Mixtures - Estimation And Applications

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.

Kerrie L. Mengersen, Queensland University of Technology, Australia.

Christian P. Robert, Universite Paris-Dauphine, France.

D. Michael Titterington, University of Glasgow, Scotland.

Preface.

Acknowledgements.

1 The EM Algorithm, Variational Approximations and Expectation Propagation for Mixtures (D.M. Titterington).

1.1 Preamble
1.2 The EM algorithm
1.3 Variational approximations
1.4 Expectation Propagation
References

2 Online Expectation-Maximisation (O. Cappe).
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 P. 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 (D. Kim and B. G. Lindsa).
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 (I.C. Gormley and T.B. 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
References

6 Modelling Conditional Densities using Finite Smooth Mixtures (F. Li, M. Villani and R. Kohn).
6.1 Introduction
6.2 The Model and Prior
6.3 Inference Methodology
6.4 Applications
6.5 Conclusions
References

7 Nonparametric Mixed Membership Modelling Using the IBP Compound Dirichlet Process (S. Williamson, C. Wang, K.A. Heller, and D.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 Non-binary Hierarchical Structures with Bayesian Rose Trees (C. Blundell, Y.W. Teh, and K.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 (G.J. McLachlan, J. Baek, and S.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 analyzers
9.11 Discussion
References

10 Dealing with Label Switching under Model Uncertainty (S. Fr¨uhwirth-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 parameters
10.5 Concluding Remarks
References

11 Exact Bayesian Analysis of Mixtures (C.P. Robert and K.L. Mengersen).
11.1 Introduction
11.2 Formal derivation of the posterior distribution
References

12 Manifold MCMC for Mixtures (V. Stathopoulos and M. Girolami).
12.1 Introduction
12.2 Markov Chain Monte Carlo Methods
12.3 Finite Gaussian Mixture Models
12.4 Experiments
12.5 Discussion
12.6 Appendix
References

13 How Many Components in a Finite Mixture? (M. Aitkin).
13.1 Introduction
13.2 The galaxy data
13.3 The normal mixture model
13.4 Bayesian analyses
13.5 Posterior distributions for K (for flat prior)
13.6 Conclusions from the Bayesian analyses
13.7 Posterior distributions of the model deviances
13.8 Asymptotic distributions
13.9 Posterior deviances for the galaxy data
13.10Conclusion
References

14 Bayesian Mixture Models: A Blood Free Dissection of a Sheep (C.L. Alston, K.L. Mengersen, and G.E. Gardner).
14.1 Introduction
14.2 Mixture Models
14.3 Altering dimensions of the mixture model
14.4 Bayesian mixture model incorporating spatial information
14.5 Volume calculation
14.6 Discussion
References

Index.