survival analysis using a scale change random effects model abstract frailty models are effective in broadening the class of survival models and inducing dependence in multivariate survival distributions in proportional hazards the random effect multiplies the hazard function the scale change model incorporates unobserved heterogeneity through a random effect that enters the baseline hazard function to change the time scale we interpret this random effect as frailty or other unobserved risks that create heterogeneity in the population this model produces a wide range of shapes for univariate survival and hazard functions we extend this model to multivariate survival data by assuming that members of a group share a common random effect this structure induces association among the survival times in a group and provides alternative association structures to the proportional hazards frailty model we present parametric and semiparametric estimation techniques and illustrate these methods with an example

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

interval censored data a note on the nonparametric maximum likelihood estimator of the distribution function summary gentleman geyer 1994 discuss the analysis of interval censored data and present results based on standard convex optimisation theory here this problem is viewed from the perspective of a mixing problem of indicator functions using an analogy with the problem of mixture distributions a variety of results are easily derived including a characterisation theorem for the maximum likelihood estimator and various reliably convergent algorithms software for the analysis of mixture distributions can be used to find the nonparametric estimate of the distribution function of the interval censored survival time examples are provided to demonstrate the theory

properties of neural networks storing spatially correlated patterns the author studies the behaviour of a feedforward neural network supplied with spatially organized data this inner structure is taken into account by a matrix cij whose coefficients equal the average correlation between two pixels i and j of the input patterns the storage capacity alpha is computed as a function of the required stability and of the eigenvalues of c the author proposes a geometrical transformation allowing an intuitive interpretation of these results numerical simulations using real and binary patterns show a very good agreement with the theory finally the author analyses the synaptic couplings correlations resulting from the training of the network with structured patterns focusing on exponentially decreasing correlations one and two dimensions the author finds that they exhibit a mexican hat profile the excitatory centre size of which depends on alpha

statistical models for intercepted data abstract consider a population of replaceable items of different ages and suppose that for each item there is a certain measurable attribute that is a monotone function perhaps random of the item s age to fix ideas we refer to this attribute as deterioration and we assume that as items age their level of deterioration increases we further assume that as the level of deterioration hits a certain threshold value perhaps unknown the item dies and disappears from the population so it is not available for sampling any more since items that deteriorate at a slower rate live longer any sample obtained over a short period of time would overrepresent slowly deteriorating items consequently under such circumstances longitudinal studies are often needed to statistically study deterioration as a function of age this article presents a statistical model that enables us to study the deterioration function from a single cross section snapshot of the population or some random parts of it specifically

mixtures of exponential distributions arbitrary nonparametric mixtures of exponential and weibull fixed shape distributions are considered as possible models for a lifetime distribution a characterization of such distributions is given by the well known characterization of laplace transforms the maximum likelihood estimate of the mixing distribution is investigated and found to be supported on a finite number of points it is shown to be unique and weakly convergent to the true mixing measure with probability one a practical algorithm for computing the maximum likelihood estimate is described its performance is briefly discussed and some illustrative examples given

nonparametric mle under two closed capture recapture models with heterogeneity we conduct nonparametric maximum likelihood estimation under two common heterogeneous closed population capture recapture models our models specify mixture models as did previous researchers models which have a common generating distribution say f for the capture probabilities using lindsay and roeder s 1992 journal of the american statistical association 87 785 794 mixture model results and the em algorithm a nonparametric maximum likelihood estimator mle of f for any specified population size n is obtained then the nonparametric mle of the n f pair and thus for n is determined perhaps most importantly since our mle pair maximizes the likelihood under the entire nonparametric probability model it provides an excellent foundation for estimating properties of estimators conducting a goodness of fit test and performing a likelihood ratio test these are illustrated in the paper

