Finite Mixture Models
An up-to-date, comprehensive account of major issues in finite mixture modeling
This volume provides an up-to-date account of the theory and applications of modeling via finite mixture distributions. With an emphasis on the applications of mixture models in both mainstream analysis and other areas such as unsupervised pattern recognition, speech recognition, and medical imaging, the book describes the formulations of the finite mixture approach, details its methodology, discusses aspects of its implementation, and illustrates its application in many common statistical contexts.
Major issues discussed in this book include identifiability problems, actual fitting of finite mixtures through use of the EM algorithm, properties of the maximum likelihood estimators so obtained, assessment of the number of components to be used in the mixture, and the applicability of asymptotic theory in providing a basis for the solutions to some of these problems. The author also considers how the EM algorithm can be scaled to handle the fitting of mixture models to very large databases, as in data mining applications. This comprehensive, practical guide:
* Provides more than 800 references-40% published since 1995
* Includes an appendix listing available mixture software
* Links statistical literature with machine learning and pattern recognition literature
* Contains more than 100 helpful graphs, charts, and tables
Finite Mixture Models is an important resource for both applied and theoretical statisticians as well as for researchers in the many areas in which finite mixture models can be used to analyze data.
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2 ML Fitting of Mixture Models
3 Multivariate Normal Mixtures
4 Bayesian Approach to Mixture Analysis
5 Mixtures with Nonnormal Components
6 Assessing the Number of Components in Mixture Models
7 Multivariate t Mixtures
8 Mixtures of Factor Analyzers
9 Fitting Mixture Models to Binned Data
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1)th iteration Aitkin algorithm American Statistical Association analysis applications approximation asymptotic Basford Bayesian bootstrap Celeux classiﬁcation clustering component densities component means component membership component-covariance matrices component-indicator computation conditional expectation considered convergence corresponding covariance matrix criterion data set deﬁned denotes E-step efﬁcient example exponential family ﬁnite mixture models ﬁrst ﬁt ﬁtted ﬁtting of mixture ﬁxed Gibbs sampler given GLMs groups hidden Markov homoscedastic identiﬁability IEM algorithm ith component joint sets Kent distributions likelihood equation likelihood function linear LRTS Markov chain maximizer maximum likelihood McLachlan method mixing proportions mixture density mixture distributions multivariate nonparametric normal components normal distribution normal mixture model null distribution number of components observed data observed information matrix obtained overdispersion P-value parameter space Plot Poisson Poisson regression posterior probabilities prior probabilities of component problem Raftery random Royal Statistical Society sample Section simulation solution speciﬁed sufﬁcient Titterington univariate normal unknown parameters updated variables variance