discriminant analysis by gaussian mixtures fisher rao linear discriminant analysis lda is a valuable tool for multigroup classification lda is equivalent to maximum likelihood classification assuming gaussian distributions for each class in this paper we fit gaussian mixtures to each class to facilitate effective classification in non normal settings especially when the classes are clustered low dimensional views are an important by product of lda our new techniques inherit this feature we can control the within class spread of the subclass centres relative to the between class spread our technique for fitting these models permits a natural blend with nonparametric versions of lda

bayesian approaches to gaussian mixture modeling a bayesian based methodology is presented which automatically penalizes overcomplex models being fitted to unknown data we show that with a gaussian mixture model the approach is able to select an optimal number of components in the model and so partition data sets the performance of the bayesian method is compared to other methods of optimal model selection and found to give good results the methods are tested on synthetic and real data sets

the asymptotic behavior of the composition of two resolvents abstract the asymptotic behavior of the composition of two resolvents in a hilbert space is investigated connections are made between the solutions of associated monotone inclusion problems and their dual versions the applications provided include a study of an alternating minimization procedure and a new proof of von neumann s classical result on the method of alternating projections

hidden markov models with nonelliptically contoured state densities hidden markov models hmms are a popular approach for modeling sequential data comprising continuous attributes in such applications the observation emission densities of the hmm hidden states are typically modeled by means of elliptically contoured distributions usually multivariate gaussian or student s t densities however elliptically contoured distributions cannot sufficiently model heavy tailed or skewed populations which are typical in many fields such as the financial and the communication signal processing domain employing finite mixtures of such elliptically contoured distributions to model the hmm state densities is a common approach for the amelioration of these issues nevertheless the nature of the modeled data often requires postulation of a large number of mixture components for each hmm state which might have a negative effect on both model efficiency and the training data set s size required to avoid overfitting to resolve these issues in this paper we advocate for the utilization of a nonelliptically contoured distribution the multivariate normal inverse gaussian mnig distribution for modeling the observation densities of hmms as we experimentally demonstrate our selection allows for more effective modeling of skewed and heavy tailed populations in a simple and computationally efficient manner

baseline risk as predictor of treatment benefit three clinical meta re analyses a relationship between baseline risk and treatment effect is increasingly investigated as a possible explanation of between study heterogeneity in clinical trial meta analysis an approach that is still often applied in the medical literature is to plot the estimated treatment effects against the estimated measures of risk in the control groups as a measure of baseline risk and to compute the ordinary weighted least squares regression line however it has been pointed out by several authors that this approach can be seriously flawed the main problem is that the observed treatment effect and baseline risk measures should be viewed as estimates rather than the true values in recent years several methods have been proposed in the statistical literature to potentially deal with the measurement errors in the estimates in this article we propose a vague priors bayesian solution to the problem which can be carried out using the bayesian inference using gibbs sampling bugs implementation of markov chain monte carlo numerical integration techniques different from other proposed methods it uses the exact rather than an approximate likelihood while it can handle many different treatment effect measures and baseline risk measures the method differs from a recently proposed bayesian method in that it explicitly models the distribution of the underlying baseline risks we apply the method to three meta analyses published in the medical literature and compare the results with the outcomes of the other recently proposed methods in particular we compare our approach to mcintosh s method for which we show how it can be carried out using standard statistical software we conclude that our proposed method offers a very general and flexible solution to the problem which can be carried out relatively easily with existing bayesian analysis software a confidence band for the underlying relationship between true effect measure and baseline risk and a confidence interval for the value of the baseline risk measure for which there is no treatment effect are easily obtained by products of our approach

detecting features in spatial point processes with clutter via model based clustering abstract we consider the problem of detecting features such as minefields or seismic faults in spatial point processes when there is substantial clutter we use model based clustering based on a mixture model for the process in which features are assumed to generate points according to highly linear multivariate normal densities and the clutter arises according to a spatial poisson process nonlinear features are represented by several densities giving a piecewise linear representation hierarchical model based clustering provides a first estimate of the features and this is then refined using the em algorithm the number of features is estimated from an approximation to its posterior distribution the method gives good results for the minefield and seismic fault problems software to implement it is available on the world wide web

model based gaussian and non gaussian clustering abstract the classification maximum likelihood approach is sufficiently general to encompass many current clustering algorithms including those based on the sum of squares criterion and on the criterion of friedman and rubin 1967 however as currently implemented it does not allow the specification of which features orientation size and shape are to be common to all clusters and which may differ between clusters also it is restricted to gaussian distributions and it does not allow for noise we propose ways of overcoming these limitations a reparameterization of the covariance matrix allows us to specify that some features but not all be the same for all clusters a practical framework for non gaussian clustering is outlined and a means of incorporating noise in the form of a poisson process is described an approximate bayesian method for choosing the number of clusters is given the performance of the proposed methods is studied by simulation with encouraging results the methods are applied to the analysis of a data set arising in the study of diabetes and the results seem better than those of previous analyses rh