triple goal estimates in two stage hierarchical models the beauty of the bayesian approach is its ability to structure complicated models inferential goals and analyses to take full advantage of it methods should be linked to an inferential goal via a loss function for example in the two stage compound sampling model the posterior means are optimal under squared error loss however they can perform poorly in estimating the histogram of the parameters or in ranking them triple goal estimates are motivated by the desire to have a set of estimates that produce good ranks a good parameter histogram and good co ordinate specific estimates no set of estimates can simultaneously optimize these three goals and we seek a set that strikes an effective trade off we evaluate and compare three candidate approaches the posterior means the constrained bayes estimates of louis and ghosh and a new approach that optimizes estimation of the histogram and the ranks mathematical and simulation based analyses support the superiority of the new approach and document its excellent performance for the three inferential goals

semiparametric estimation in the rasch model and related exponential response models including a simple latent class model for item analysis abstract the rasch model for item analysis is an important member of the class of exponential response models in which the number of nuisance parameters increases with the number of subjects leading to the failure of the usual likelihood methodology both conditional likelihood methods and mixture model techniques have been used to circumvent these problems in this article we show that these seemingly unrelated analyses are in fact closely linked to each other despite dramatic structural differences between the classes of models implied by each approach we show that the finite mixture model for j dichotomous items having t latent classes gives the same estimates of item parameters as conditional likelihood on a set whose probability approaches one if t j 1 2 unconditional maximum likelihood estimators for the finite mixture model can be viewed as keifer wolfowitz estimators for the random effects version of the rasch model latent class versions of the model are especially attractive when t is

the geometry of mixture likelihoods a general theory in this paper certain fundamental properties of the maximum likelihood estimator of a mixing distribution are shown to be geometric properties of the likelihood set the existence support size likelihood equations and uniqueness of the estimator are revealed to be directly related to the properties of the convex hull of the likelihood set and the support hyperplanes of that hull it is shown using geometric techniques that the estimator exists under quite general conditions with a support size no larger than the number of distinct observations analysis of the convex dual of the likelihood set leads to a dual maximization problem a convergent algorithm is described the defining equations for the estimator are compared with the usual parametric likelihood equations for finite mixtures sufficient conditions for uniqueness are given part ii will deal with a special theory for exponential family mixtures

a simple nonparametric approach to estimating the distribution of random coefficients in structural models abstract we explore least squares and likelihood nonparametric mixtures estimators of the joint distribution of random coefficients in structural models the estimators fix a grid of heterogeneous parameters and estimate only the weights on the grid points an approach that is computationally attractive compared to alternative nonparametric estimators we provide conditions under which the estimated distribution function converges to the true distribution in the weak topology on the space of distributions we verify most of the consistency conditions for three discrete choice models we also derive the convergence rates of the least squares nonparametric mixtures estimator under additional restrictions we perform a monte carlo study on a dynamic programming model

binomial mixtures geometric estimation of the mixing distribution given a mixture of binomial distributions how do we estimate the unknown mixing distribution we build on earlier work of lindsay and further elucidate the geometry underlying this question exploring the approximating role played by cyclic polytopes convergence of a resulting maximum likelihood fitting algorithm is proved and numerical examples given problems over the lack of identifiability of the mixing distribution in part disappear

on the design of efficient atm routing schemes in this paper we deal with the problem of designing virtual path layouts in atm networks when the hop count is given and the load has to be minimized we first prove a lower bound for networks with arbitrary topology and arbitrary set of connection requests this result is then applied to derive lower bounds for the following settings i one to all one node has to be connected to all other nodes of the network in arbitrary networks ii all to all each node has to be connected to all other nodes in the network in several classes of networks including planar and k separable networks and networks of bounded genus we finally study the all to all setting on two dimensional meshes and we design a virtual path layout for this problem when the hop count and the network degree are bounded by constants our results show that the upper bounds proposed in this paper for the one to all problem in arbitrary networks and for the all to all problem in two dimensional mesh networks are asymptotically optimal moreover the general lower bound shows that the algorithm proposed in gerstel ph d thesis technion haifa israel 1995 for the all to all problem in k separable networks is also asymptotically optimal the upper bound for mesh networks also shows that the lower bound presented in this paper for the all to all problem in planar networks is asymptotically tight

