameter subregion they are switched so that the closed loop system remains stable and its performance is optimized two switching logics hysteresis switching and switching with average dwell time are examined the control synthesis conditions for both switching logics are formulated as matrix optimization problems which are generally non convex but can be convexified under some simplifying assumptions the hysteresis switching lpv control scheme is then applied to an active magnetic bearing problem

testing goodness of fit for a parametric family of link functions abstract we concern ourselves with the methods for testing the overall goodness of fit of a parametric family of link functions used for modeling the conditional mean of the response variable y given the covariates x x r p the null hypothesis is that the conditional mean function is a known functional depending on x and a finite number of parameters 1 q where is a p dimensional row vector of regression parameters and x is a column vector the proposed test statistic is derived from an information equivalence result and a dimension reduction technique the new test is very simple in computation also it is generally consistent against broad class of alternatives and asymptotically the null distribution is independent of the underlying distribution of y given x x practical examples are given to show the advantage of the proposed test furthermore power comparisons with the test used by su and wei are also performed to indicate the usefulness of the new test particularly we fi

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

modelling complexity applications of gibbs sampling in medicine summary we review applications of gibbs sampling in medicine involving longitudinal spatial covariate measurement and survival models applications in immunology pharmacology transplantation cancer screening industrial epidemiology and genetic epidemiology are discussed

bayesian inference for semiparametric binary regression abstract we propose a regression model for binary response data that places no structural restrictions on the link function except monotonicity and known location and scale predictors enter linearly we demonstrate bayesian inference calculations in this model by modifying the dirichlet process we obtain a natural prior measure over this semiparametric model and we use polya sequence theory to formulate this measure in terms of a finite number of unobserved variables we design a markov chain monte carlo algorithm for posterior simulation and apply the methodology to data on radiotherapy treatments for cancer

mode identifying time estimation and switching delay tolerant control for switched systems in this paper an elementary time unit etu method is proposed to study the problem of estimating the admissible delay in the identification of the active mode in the analysis and design of switched systems the activation interval of a subsystem is considered to consist of a finite time number of segments called etus by which a novel class of time scheduled lyapunov function is used to estimate the admissible delay in mode identification for switched systems further the etu method is applied for switching delay tolerant control problem and a class of time scheduled state feedback controllers are designed to achieve the exponentially stability several numerical examples are presented to validate the theoretic findings

a bayesian semiparametric accelerated failure time model a bayesian semiparametric approach is described for an accelerated failure time model the error distribution is assigned a polya tree prior and the regression parameters a noninformative hierarchical prior two cases are considered the first assumes error terms are exchangeable the second assumes that error terms are partially exchangeable a markov chain monte carlo algorithm is described to obtain a predictive distribution for a future observation given both uncensored and censored data

dirichlet process mixed generalized linear models abstract although generalized linear models glm s are an attractive and widely used class of models they are limited in the range of density shapes that they can provide for instance they are unimodal exponential families of densities in the response variable with tail behavior determined by the implicit mean variance relationship dirichlet process dp mixing adds considerable flexibility to these models using such mixing we develop models that we call dpmglm s which still retain the glm character with regard to the mean overdispersed glm s oglm s provide an alternative class of models to cope with extra variability in samples we show that how oglm s may be dp mixed leading to what we call dpmoglm s these models are extremely rich moreover recent computational advances enable them to be fitted straightforwardly we illustrate this with both simulated and real datasets we also address the question of choosing between the glm oglm dpmglm and dpmoglm finally we consider extensions by

a bayesian semiparametric model for random effects meta analysis in meta analysis there is an increasing trend to explicitly acknowledge the presence of study variability through random effects models that is one assumes that for each study there is a study specific effect and one is observing an estimate of this latent variable in a random effects model one assumes that these study specific effects come from some distribution and one can estimate the parameters of this distribution as well as the study specific effects themselves this distribution is most often modeled through a parametric family usually a family of normal distributions the advantage of using a normal distribution is that the mean parameter plays an important role and much of the focus is on determining whether or not this mean is 0 for example it may be easier to justify funding further studies if it is determined that this mean is not 0 typically this normality assumption is made for the sake of convenience rather than from some theoretical justification and may not actually hold w