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

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

assessing a mixture model for clustering with the integrated completed likelihood we propose an assessing method of mixture model in a cluster analysis setting with integrated completed likelihood for this purpose the observed data are assigned to unknown clusters using a maximum a posteriori operator then the integrated completed likelihood icl is approximated using the bayesian information criterion bic numerical experiments on simulated and real data of the resulting icl criterion show that it performs well both for choosing a mixture model and a relevant number of clusters in particular icl appears to be more robust than bic to violation of some of the mixture model assumptions and it can select a number of dusters leading to a sensible partitioning of the data

deterministic annealing for density estimation by multivariate normal mixtures an approach to maximum likelihood density estimation by mixtures of multivariate normal distributions for large high dimensional data sets is presented conventionally that problem is tackled by notoriously unstable expectation maximization em algorithms we remove these instabilities by the introduction of soft constraints enabling deterministic annealing our developments are motivated by the proof that algorithmically stable fuzzy clustering methods that are derived from statistical physics analogs are special cases of em procedures

bayesian methods of analysis for cluster randomized trials with binary outcome data we explore the potential of bayesian hierarchical modelling for the analysis of cluster randomized trials with binary outcome data and apply the methods to a trial randomized by general practice an approximate relationship is derived between the intracluster correlation coefficient icc and the between cluster variance used in a hierarchical logistic regression model by constructing an informative prior for the icc on the basis of available information we are thus able implicitly to specify an informative prior for the between cluster variance the approach also provides us with a credible interval for the icc for binary outcome data several approaches to constructing informative priors from empirical icc values are described we investigate the sensitivity of results to the prior specified and find that the estimate of intervention effect changes very little in this data set while its interval estimate is more sensitive the bayesian approach allows us to assume distributions other than normality for the random effects used to model the clustering this enables us to gain insight into the robustness of our parameter estimates to the classical normality assumption in a model with a more complex variance structure bayesian methods can provide credible intervals for a difference between two variance components in order for example to investigate whether the effect of intervention varies across clusters we compare our results with those obtained from classical estimation discuss the relative merits of the bayesian framework and conclude that the flexibility of the bayesian approach offers some substantial advantages although selection of prior distributions is not straightforward

the effects of mixture distribution misspecification when fitting mixed effects logistic models summary mixed effects logistic models are often used to analyze binary response data which have been gathered in clusters or groups responses are assumed to follow a logistic model within clusters with an intercept which varies across clusters according to a specified probability distribution g in this paper we examine the performance of mixed effects logistic regression analysis when a main component of the model the mixture distribution is misspecified we show that when the mixture distribution is misspecified estimates of model parameters including the effects of covariates typically are asymptotically biased i e inconsistent however we present some approximations which suggest that the magnitude of the bias in the estimated covariate effects is typically small these findings are corroborated by a set of simulations which also suggest that valid variance estimates of estimated covariate effects can be obtained when the mixture distribution is misspecified

statistical applications of the multivariate skew normal distribution azzalini and dalla valle have recently discussed the multivariate skew normal distribution which extends the class of normal distributions by the addition of a shape parameter the first part of the present paper examines further probabilistic properties of the distribution with special emphasis on aspects of statistical relevance inferential and other statistical issues are discussed in the following part with applications to some multivariate statistics problems illustrated by numerical examples finally a further extension is described which introduces a skewing factor of an elliptical density