duration dependence and nonparametric heterogeneity a monte carlo study we examine the behaviour of the nonparametric maximum likelihood estimator npmle for a discrete duration model with unobserved heterogeneity and unknown duration dependence we find that a nonparametric specification of either the duration dependence or unobserved heterogeneity when the other feature of the hazard is known to be absent leads to estimators that are well behaved even in modestly sized samples in contrast there is a large and systematic bias in the parameters of these components when both are specified nonparametrically as well as a complementary bias in the coefficients on observed heterogeneity furthermore these biases diminish very gradually as sample size increases we find that a minor modification of the quasilikelihood that penalizes specifications with many points of support leads to a dramatic improvement

edge separators for graphs of bounded genus with applications we prove that every n vertex graph of genus g and maximal degree k has an edge separator of size o gkn the upper bound is best possible to within a constant factor this extends known results on planar graphs and similar results about vertex separators we apply the edge separator to the isoperimetric number problem graph embeddings and lower bounds for crossing numbers

likelihood inference for mixtures geometrical and other constructions of monotone step length algorithms summary this paper considers algorithms for the maximum likelihood estimator of the mixing distribution of a family of parametric densities specific interest is devoted to the monotonicity of the step length of the solution in 2 we introduce the idea of estimating the area above the second derivative curve and in theorem 1 we relate area overestimation to the monotonicity of the associated algorithm in 3 we apply theorem 1 to the monotonicity analysis of well known algorithms as well as to the construction of a new class of monotone step length choices which is particularly simple in the mixture setting numerical comparisons and refinements in keeping the monotonic step length from becoming too conservative are given theorem 3 characterizes conditions under which the newton raphson step is monotonic and if these conditions fail to hold states that the regula falsi step is monotonic

on fast computation of the non parametric maximum likelihood estimate of a mixing distribution summary a fast algorithm for computing the non parametric maximum likelihood estimate of a mixing distribution is presented at each iteration the algorithm adds new important points to the support set as guided by the gradient function updates all mixing proportions via a quadratically convergent method and discards redundant support points straightaway with its convergence being theoretically established numerical studies show that it is very fast and stable compared with several other algorithms that are available in the literature

information and topology in attractor neural networks a wide range of networks including those with small world topology can be modeled by the connectivity ratio and randomness of the links both learning and attractor abilities of a neural network can be measured by the mutual information mi as a function of the load and the overlap between patterns and retrieval states in this letter we use mi to search for the optimal topology with regard to the storage and attractor properties of the network in an amari hopfield model we find that while an optimal storage implies an extremely diluted topology a large basin of attraction leads to moderate levels of connectivity this optimal topology is related to the clustering and path length of the network we also build a diagram for the dynamical phases with random or local initial overlap and show that very diluted networks lose their attractor ability

semiparametric estimation of normal mixture densities a semiparametric method for estimating densities of normal mean mixtures is presented this consistent data driven method of estimation is based on probability spacings the estimation technique involves iteratively fixing the standard deviation of the normal kernel that serves as a smoothing parameter and then maximizing a function of the probability spacings over all mixing distributions based on the distribution of uniform spacings a distribution free goodness of fit criterion is developed to guide the selection of the smoothing parameter the result is a set of consistent estimators indexed by a range of smoothing parameters empirical process results are used to prove consistency

estimating the number of classes estimating the unknown number of classes in a population has numerous important applications in a poisson mixture model the problem is reduced to estimating the odds that a class is undetected in a sample the discontinuity of the odds prevents the existence of locally unbiased and informative estimators and restricts confidence intervals to be one sided confidence intervals for the number of classes are also necessarily one sided a sequence of lower bounds to the odds is developed and used to define pseudo maximum likelihood estimators for the number of classes