evaluation of removable statistical interaction for binary traits this paper is concerned with evaluating whether an interaction between two sets of risk factors for a binary trait is removable and when it is removable fitting a parsimonious additive model using a suitable link function to estimate the disease odds on the natural logarithm scale statisticians define the term interaction as a departure from additivity in a linear model on a specific scale on which the data are measured certain interactions may be eliminated via a transformation of the outcome such that the relationship between the risk factors and the outcome is additive on the transformed scale such interactions are known as removable interactions we develop a novel test statistic for detecting the presence of a removable interaction in case control studies we consider the guerrero and johnson family of transformations and show that this family constitutes an appropriate link function for fitting an additive model when an interaction is removable we use simulation studies to examine the type i error and power of the proposed test and to show that when an interaction is removable an additive model based on the guerrero and johnson link function leads to more precise estimates of the disease odds parameters and a better fit we illustrate the proposed test and use of the transformation by using case control data from three published studies finally we indicate how one can check that after transformation no further interaction is significant

a center sliding bayesian binary classifier adopting orthogonal polynomials a center sliding bayesian design adopting orthogonal polynomials for binary pattern classification is studied in this paper essentially a bayesian weight solution is coupled with a center sliding scheme in feature space which provides an easy tuning capability for binary classification the proposed method is compared with several state of the art binary classifiers in terms of their solution forms decision thresholds and decision boundaries based on the center sliding bayesian framework a novel orthogonal polynomial classifier is subsequently developed the orthogonal polynomial classifier is evaluated using two representative orthogonal polynomials for feature mapping our experimental results show promising potential of the orthogonal polynomial classifier since it achieves both desired accuracy and computational efficiency highlightsproposed a center sliding bayesian classifier with deterministic solution proposed to adopt orthogonal polynomials for efficient feature expansion developed an easy tuning mechanism for the classification framework provided an extensive evaluation of the proposed classifier

semiparametric bayesian analysis of structural equation models with fixed covariates latent variables play the most important role in structural equation modeling in almost all existing structural equation models sems it is assumed that the distribution of the latent variables is normal as this assumption is likely to be violated in many biomedical researches a semiparametric bayesian approach for relaxing it is developed in this paper in the context of sems with covariates we provide a general bayesian framework in which a semiparametric hierarchical modeling with an approximate truncation dirichlet process prior distribution is specified for the latent variables the stick breaking prior and the blocked gibbs sampler are used for efficient simulation in the posterior analysis the developed methodology is applied to a study of kidney disease in diabetes patients a simulation study is conducted to reveal the empirical performance of the proposed approach supplementary electronic material for this paper is available in wiley interscience at http www mrw interscience wiley com suppmat 1097 0258 suppmat

nonparametric estimation of convex models via mixtures we present a general approach to estimating probability measures constrained to lie in a convex set we represent constrained measures as mixtures of simple known extreme measures and so the problem of estimating a constrained measure becomes one of estimating an unconstrained mixing measure convex constraints arise in many modeling situations such as estimation of the mean and estimation under stochastic ordering constraints we describe mixture representation techniques for these and other situations and discuss applications to maximum likelihood and bayesian estimation

bayesian density estimation and inference using mixtures abstract we describe and illustrate bayesian inference in models for density estimation using mixtures of dirichlet processes these models provide natural settings for density estimation and are exemplified by special cases where data are modeled as a sample from mixtures of normal distributions efficient simulation methods are used to approximate various prior posterior and predictive distributions this allows for direct inference on a variety of practical issues including problems of local versus global smoothing uncertainty about density estimates assessment of modality and the inference on the numbers of components also convergence results are established for a general class of normal mixture models

the cost of generalizing logistic regression abstract binary response regression models in which the link function is a family defined by one or more unknown shape parameters are considered detailed attention is given to the two single parameter families proposed by aranda ordaz 1981 that incorporate the logistic linear and complementary log log link functions as special cases one model is a symmetric family of alternatives to the logistic shape and the second model is an asymmetric family the increase in variance of quantities of interest due to the addition of an extra parameter is calculated using asymptotic methods this inflation in variance is interpreted as the cost of adding an additional parameter to the model in considering the seriousness of this cost the reduction in bias due to the estimation of the additional parameter should also be taken into account three quantities of interest predicted probabilities for a fixed value of the explanatory variable predicted value of the explanatory variable to obtain a specific probability