random effects meta analysis coverage performance of 95 confidence and prediction intervals following reml estimation a random effects meta analysis combines the results of several independent studies to summarise the evidence about a particular measure of interest such as a treatment effect the approach allows for unexplained between study heterogeneity in the true treatment effect by incorporating random study effects about the overall mean the variance of the mean effect estimate is conventionally calculated by assuming that the between study variance is known however it has been demonstrated that this approach may be inappropriate especially when there are few studies alternative methods that aim to account for this uncertainty such as hartung knapp sidik jonkman and kenward roger have been proposed and shown to improve upon the conventional approach in some situations in this paper we use a simulation study to examine the performance of several of these methods in terms of the coverage of the 95 confidence and prediction intervals derived from a random effects meta analysis estimated using restricted maximum likelihood we show that in terms of the confidence intervals the hartung knapp correction performs well across a wide range of scenarios and outperforms other methods when heterogeneity was large and or study sizes were similar however the coverage of the hartung knapp method is slightly too low when the heterogeneity is low i2 30 and study sizes are similar in other situations especially when heterogeneity is small and the study sizes are quite varied the coverage is far too low and could not be consistently improved by either increasing the number of studies altering the degrees of freedom or using variance inflation methods therefore researchers should be cautious in deriving 95 prediction intervals following a frequentist random effects meta analysis until a more reliable solution is identified 2016 the authors statistics in medicine published by john wiley sons ltd

unsupervised texture segmentation using gabor filters abstract this paper presents a texture segmentation algorithm inspired by the multi channel filtering theory for visual information processing in the early stages of human visual system the channels are characterized by a bank of gabor filters that nearly uniformly covers the spatial frequency domain and a systematic filter selection scheme is proposed which is based on reconstruction of the input image from the filtered images texture features are obtained by subjecting each selected filtered image to a nonlinear transformation and computing a measure of energy in a window around each pixel a square error clustering algorithm is then used to integrate the feature images and produce a segmentation a simple procedure to incorporate spatial information in the clustering process is proposed a relative index is used to estimate the true number of texture categories

a bivariate approach to meta analysis the usual meta analysis of a sequence of randomized clinical trials only considers the difference between two treatments and produces a point estimate and a confidence interval for a parameter that measures this difference the usual parameter is the log odds ratio linked to mantel haenszel methodology inference is made either under the assumption of homogeneity or in a random effects model that takes account of heterogeneity between trials this paper has two goals the first is to present a likelihood based method for the estimation of the parameters in the random effects model which avoids the use of approximating normal distributions the second goal is to extend this method to a bivariate random effects model in which the effects in both groups are supposed random in this way inference can be made about the relationship between improvement and baseline effect the method is demonstrated by a meta analysis dataset of collins and langman

non iterative robust estimators of variance components in within subject designs classic estimators of variance components break down in the presence of outliers and perform less efficiently under non normality in this article i present simple non iterative estimators of variance components that are resistant to outliers and robust to systematic departures from normality such as heavy tailedness of the distribution of responses the proposed estimators are based on a robust extension of hocking s ave approach and are thus called rave estimators i present results from a monte carlo comparison of rave versus classic estimation methods including maximum likelihood ml restricted maximum likelihood reml and minimum variance quadratic unbiased estimation mivque under simulated deviations from normality rave estimators are associated with smaller mean squared errors than all the comparators and in the normal case they exhibit a minimal loss in relative efficiency a numerical example illustrates the proposed methodology

beta binomial model for meta analysis of odds ratios in meta analysis of odds ratios ors heterogeneity between the studies is usually modelled via the additive random effects model rem an alternative multiplicative rem for ors uses overdispersion the multiplicative factor in this overdispersion model odm can be interpreted as an intra class correlation icc parameter this model naturally arises when the probabilities of an event in one or both arms of a comparative study are themselves beta distributed resulting in beta binomial distributions we propose two new estimators of the icc for meta analysis in this setting one is based on the inverted breslow day test and the other on the improved gamma approximation by kulinskaya and dollinger 2015 p 26 to the distribution of cochran s q the performance of these and several other estimators of icc on bias and coverage is studied by simulation additionally the mantel haenszel approach to estimation of ors is extended to the beta binomial model and we study performance of various icc estimators when used in the mantel haenszel or the inverse variance method to combine ors in meta analysis the results of the simulations show that the improved gamma based estimator of icc is superior for small sample sizes and the breslow day based estimator is the best for n 100 the mantel haenszel based estimator of or is very biased and is not recommended the inverse variance approach is also somewhat biased for ors 1 but this bias is not very large in practical settings developed methods and r programs provided in the web appendix make the beta binomial model a feasible alternative to the standard rem for meta analysis of ors 2017 the authors statistics in medicine published by john wiley sons ltd

