Mixtures - Estimation and Applications

Klappentext Research on inference and computational techniques for mixture-type models is experiencing new and major advances and the call to mixture modelling in various science and business areas is omnipresent.Mixtures: Estimation and Applications contains a collection of chapters written by international experts in the field, representing the state of the art in mixture modelling, inference and computation. A wide and representative array of applications of mixtures, for instance in biology and economics, are covered. Both Bayesian and non-Bayesian methodologies, parametric and non-parametric perspectives, statistics and machine learning schools appear in the book.This book:* Provides a contemporary account of mixture inference, with Bayesian, non-parametric and learning interpretations.* Explores recent developments about the EM (expectation maximization) algorithm for maximum likelihood estimation.* Looks at the online algorithms used to process unlimited amounts of data as well as large dataset applications.* Compares testing methodologies and details asymptotics in finite mixture models.* Introduces mixture of experts modeling and mixed membership models with social science applications.* Addresses exact Bayesian analysis, the label switching debate, and manifold Markov Chain Monte Carlo for mixtures.* Includes coverage of classification and machine learning extensions.* Features contributions from leading statisticians and computer scientists.This area of statistics is important to a range of disciplines, including bioinformatics, computer science, ecology, social sciences, signal processing, and finance. This collection will prove useful to active researchers and practitioners in these areas. Zusammenfassung This book uses the EM (expectation maximization) algorithm to simultaneously estimate the missing data and unknown parameter(s) associated with a data set. The parameters describe the component distributions of the mixture; the distributions may be continuous or discrete.The editors provide a complete account of the applications, mathematical structure and statistical analysis of finite mixture distributions along with MCMC computational methods, together with a range of detailed discussions covering the applications of the methods and features chapters from the leading experts on the subject. The applications are drawn from scientific discipline, including biostatistics, computer science, ecology and finance. This area of statistics is important to a range of disciplines, and its methodology attracts interest from researchers in the fields in which it can be applied. Inhaltsverzeichnis PrefaceAcknowledgementsList of Contributors1 The EM algorithm, variational approximations and expectation propagation for mixturesD.Michael Titterington1.1 Preamble1.2 The EM algorithm1.3 Variational approximations1.4 Expectation-propagationAcknowledgementsReferences2 Online expectation maximisationOlivier Cappé2.1 Introduction2.2 Model and assumptions2.3 The EM algorithm and the limiting EM recursion2.4 Online expectation maximisation2.5 DiscussionReferences3 The limiting distribution of the EM test of the order of a finite mixtureJ. Chen and Pengfei Li3.1 Introduction3.2 The method and theory of the EM test3.3 Proofs3.4 DiscussionReferences4 Comparing Wald and likelihood regions applied to locally identifiable mixture modelsDaeyoung Kim and Bruce G. Lindsay4.1 Introduction4.2 Background on likelihood confidence regions4.3 Background on simulation and visualisation of the likelihood regions4.4 Comparison between the likelihood regions and the Wald regions4.5 Application to a finite mixture model4.6 Data analysis4.7 DiscussionReferences5 Mixture of experts modelling with social science applicationsIsobel Claire Gormley and Thomas Brendan Murphy5.1 Introduction5.2 Motivating examples5.3 Mixture models5.4 Mixt...