a set of new chebyshev kernel functions for support vector machine pattern classification in this study we introduce a set of new kernel functions derived from the generalized chebyshev polynomials the proposed generalized chebyshev polynomials allow us to derive different kernel functions by using these polynomial functions we generalize recently introduced chebyshev kernel function for vector inputs and as a result we obtain a robust set of kernel functions for support vector machine svm classification thus in this study besides clarifying how to apply the chebyshev kernel functions on vector inputs we also increase the generalization capability of the previously proposed chebyshev kernels and show how to derive new kernel functions by using the generalized chebyshev polynomials the proposed set of kernel functions provides competitive performance when compared to all other common kernel functions on average for the simulation datasets the results indicate that they can be used as a good alternative to other common kernel functions for svm classification in order to obtain better accuracy moreover test results show that the generalized chebyshev kernel approaches to the minimum support vector number for classification in general

use of the box cox transformation with binary response models abstract the power transformation is applied to the odds ratio to generalize the logistic model and to parameterize a certain type of lack of fit transformation of the design variable within the context of the dose response problem is also considered

legendre polynomials based feature extraction for online signature verification consistency analysis of feature combinations in this paper feature combinations associated with the most commonly used time functions related to the signing process are analyzed in order to provide some insight on their actual discriminative power for online signature verification a consistency factor is defined to quantify the discriminative power of these different feature combinations a fixed length representation of the time functions associated with the signatures based on legendre polynomials series expansions is proposed the expansion coefficients in these series are used as features to model the signatures two different signature styles namely western and chinese from a publicly available signature database are considered to evaluate the performance of the verification system two state of the art classifiers namely support vector machines and random forests are used in the verification experiments error rates comparable to the ones reported over the same signature datasets in a recent signature verification competition show the potential of the proposed approach the experimental results also show that there is a good correlation between the consistency factor and the verification errors suggesting that consistency values could be used to select the optimal feature combination highlightsa feature extraction approach based on legendre series representation of the time functions associated with the signatures is proposed a consistency factor is proposed to quantify the discriminative power of different combinations of the time functions the correlation between the proposed consistency factor and the verification performance of a feature combination is analyzed a recent signature database containing western and chinese signatures is used the verification performance is quantified based on log likelihood ratios

discussion on stability l _ 2 gain and asynchronous h _ infty control of discrete time switched systems with average dwell time this note addresses a defect occurring in in which the desired l 2 gain should be replaced by weighted l 2 gain performance the corrected results and proof are presented

asynchronous switching output feedback control of discrete time switched linear systems in this paper the problem of dynamic output feedback control synthesis is addressed for discrete time switched linear systems under asynchronous switching the proposed hybrid controller consists of a standard dynamic output feedback switching control law and an impulsive reset law induced by controller state jumps using the average dwell time technique incorporating with multiple quadratic lyapunov functions the switching control synthesis conditions for asymptotic stability with guaranteed weighted l2 gain performance are derived as a set of linear matrix inequalities lmis the proposed hybrid synthesis scheme advances existing design methods for output feedback asynchronous switching control of switched linear systems in two important aspects lmi formulation of the synthesis problem and arbitrary order of the controller state a numerical example is used to illustrate the effectiveness and advantages of the proposed design technique

on two families of transformations to additivity for binary response data summary two families of power transformations for probabilities are introduced to model symmetric and asymmetric departures from the logistic model the aim is to provide in a comprehensive way a representation of alternative scales in terms of which to carry out the analysis of binary response data maximum likelihood methods are employed to estimate an appropriate transformation using glim tests for detection of symmetric and asymmetric departures are proposed

likelihood based inference for monotone response models the behavior of maximum likelihood estimates mles and the likelihood ratio statistic in a family of problems involving pointwise nonparametric estimation of a monotone function is studied this class of problems differs radically from the usual parametric or semiparametric situations in that the mle of the monotone function at a point converges to the truth at rate n 1 3 slower than the usual n rate with a non gaussian limit distribution a framework for likelihood based estimation of monotone functions is developed and limit theorems describing the behavior of the mles and the likelihood ratio statistic are established in particular the likelihood ratio statistic is found to be asymptotically pivotal with a limit distribution that is no longer 2 but can be explicitly characterized in terms of a functional of brownian motion applications of the main results are presented and potential extensions discussed