the impact of a misspecified random effects distribution on the estimation and the performance of inferential procedures in generalized linear mixed models estimation in generalized linear mixed models glmms is often based on maximum likelihood theory assuming that the underlying probability model is correctly specified however the validity of this assumption is sometimes difficult to verify in this paper we study through simulations the impact of misspecifying the random effects distribution on the estimation and hypothesis testing in glmms it is shown that the maximum likelihood estimators are inconsistent in the presence of misspecification the bias induced in the mean structure parameters is generally small as far as the variability of the underlying random effects distribution is small as well however the estimates of this variability are always severely biased given that the variance components are the only tool to study the variability of the true distribution it is difficult to assess whether problems in the estimation of the mean structure occur the type i error rate and the power of the commonly used inferential procedures are also severely affected the situation is aggravated if more than one random effect is included in the model further we propose to deal with possible misspecification by way of sensitivity analysis considering several random effects distributions all the results are illustrated using data from a clinical trial in schizophrenia

applications of splitting algorithm to decomposition in convex programming and variational inequalities recently han and lou proposed a highly parallelizable decomposition algorithm for minimizing a strongly convex cost over the intersection of closed convex sets it is shown that their algorithm is in fact a special case of a splitting algorithm analyzed by gabay for finding a zero of the sum of two maximal monotone operators gabay s convergence analysis for the splitting algorithm is sharpened and new applications of this algorithm to variational inequalities convex programming and the solution of linear complementarily problems are proposed for convex programs with a certain separable structure a multiplier method that is closely related to the alternating direction method of multipliers of gabay mercier and of glowinski marrocco but which uses both ordinary and augmented lagrangians is obtained

on convergence properties of the em algorithm for gaussian mixtures we build up the mathematical connection between the expectation maximization em algorithm and gradient based approaches for maximum likelihood learning of finite gaussian mixtures we show that the em step in parameter space is obtained from the gradient via a projection matrix p and we provide an explicit expression for the matrix we then analyze the convergence of em in terms of special properties of p and provide new results analyzing the effect that p has on the likelihood surface based on these mathematical results we present a comparative discussion of the advantages and disadvantages of em and other algorithms for the learning of gaussian mixture models

on bayesian modeling of fat tails and skewness abstract we consider a bayesian analysis of linear regression models that can account for skewed error distributions with fat tails the latter two features are often observed characteristics of empirical datasets and we formally incorporate them in the inferential process a general procedure for introducing skewness into symmetric distributions is first proposed even though this allows for a great deal of flexibility in distributional shape tail behavior is not affected applying this skewness procedure to a student t distribution we generate a skewed student distribution which displays both flexible tails and possible skewness each entirely controlled by a separate scalar parameter the linear regression model with a skewed student error term is the main focus of the article we first characterize existence of the posterior distribution and its moments using standard improper priors and allowing for inference on skewness and tail parameters for posterior inference with this model we suggest

maximum likelihood training of probabilistic neural networks a maximum likelihood method is presented for training probabilistic neural networks pnn s using a gaussian kernel or parzen window the proposed training algorithm enables general nonlinear discrimination and is a generalization of fisher s method for linear discrimination important features of maximum likelihood training for pnn s are 1 it economizes the well known parzen window estimator while preserving feedforward nn architecture 2 it utilizes class pooling to generalize classes represented by small training sets 3 it gives smooth discriminant boundaries that often are piece wise flat for statistical robustness 4 it is very fast computationally compared to backpropagation and 5 it is numerically stable the effectiveness of the proposed maximum likelihood training algorithm is assessed using nonparametric statistical methods to define tolerance intervals on pnn classification performance

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

visco penalization of the sum of two monotone operators a new type of approximating curve for finding a particular zero of the sum of two maximal monotone operators in a hilbert space is investigated this curve consists of the zeros of perturbed problems in which one operator is replaced with its yosida approximation and a viscosity term is added as the perturbation vanishes the curve is shown to converge to the zero of the sum that solves a particular strictly monotone variational inequality as an off spring of this result we obtain an approximating curve for finding a particular zero of the sum of several maximal monotone operators applications to convex optimization are discussed