List of contents

PrefaceAcknowledgementsList of Contributors1 The EM algorithm, variational approximations and expectation propagation for mixturesD.Michael Titterington1.1 Preamble1.2 The EM algorithm1.3 Variational approximations1.4 Expectation-propagationAcknowledgementsReferences2 Online expectation maximisationOlivier Cappé2.1 Introduction2.2 Model and assumptions2.3 The EM algorithm and the limiting EM recursion2.4 Online expectation maximisation2.5 DiscussionReferences3 The limiting distribution of the EM test of the order of a finite mixtureJ. Chen and Pengfei Li3.1 Introduction3.2 The method and theory of the EM test3.3 Proofs3.4 DiscussionReferences4 Comparing Wald and likelihood regions applied to locally identifiable mixture modelsDaeyoung Kim and Bruce G. Lindsay4.1 Introduction4.2 Background on likelihood confidence regions4.3 Background on simulation and visualisation of the likelihood regions4.4 Comparison between the likelihood regions and the Wald regions4.5 Application to a finite mixture model4.6 Data analysis4.7 DiscussionReferences5 Mixture of experts modelling with social science applicationsIsobel Claire Gormley and Thomas Brendan Murphy5.1 Introduction5.2 Motivating examples5.3 Mixture models5.4 Mixture of experts models5.5 A Mixture of experts model for ranked preference data5.6 A Mixture of experts latent position cluster model5.7 DiscussionAcknowledgementsReferences6 Modelling conditional densities using finite smooth mixturesFeng Li, Mattias Villani and Robert Kohn6.1 Introduction6.2 The model and prior6.3 Inference methodology6.4 Applications6.5 ConclusionsAcknowledgementsAppendix: Implementation details for the gamma and log-normal modelsReferences7 Nonparametric mixed membership modelling using the IBP compound Dirichlet processSinead Williamson, Chong Wang, Katherine A. Heller, and David M. Blei7.1 Introduction7.2 Mixed membership models7.3 Motivation7.4 Decorrelating prevalence and proportion7.5 Related models7.6 Empirical studies7.7 DiscussionReferences8 Discovering nonbinary hierarchical structures with Bayesian rose treesCharles Blundell, Yee Whye Teh, and Katherine A. Heller8.1 Introduction8.2 Prior work8.3 Rose trees, partitions and mixtures8.4 Greedy Construction of Bayesian Rose Tree Mixtures8.5 Bayesian hierarchical clustering, Dirichlet process models and product partition models8.6 Results8.7 DiscussionReferences9 Mixtures of factor analyzers for the analysis of high-dimensional dataGeoffrey J. McLachlan, Jangsun Baek, and Suren I. Rathnayake9.1 Introduction9.2 Single-factor analysis model9.3 Mixtures of factor analyzers9.4 Mixtures of common factor analyzers (MCFA)9.5 Some related approaches9.6 Fitting of factor-analytic models9.7 Choice of the number of factors q9.8 Example9.9 Low-dimensional plots via MCFA approach9.10 Multivariate t-factor analysers9.11 DiscussionAppendixReferences10 Dealing with Label Switching under model uncertaintySylvia Frühwirth-Schnatter10.1 Introduction10.2 Labelling through clustering in the point-process representation10.3 Identifying mixtures when the number of components is unknown10.4 Overfitting heterogeneity of component-specific parameters10.5 Concluding remarksReferences11 Exact Bayesian analysis of mixturesChristian .P. Robert and Kerrie L. Mengersen11.1 Introduction11.2 Formal derivation of the posterior distributionReferences12 Manifold MCMC for mixturesVassilios Stathopoulos and Mark Girolami12.1 Introduction12.2 Markov chain Monte Carlo methods12.3 Finite Gaussian mixture models12.4 Experiments12.5 DiscussionAcknowledgementsAppendixReferences13 How many components in a finite mixture?Murray Aitkin13.1 Introduction13.2 The galaxy data13.3 The normal mixture model13.4 Bayesian analyses13.5 Posterior distributions for K (for flat prior)13.6 Conclusions from the Bayesian analyses13.7 Posterior distributions of the model deviances13.8 Asymptotic distributions13.9 Posterior deviances for the galaxy data13.10 ConclusionReferences14 Bayesian mixture models: a blood-free dissection of a sheepClair L. Alston, Kerrie L. Mengersen, and Graham E. Gardner14.1 Introduction14.2 Mixture models14.3 Altering dimensions of the mixture model14.4 Bayesian mixture model incorporating spatial information14.5 Volume calculation14.6 DiscussionReferencesIndex.

Product details

• Authors: Kerrie Mengersen, Kerrie L. (Queensland University of Tec Mengersen, Mengersen Kerrie L., Christian Robert, Robert Christian, Titterington, Mike Titterington, Titterington Mike
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 06.05.2011
• EAN: 9781119993896
• ISBN: 978-1-119-99389-6
• No. of pages: 330
• Series: Wiley Series in Probability and Statistics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Statistik, Statistics, Biostatistik, Biostatistics, Angewandte Wahrscheinlichkeitsrechnung u. Statistik, Applied Probability & Statistics