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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...