subspace estimation and prediction methods for hidden markov models hidden markov models hmms are probabilistic functions of finite markov chains or put in other words state space models with finite state space in this paper we examine subspace estimation methods for hmms whose output lies a finite set as well in particular we study the geometric structure arising from the nonminimality of the linear state space representation of hmms and consistency of a subspace algorithm arising from a certain factorization of the singular value decomposition of the estimated linear prediction matrix for this algorithm we show that the estimates of the transition and emission probability matrices are consistent up to a similarity transformation and that the m step linear predictor computed from the estimated system matrices is consistent i e converges to the true optimal linear m step predictor

a mixed non homogeneous hidden markov model for categorical data with application to alcohol consumption hidden markov models hmms are frequently used to analyse longitudinal data where the same set of subjects is repeatedly observed over time in this context several sources of heterogeneity may arise at individual and or time level which affect the hidden process that is the transition probabilities between the hidden states in this paper we propose the use of a finite mixture of non homogeneous hmms nh hmms to face the heterogeneity problem the non homogeneity of the model allows us to take into account observed sources of heterogeneity by means of a proper set of covariates time and or individual dependent explaining the variations in the transition probabilities moreover we handle the unobserved sources of heterogeneity at the individual level due to for example omitted covariates by introducing a random term with a discrete distribution the resulting model is a finite mixture of nh hmm that can be used to classify individuals according to their dynamic behaviour or to estimate a mixed nh hmm without any assumption regarding the distribution of the random term following the non parametric maximum likelihood approach we test the effectiveness of the proposal through a simulation study and an application to real data on alcohol abuse

estimating heterogeneity variance in meta analysis summary several new estimators of the between study variability in a heterogeneous random effects meta analysis model are derived one is the unbiased statistic which is locally optimal for small values of the parameter others are bayes procedures within a class of quadratic statistics for a diffuse prior with different choices of the prior mean these estimators are compared with the dersimonian laird procedure and the hedges statistic in particular via the quadratic risk of the treatment effect estimator a monte carlo study supports the usage of confidence intervals derived from the new estimators

proportional data modeling with hidden markov models based on generalized dirichlet and beta liouville mixtures applied to anomaly detection in public areas the recent and rapid deployment of cctv cameras in public areas invokes the need for a capability to assist human operators in the real time detection of threats and anomalous events the main difficulty in this regard is the rare and unpredictable nature of the events to be detected a typical strategy consists in modeling situations considered as normal and detecting outliers to this model in this paper we theoretically derive two variants of the hidden markov model for proportional data modeling and assess their performance for unusual event detection in several public surveillance situations proportional data arise in a number of pattern recognition applications and classic hidden markov models are not well adapted so far for their specific processing our models are based on the use of the generalized dirichlet and beta liouville distributions as emission probability functions and yield enhanced performance compared to the use of the dirichlet distribution highlightsderivation of the equations of a generalized dirichlet based hidden markov model derivation of the equations of a beta liouville based hidden markov model application of the new models to public areas surveillance scenarios better performance over the dirichlet based hidden markov models analysis of the behavior of the models and guidelines for parameter tuning

flexible parametric models for random effects distributions it is commonly assumed that random effects in hierarchical models follow a normal distribution this can be extremely restrictive in practice we explore the use of more flexible alternatives for this assumption namely the t distribution and skew extensions to the normal and t distributions implemented using markov chain monte carlo methods models are compared in terms of parameter estimates deviance information criteria and predictive distributions these methods are applied to examples in meta analysis and health professional variation where the distribution of the random effects is of direct interest the results highlight the importance of allowing for potential skewing and heavy tails in random effects distributions especially when estimating a predictive distribution we describe the extension of these random effects models to the bivariate case with application to a meta analysis examining the relationship between treatment effect and baseline response we conclude that inferences regarding the random effects can crucially depend on the assumptions made and recommend using a distribution such as those suggested here which is more flexible than the normal

bayesian approaches to random effects meta analysis a comparative study current methods for meta analysis still leave a number of unresolved issues such as the choice between fixed and random effects models the choice of population distribution in a random effects analysis the treatment of small studies and extreme results and incorporation of study specific covariates we describe how a full bayesian analysis can deal with these and other issues in a natural way illustrated by a recent published example that displays a number of problems such analyses are now generally available using the bugs implementation of markov chain monte carlo numerical integration techniques appropriate proper prior distributions are derived and sensitivity analysis to a variety of prior assumptions carried out current methods are briefly summarized and compared to the full bayes analysis