nonparametric bayesian analysis for assessing homogeneity in k l contingency tables with fixed right margin totals abstract in this work i postulate a nonparametric bayesian model for data that can be accommodated in a contingency table with fixed right margin totals this data structure usually arises when comparing different groups regarding classification probabilities for a number of categories i assume that cell count vectors for each group are conditionally independent with multinomial distribution given vectors of classification probabilities in turn these vectors of probabilities are assumed to be a sample from a distribution f and the prior distribution of f is assumed to be a dirichlet process centered on a probability measure and with weight c i also assume a prior distribution for c as a way of obtaining a better control on the clustering structure induced by the dirichlet process i use this setting to assess homogeneity of classification probabilities and propose a bayes factor i derive exact expressions for the relevant quantities these can be directly computed when the number of rows k i

nonparametric bayesian bioassay including ordered polytomous response abstract previous attempts at implementing fully bayesian nonparametric bioassay have enjoyed limited success due to computational difficulties we show here how this problem may be generally handled using a sampling based approach to develop desired marginal posterior distributions and their features a useful extension is presented which treats the case of ordered polytomous response illustrative examples are provided

a recursive algorithm for nonparametric analysis with missing data summary the mixture of dirichlet processes posterior that arises in nonparametric bayesian analysis has been analysed most effectively using markov chain monte carlo as a computationally simple alternative we introduce a recursive approximation based on one step posterior predictive distributions asymptotic calculations provide theoretical support for this approximation and we investigate its actual behaviour in several numerical examples from a non bayesian perspective this new recursion may be used to obtain solutions of the self consistency equations

spatial statistics and bayesian computation on wednesday may 6th 1992 professor b w silverman in the chair summary markov chain monte carlo mcmc algorithms such as the gibbs sampler have provided a bayesian inference machine in image analysis and in other areas of spatial statistics for several years founded on the pioneering ideas of ulf grenander more recently the observation that hyperparameters can be included as part of the updating schedule and the fact that almost any multivariate distribution is equivalently a markov random field has opened the way to the use of mcmc in general bayesian computation in this paper we trace the early development of mcmc in bayesian inference review some recent computational progress in statistical physics based on the introduction of auxiliary variables and discuss its current and future relevance in bayesian applications we briefly describe a simple mcmc implementation for the bayesian analysis of agricultural field experiments with which we have some practical experience

brief paper weighted h model reduction for linear switched systems with time varying delay this paper is concerned with model reduction for continuous time linear switched systems with time varying delay for a given stable switched system our attention is focused on construction of a reduced order model such that the error system is exponentially stable with a prescribed weighted performance by applying the average dwell time approach and the piecewise lyapunov function technique delay dependent deley independent sufficient conditions are proposed in terms of linear matrix inequality lmi to guarantee the exponential stability and the weighted performance for the error system the model reduction problem is solved by using the projection approach which casts the model reduction problem into a sequential minimization problem subject to lmi constraints by employing the cone complementary linearization algorithm a numerical example is provided to illustrate the effectiveness of the proposed theory

nonparametric hierarchical bayes via sequential imputations we consider the empirical bayes estimation of a distribution using binary data via the dirichlet process let d denote a dirichlet process with being a finite measure on 0 1 instead of having direct samples from an unknown random distribution f from d we assume that only indirect binomial data are observable this paper presents a new interpretation of lo s formula and thereby relates the predictive density of the observations based on a dirichlet process model to likelihoods of much simpler models as a consequence the log likelihood surface as well as the maximum likelihood estimate of c 0 1 is found when the shape of is assumed known together with a formula for the fisher information evaluated at the estimate the sequential imputation method of kong liu and wong is recommended for overcoming computational difficulties commonly encountered in this area the related approximation formulas are provided an analysis of the tack data of beckett and diaconis which motivated this study is supplemented to illustrate our methods

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea