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.
Autorentext
Kerrie L. Mengersen, Queensland University of Technology, Australia.
Christian P. Robert, Universite Paris-Dauphine, France.
D. Michael Titterington, University of Glasgow, Scotland.
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.
Inhalt
Preface
Acknowledgements
List of Contributors
1 The EM algorithm, variational approximations and expectation propagation for mixtures D.Michael Titterington
1.1 Preamble
1.2 The EM algorithm
1.3 Variational approximations
1.4 Expectation-propagation
Acknowledgements
References
2 Online expectation maximisation Olivier Cappé
2.1 Introduction
2.2 Model and assumptions
2.3 The EM algorithm and the limiting EM recursion
2.4 Online expectation maximisation
2.5 Discussion
References
3 The limiting distribution of the EM test of the order of a finite mixture J. Chen and Pengfei Li
3.1 Introduction
3.2 The method and theory of the EM test
3.3 Proofs
3.4 Discussion
References
4 Comparing Wald and likelihood regions applied to locally identifiable mixture models Daeyoung Kim and Bruce G. Lindsay
4.1 Introduction
4.2 Background on likelihood confidence regions
4.3 Background on simulation and visualisation of the likelihood regions
4.4 Comparison between the likelihood regions and the Wald regions
4.5 Application to a finite mixture model
4.6 Data analysis
4.7 Discussion
References
5 Mixture of experts modelling with social science applications Isobel Claire Gormley and Thomas Brendan Murphy
5.1 Introduction
5.2 Motivating examples
5.3 Mixture models
5.4 Mixture of experts models
5.5 A Mixture of experts model for ranked preference data
5.6 A Mixture of experts latent position cluster model
5.7 Discussion
Acknowledgements
References
6 Modelling conditional densities using finite smooth mixtures Feng Li, Mattias Villani and Robert Kohn
6.1 Introduction
6.2 The model and prior
6.3 Inference methodology
6.4 Applications
6.5 Conclusions
Acknowledgements
Appendix: Implementation details for the gamma and log-normal models
References
7 Nonparametric mixed membership modelling using the IBP compound Dirichlet process Sinead Williamson, Chong Wang, Katherine A. Heller, and David M. Blei
7.1 Introduction
7.2 Mixed membership models
7.3 Motivation
7.4 Decorrelating prevalence and proportion
7.5 Related models
7.6 Empirical studies
7.7 Discussion
References
8 Discovering nonbinary hierarchical structures with Bayesian rose trees Charles Blundell, Yee Whye Teh, and Katherine A. Heller
8.1 Introduction
8.2 Prior work
8.3 Rose trees, partitions and mixtures
8.4 Greedy Construction of Bayesian Rose Tree Mixtures
8.5 Bayesian hierarchical clustering, Dirichlet process models and product partition models
8.6 Results
8.7 Discussion
References
9 Mixtures of factor analyzers for the analysis of high-dimensional data Geoffrey J. McLachlan, Jangsun Baek, and Suren I. Rathnayake
9.1 Introduction
9.2 Single-factor analysis model
9.3 Mixtures of factor analyzers
9.4 Mixtures of common factor analyzers (MCFA)
9.5 Some related approaches
9.6 Fitting of factor-analytic models
9.7 Choice of the number of factors q
9.8 Example
9.9 Low-dimensional plots via MCFA approach
9.10 Multivariate t-factor analysers
9.11 Discussion
Appendix
References
10 Dealing with Label Switching under model uncertainty Sylvia Frühwirth-Schnatter
10.1 Introduction
10.2 Labelling through clustering in the point-process representation
10.3 Identifying mixtures when the number of components is unknown
10.4 Overfitting heterogeneity of component-specific…