on bayesian analysis of mixtures with an unknown number of components with discussion new methodology for fully bayesian mixture analysis is developed making use of reversible jump markov chain monte carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture a sample from the full joint distribution of all unknown variables is thereby generated and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution the methodology is applied here to the analysis of univariate normal mixtures using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context

robust sequential data modeling using an outlier tolerant hidden markov model hidden markov chain models using finite gaussian mixture models as their hidden state distributions have been successfully applied in sequential data modeling and classification applications nevertheless gaussian mixture models are well known to be highly intolerant to the presence of untypical data within the fitting data sets used for their estimation finite student s t mixture models have recently emerged as a heavier tailed robust alternative to gaussian mixture models overcoming these hurdles to exploit these merits of student s t mixture models in the context of a sequential data modeling setting we introduce in this paper a novel hidden markov model where the hidden state distributions are considered to be finite mixtures of multivariate student s t densities we derive an algorithm for the model parameters estimation under a maximum likelihood framework assuming full diagonal and factor analyzed covariance matrices the advantages of the proposed model over conventional approaches are experimentally demonstrated through a series of sequential data modeling applications

the exact distribution of cochran s heterogeneity statistic in one way random effects meta analysis the presence and impact of heterogeneity in the standard one way random effects model in meta analysis are often assessed using the q statistic due to cochran we derive the exact distribution of this statistic under the assumptions of the random effects model and also suggest two moment based approximations and a saddlepoint approximation for q the exact and approximate distributions are then applied to obtain the corresponding distributions of the recently proposed heterogeneity measures i 2 and h m 2 the power of the standard test for the presence of heterogeneity and confidence intervals for the between study variance parameter when the dersimonian laird or the hartung makambi estimator is used the methodology is illustrated by revisiting a recent simulation study concerning the heterogeneity measures and applying all the proposed methods to four published meta analyses

bayesian inference for stable distributions abstract very little work on stable distribution parameter estimation and inference appears in the literature due to the nonexistence of the probability density function this has led in particular to a dearth of bayesian work in this area but bayesian computation via markov chain monte carlo allows us to sample from the distribution of the parameters of the stable distributions by exploiting a particular mathematical representation involving the stable density

proportional hazards model with random effects we propose a general proportional hazards model with random effects for handling clustered survival data this generalizes the usual frailty model by allowing a multivariate random effect with arbitrary design matrix in the log relative risk in a way similar to the modelling of random effects in linear generalized linear and non linear mixed models the distribution of the random effects is generally assumed to be multivariate normal but other preferably symmetrical distributions are also possible maximum likelihood estimates of the regression parameters the variance components and the baseline hazard function are obtained via the em algorithm the e step of the algorithm involves computation of the conditional expectations of functions of the random effects for which we use markov chain monte carlo mcmc methods approximate variances of the estimates are computed by louis formula and posterior expectations and variances of the individual random effects can be obtained as a by product of the estimation the inference procedure is exemplified on two data sets

decomposition through formalization in a product space when an optimization problem is posed in a product space it is classical to decompose this problem the goal of this paper is to show how such an approach can be used when the problem to be solved is not naturally posed in a product space by associating systematically to this problem an equivalent one posed in ann fold cartesian product space we obtain by decomposition of the latter both a splitting of operators and a desintegration of constraints for the former applications to three rather classical mathematical programming problems are given

modeling the manifolds of images of handwritten digits this paper describes two new methods for modeling the manifolds of digitized images of handwritten digits the models allow a priori information about the structure of the manifolds to be combined with empirical data accurate modeling of the manifolds allows digits to be discriminated using the relative probability densities under the alternative models one of the methods is grounded in principal components analysis the other in factor analysis both methods are based on locally linear low dimensional approximations to the underlying data manifold links with other methods that model the manifold are discussed

information ratios for validating mixture analyses abstract determining the number of components in a mixture of distributions is an important but difficult problem this article introduces a procedure called minimum information ratio estimation and validation mirev which is based on a ratio of fisher information matrices the smallest eigenvalue of the information ratio matrix is used to determine the number of components a measure of uncertainty may be obtained using a bootstrap technique simulations illustrate the effectiveness of the procedure for mixtures of exponential families an expression for the observed information ratio matrix provides insight to the success of the procedure cluster analysis attempts to identify and characterize subpopulations believed to be present in a population a wide variety of methods are available including criterion optimization hierarchical methods and various heuristic methods criterion optimization techniques such as mixture analysis fuzzy clustering and partitioning methods are popular because they