predicting the conditional probability of discovering a new class consider a population comprising disjoint classes an important problem arising from various fields is prediction of the random conditional probability of discovering a new class the asymptotic normality of the discovery probability is established in a poisson model where the number of individuals from each class is a poisson process with a class specific rate a new derivation is presented for the well known good toulmin predictor as a moment based estimator for the asymptotic limit of the discovery probability the good toulmin predictor is also shown to be a nonparametric empirical bayes estimator for the expectation of the discovery probability given the rates of the poisson processes and an approximation to an unbiased estimator only for the identifiable part of the expectation of the discovery probability in a multinomial model the properties of the moment based estimator are investigated so that confidence and prediction intervals can be constructed the good toulmin predictor and the discovery

convex optimization shape constraints compound decisions and empirical bayes rules estimation of mixture densities for the classical gaussian compound decision problem and their associated empirical bayes rules is considered from two new perspectives the first motivated by brown and greenshtein introduces a nonparametric maximum likelihood estimator of the mixture density subject to a monotonicity constraint on the resulting bayes rule the second motivated by jiang and zhang proposes a new approach to computing the kiefer wolfowitz nonparametric maximum likelihood estimator for mixtures in contrast to prior methods for these problems our new approaches are cast as convex optimization problems that can be efficiently solved by modern interior point methods in particular we show that the reformulation of the kiefer wolfowitz estimator as a convex optimization problem reduces the computational effort by several orders of magnitude for typical problems by comparison to prior em algorithm based methods and thus greatly expands the practical applicability of the resulting method

nonparametric estimation for a form of doubly censored data with application to two problems in aids abstract in many epidemiologic studies of human immunodeficiency virus hiv disease interest focuses on the distribution of the length of the interval of time between two events two such problems are considered here estimation of the distribution of time or number of sexual contacts between infection of an individual an index case and transmission of hiv to their sexual partner and estimation of the distribution of time between infectiousness as a blood donor and the development of detectable antibody data regarding these two problems are available from certain partner studies and the hiv lookback study in both cases the statistical development is complicated by the fact that the times of both events are interval censored so that the length of time between the events is never observed exactly nonparametric methods for estimation of the interval length distribution are developed by casting the problem in terms of nonparametric estimation of a mixing distribution particular attention is paid to

non parametric estimation and doubly censored data general ideas and applications to aids in many epidemiologic studies of human immunodeficiency virus hiv disease interest focuses on the distribution of the length of the interval of time between two events in many such cases statistical estimation of properties of this distribution is complicated by the fact that observation of the times of both events is subject to intervalcensoring so that the length of time between the events is never observed exactly following degruttola and lagakos we call such data doubly censored jewell malani and vittinghoff showed that with certain assumptions and for a particular doubly censored data structure non parametric maximum likelihood estimation of the interval length distribution is equivalent to non parametric estimation of a mixing distribution here we extend these ideas to various other kinds of doubly censored data we consider application of the methods to various studies generated by investigations into the natural history of hiv disease with particular attention given to estimation of the distribution of time between infection of an individual an index case and transmission of hiv to their sexual partner

residual diagnostics for mixture models abstract a sample is commonly modeled by a mixture distribution if the observations follow a common distribution but the parameter of interest differs between observations for example we observe the lengths but not the ages of a sample offish it may be reasonable to assume that length is normally distributed about an unknown mean that depends on the age of the fish provided there is more than one age class in the sample then the data are distributed as a mixture of normals in this article we assume that the data are a random sample from a mixture of exponential family distributions and that for each observation the parameter of interest is sampled independently from an unknown mixing distribution q the adequacy of a fitted mixture model can be assessed by examining residuals based on the ratio of the observed to expected fit residuals based on the homogeneity model in which q is a one point distribution display a convexity property when the data follow a mixture model this becomes the basis fo

a semiparametric mixture approach to case control studies with errors in covariables abstract methods are devised for estimating the parameters of a prospective logistic model in a case control study with dichotomous response d that depends on a covariate x for a portion of the sample both the gold standard x and a surrogate covariate w are available however for the greater portion of the data only the surrogate covariate w is available by using a mixture model the relationship between the true covariate and the response can be modeled appropriately for both types of data the likelihood depends on the marginal distribution of x and the measurement error density w x d the latter is modeled parametrically based on the validation sample the marginal distribution of the true covariate is modeled using a nonparametric mixture distribution in this way we can improve the efficiency and reduce the bias of the parameter estimates the results also apply when there is no validation data provided the error distribution is known or estimated from an independent data source many of the

