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Finite Mixture (finite + mixture)

Distribution by Scientific Domains

Mathematics and Statistics	100%

Terms modified by Finite Mixture

finite mixture models

Selected Abstracts

ESTIMATING COMPONENTS IN FINITE MIXTURES AND HIDDEN MARKOV MODELS

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 3 2005
D.S. Poskitt
Summary When the unobservable Markov chain in a hidden Markov model is stationary the marginal distribution of the observations is a finite mixture with the number of terms equal to the number of the states of the Markov chain. This suggests the number of states of the unobservable Markov chain can be estimated by determining the number of mixture components in the marginal distribution. This paper presents new methods for estimating the number of states in a hidden Markov model, and coincidentally the unknown number of components in a finite mixture, based on penalized quasi-likelihood and generalized quasi-likelihood ratio methods constructed from the marginal distribution. The procedures advocated are simple to calculate, and results obtained in empirical applications indicate that they are as effective as current available methods based on the full likelihood. Under fairly general regularity conditions, the methods proposed generate strongly consistent estimates of the unknown number of states or components. [source]

Capture,Recapture Estimation Using Finite Mixtures of Arbitrary Dimension

BIOMETRICS, Issue 2 2010
Richard Arnold
Summary Reversible jump Markov chain Monte Carlo (RJMCMC) methods are used to fit Bayesian capture,recapture models incorporating heterogeneity in individuals and samples. Heterogeneity in capture probabilities comes from finite mixtures and/or fixed sample effects allowing for interactions. Estimation by RJMCMC allows automatic model selection and/or model averaging. Priors on the parameters stabilize the estimates and produce realistic credible intervals for population size for overparameterized models, in contrast to likelihood-based methods. To demonstrate the approach we analyze the standard Snowshoe hare and Cottontail rabbit data sets from ecology, a reliability testing data set. [source]

INAR(1) modeling of overdispersed count series with an environmental application

ENVIRONMETRICS, Issue 4 2008
Harry Pavlopoulos
Abstract This paper is concerned with a novel version of the INAR(1) model, a non-linear auto-regressive Markov chain on ,, with innovations following a finite mixture distribution of Poisson laws. For , the stationary marginal probability distribution of the chain is overdispersed relative to a Poisson, thus making INAR(1) suitable for modeling time series of counts with arbitrary overdispersion. The one-step transition probability function of the chain is also a finite mixture, of m Poisson-Binomial laws, facilitating likelihood-based inference for model parameters. An explicit EM-algorithm is devised for inference by maximization of a conditional likelihood. Alternative options for inference are discussed along with criteria for selecting m. Integer-valued prediction (IP) is developed by a parametric bootstrap approach to ,coherent' forecasting, and a certain test statistic based on predictions is introduced for assessing performance of the fitted model. The proposed model is fitted to time series of counts of pixels where spatially averaged rain rate exceeds a given threshold level, illustrating its capabilities in challenging cases of highly overdispersed count data. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Treating missing values in INAR(1) models: An application to syndromic surveillance data

JOURNAL OF TIME SERIES ANALYSIS, Issue 1 2010
Jonas Andersson
Time-series models for count data have found increased interest in recent years. The existing literature refers to the case of data that have been fully observed. In this article, methods for estimating the parameters of the first-order integer-valued autoregressive model in the presence of missing data are proposed. The first method maximizes a conditional likelihood constructed via the observed data based on the k -step-ahead conditional distributions to account for the gaps in the data. The second approach is based on an iterative scheme where missing values are imputed so as to update the estimated parameters. The first method is useful when the predictive distributions have simple forms. We derive in full details this approach when the innovations are assumed to follow a finite mixture of Poisson distributions. The second method is applicable when there are no closed form expression for the conditional likelihood or they are hard to derive. The proposed methods are applied to a dataset concerning syndromic surveillance during the Athens 2004 Olympic Games. [source]

ESTIMATING COMPONENTS IN FINITE MIXTURES AND HIDDEN MARKOV MODELS

A general class of hierarchical ordinal regression models with applications to correlated roc analysis

THE CANADIAN JOURNAL OF STATISTICS, Issue 4 2000
Hemant Ishwaran
Abstract The authors discuss a general class of hierarchical ordinal regression models that includes both location and scale parameters, allows link functions to be selected adaptively as finite mixtures of normal cumulative distribution functions, and incorporates flexible correlation structures for the latent scale variables. Exploiting the well-known correspondence between ordinal regression models and parametric ROC (Receiver Operating Characteristic) curves makes it possible to use a hierarchical ROC (HROC) analysis to study multilevel clustered data in diagnostic imaging studies. The authors present a Bayesian approach to model fitting using Markov chain Monte Carlo methods and discuss HROC applications to the analysis of data from two diagnostic radiology studies involving multiple interpreters. RÉSUMÉ Les auteurs s'intéressent à une classe assez vaste de modèles de régression ordinale avec paramètres de localisation et d'échelle, laquelle permet la sélection adaptative de fonctions de lien s'exprimant comme mélanges finis de fonctions de répartition normales et fournit des structures de correlation flexibles pour les variables d'échelle latentes. En exploitant la correspondance bien connue entre les modèles de régression ordinale et les courbes d'efficacité paramétriques (CEP) des tests diagnostiques, il est possible d'analyser des données d'imagerie médicate diagnostique regroupées à plusieurs niveaux au moyen d'une CEP hiéiarchique. Les auteurs décrivent une approche bayésienne pour l'ajustement de tels modèles au moyen des méthodes de Monte Carlo à cha,ne de Markov et présentent deux applications concrètes concernant l'interprétation de clichés radiologiques [source]

Bayesian nonparametric hierarchical modeling

BIOMETRICAL JOURNAL, Issue 2 2009
David B. Dunson
Abstract In biomedical research, hierarchical models are very widely used to accommodate dependence in multivariate and longitudinal data and for borrowing of information across data from different sources. A primary concern in hierarchical modeling is sensitivity to parametric assumptions, such as linearity and normality of the random effects. Parametric assumptions on latent variable distributions can be challenging to check and are typically unwarranted, given available prior knowledge. This article reviews some recent developments in Bayesian nonparametric methods motivated by complex, multivariate and functional data collected in biomedical studies. The author provides a brief review of flexible parametric approaches relying on finite mixtures and latent class modeling. Dirichlet process mixture models are motivated by the need to generalize these approaches to avoid assuming a fixed finite number of classes. Focusing on an epidemiology application, the author illustrates the practical utility and potential of nonparametric Bayes methods. [source]