ISBN-10:
111999389X
ISBN-13:
9781119993896
Pub. Date:
07/05/2011
Publisher:
Wiley
Mixtures: Estimation and Applications / Edition 1

Mixtures: Estimation and Applications / Edition 1

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Product Details

ISBN-13: 9781119993896
Publisher: Wiley
Publication date: 07/05/2011
Series: Wiley Series in Probability and Statistics Series , #887
Pages: 330
Product dimensions: 6.20(w) x 9.20(h) x 0.90(d)

About the Author

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

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

D. Michael Titterington, University of Glasgow, Scotland.

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Table of Contents

Preface

Acknowledgements

List of Contributors 

1 The EM algorithm, variational approximations andexpectation 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 afinite 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 locallyidentifiable 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 likelihoodregions

4.4 Comparison between the likelihood regions and the Waldregions

4.5 Application to a finite mixture model

4.6 Data analysis

4.7 Discussion

References

5 Mixture of experts modelling with social scienceapplications
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 smoothmixtures
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-normalmodels

References

7 Nonparametric mixed membership modelling using the IBPcompound Dirichlet process
Sinead Williamson, Chong Wang, Katherine A. Heller, andDavid 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 Bayesianrose 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 modelsand product partition models

8.6 Results

8.7 Discussion

References

9 Mixtures of factor analyzers for the analysis ofhigh-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-processrepresentation

10.3 Identifying mixtures when the number of components isunknown

10.4 Overfitting heterogeneity of component-specificparameters

10.5 Concluding remarks

References

11 Exact Bayesian analysis of mixtures
Christian .P. Robert and Kerrie L. Mengersen

11.1 Introduction

11.2 Formal derivation of the posterior distribution

References

12 Manifold MCMC for mixtures
Vassilios Stathopoulos and Mark Girolami

12.1 Introduction

12.2 Markov chain Monte Carlo methods

12.3 Finite Gaussian mixture models

12.4 Experiments

12.5 Discussion

Acknowledgements 

Appendix

References

13 How many components in a finite mixture?
Murray 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

13.10 Conclusion

References

14 Bayesian mixture models: a blood-free dissection of asheep
Clair L. Alston, Kerrie L. Mengersen, and Graham E.Gardner

14.1 Introduction

14.2 Mixture models

14.3 Altering dimensions of the mixture model

14.4 Bayesian mixture model incorporating spatialinformation

14.5 Volume calculation

14.6 Discussion

References

Index.

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