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

a partial k arboretum of graphs with bounded treewidth the notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies this survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class also some mutual relations between such classes are discussed

nonparametric estimation of component distributions in a multivariate mixture suppose k variate data are drawn from a mixture of two distributions each having independent components it is desired to estimate the univariate marginal distributions in each of the products as well as the mixing proportion this is the setting of two class fully parametrized latent models that has been proposed for estimating the distributions of medical test results when disease status is unavailable the problem is one of inference in a mixture of distributions without training data and until now it has been tackled only in a fully parametric setting we investigate the possibility of using nonparametric methods of course when k 1 the problem is not identifiable from a nonparametric viewpoint we show that the problem is almost identifiable when k 2 there the set of all possible representations can be expressed in terms of any one of those representations as a two parameter family furthermore it is proved that when k geq3 the problem is nonparametrically identifiable under particularly mild regularity conditions in this case we introduce root n consistent nonparametric estimators of the 2k univariate marginal distributions and the mixing proportion finite sample and asymptotic properties of the estimators are described

sensitivity of dynamical systems to banach space parameters we consider general nonlinear dynamical systems in a banach space with dependence on parameters in a second banach space an abstract theoretical framework for sensitivity equations is developed an application to measure dependent delay differential systems arising in a class of hiv models is presented

structured patterns retrieval using a metric attractor network application to fingerprint recognition abstract the ability of a metric attractor neural networks mann to learn structured patterns is analyzed in particular we consider collections of fingerprints which present some local features rather than being modeled by random patterns the network retrieval proved to be robust to varying the pattern activity the threshold strategy the topological arrangement of the connections and for several types of noisy configuration we found that the lower the fingerprint patterns activity is the higher the load ratio and retrieval quality are a simplified theoretical framework for the unbiased case is developed as a function of five parameters the load ratio the finiteness connectivity the density degree of the network randomness ratio and the spatial pattern correlation linked to the latter appears a new neural dynamics variable the spatial neural correlation the theory agrees quite well with the experimental results

bayesian model selection in finite mixtures by marginal density decompositions we consider the problem of estimating the number of components d and the unknown mixing distribution in a finite mixture model in which d is bounded by some fixed finite number n our approach relies on the use of a prior over the space of mixing distributions with at most n components by decomposing the resulting marginal density under this prior we discover a weighted bayes factor method for consistently estimating d that can be implemented by an iid generalized weighted chinese restaurant gwcr monte carlo algorithm we also discuss a gibbs sampling method the blocked gibbs sampler for estimating d and also the mixing distribution we show that our resulting posterior is consistent and achieves the frequentist optimal op n 1 4 rate of estimation we compare the performance of the new gwcr model selection procedure with that of the akaike information criterion and the bayes information criterion implemented through an em algorithm applications of our methods to five real datasets and simulation

efficient greedy learning of gaussian mixture models this article concerns the greedy learning of gaussian mixtures in the greedy approach mixture components are inserted into the mixture one after the other we propose a heuristic for searching for the optimal component to insert in a randomized manner a set of candidate new components is generated for each of these candidates we find the locally optimal new component and insert it into the existing mixture the resulting algorithm resolves the sensitivity to initialization of state of the art methods like expectation maximization and has running time linear in the number of data points and quadratic in the final number of mixture components due to its greedy nature the algorithm can be particularly useful when the optimal number of mixture components is unknown experimental results comparing the proposed algorithm to other methods on density estimation and texture segmentation are provided