Dealing with label switching under model uncertainty

Mixtures: Estimation and Applications

Volumn , Issue , 2011, Pages 213-239

  Frühwirth Schnatter, Sylvia ^a  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

Dealing with label switching under model uncertainty; Final issue, model uncertainty with respect to distribution family underlying mixture; Identification of finite mixture models overfitting heterogeneity in component specific parameters; Identifying a finite mixture model under uncertainty, with respect to model specification; Identifying a unique labelling under model uncertainty; Labelling through clustering in point process representation; Overfitting heterogeneity of component specific parameters; Point process representation of a finite mixture model; Useful methods, forcing a unique labelling on draws from this posterior distribution; Using shrinkage priors on component specific location parameters

Indexed keywords

MIXTURES;

FINITE MIXTURE MODELING; FINITE MIXTURE MODELS; MODEL SPECIFICATIONS; MODEL UNCERTAINTIES; OVERFITTING; POINT PROCESS; POSTERIOR DISTRIBUTIONS; SPECIFIC LOCATION;

UNCERTAINTY ANALYSIS;

EID: 84955377181     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9781119995678.ch10     Document Type: Chapter

References (36)

1. Bernardo, J. M. and Girón, F. G. (1988) A Bayesian analysis of simple mixture problems. In Bayesian Statistics 3 (eds J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith) pp. 67-78, Clarendon.
2. Biernacki, C., Celeux, G. and Govaert, G. (2000) Assessing a mixture model for clustering with the integrated completed likelihood. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22, 719-725.
3. Celeux, G. (1998) Bayesian inference for mixture: the label switching problem. In COMPSTAT 98 (eds P. J. Green and R. Rayne), pp. 227-232. Physica, Heidelberg.
4. Celeux, G., Hurn, M. and Robert, C. P. (2000) Computational and inferential difficulties with mixture posterior distributions. Journal of the American Statistical Association, 95, 957-970.
5. Dellaportas, P. and Papageorgiou, I. (2006) Multivariate mixtures of normals with unknown number of components. Statistics and Computing, 16, 57-68.
6. Diebolt, J. and Robert, C. P. (1994) Estimation of finite mixture distributions through Bayesian sampling. Journal of the Royal Statistical Society, Series B, 56, 363-375.
7. Fahrmeir, L., Kneib, T. and Konrath, S. (2010) Bayesian regularisation in structured additive regression: a unifying perspective on shrinkage, smoothing and predictor selection. Statistics and Computing, 20, 203-219.
8. Ferguson, T. S. (1973) A Bayesian analysis of some nonparametric problems. Annals of Statistics, 1, 209-230.
9. Frühwirth-Schnatter, S. (2001a) Fully Bayesian analysis of switching Gaussian state space models. Annals of the Institute of Statistical Mathematics, 53, 31-49.
10. Frühwirth-Schnatter, S. (2001b) Markov chain Monte Carlo estimation of classical and dynamic switching and mixture models. Journal of the American Statistical Association, 96, 194-209.
11. Frühwirth-Schnatter, S. (2004) Estimating marginal likelihoods for mixture and Markov switching models using bridge sampling techniques. The Econometrics Journal, 7, 143-167.
12. Frühwirth-Schnatter, S. (2006) Finite Mixture and Markov Switching Models. Springer.
13. Frühwirth-Schnatter, S. (2008) Comment on article by T. Rydën on 'EM versus Markov chain Monte Carlo for estimation of hidden Markov models'. Bayesian Analysis, 3, 689-698.
14. Frühwirth-Schnatter, S. and Pyne, S. (2010) Bayesian Inference for finite mixtures of univariate and multivariate skew normal and skew-t distributions. Biostatistics, 11, 317-336.
15. Green, P. J. and Richardson, S. (2001) Modelling heterogeneity with and without the Dirichlet process. Scandinavian Journal of Statistics, 28, 355-375.
16. Griffin, J. E. and Brown, P. J. (2010) Inference with normal-gamma prior distributions in regression problems. Bayesian Analysis, 5, 171-188.
17. Grün, B. and Leisch, F. (2009) Dealing with label switching in mixture models under genuine multimodality. Journal of Multivariate Analysis, 100, 851-861.
18. Hahn, M., Frühwirth-Schnatter, S. and Sass, J. (2010) Markov chain Monte Carlo methods for parameter estimation in multidimensional continuous time Markov switching models. Journal of Financial Econometrics, 8, 88-121.
19. Ishwaran, H., James, L. F. and Sun, J. (2001) Bayesian model selection in finite mixtures by marginal density decompositions. Journal of the American Statistical Association, 96, 1316-1332.
20. Jasra, A., Holmes, C. C. and Stephens, D. A. (2005) Markov chain Monte Carlo methods and the label switching problem in Bayesian mixture modelling. Statistical Science, 20, 50-67.
21. Keribin, C. (2000) Consistent estimation of the order of mixture models. Sankhya A, 62, 49-66.
22. Marin, J. M., Mengersen, K. and Robert, C. P. (2005) Bayesian modelling and inference on mixtures of distributions. In Bayesian Thinking, Modelling and Computation (eds D. Dey and C. Rao) Vol. 25 of Handbook of Statistics, pp. 459-507, North-Holland.
23. McLachlan, G. J. and Peel, D. (2000) Finite Mixture Models. John Wiley & Sons, Ltd.
24. Nobile, A. (2004) On the posterior distribution of the number of components in a finite mixture. Annals of Statistics, 32, 2044-2073.
25. Nobile, A. and Fearnside, A. (2007) Bayesian finite mixtures with an unknown number of components: the allocation sampler. Statistics and Computing, 17, 147-162.
26. Pamminger, C. and Frühwirth-Schnatter, S. (2010) Bayesian clustering of categorical time series. Bayesian Analysis, 5, 345-368.
27. Park, T. and Casella, G. (2008) The Bayesian Lasso. Journal of the American Statistical Association, 103, 681-686.
28. Richardson, S. and Green, P. J. (1997) On Bayesian analysis of mixtures with an unknown number of components. Journal of the Royal Statistical Society, Series B, 59, 731-792.
29. Rousseau, J. and Mengersen, K. (2010) Asymptotic behaviour of the posterior distribution in overfitted mixture models. Technical Report, ENSEA-CREST.
30. Sperrin, M., Jaki, T. and Wit, E. (2010) Probabilistic relabelling strategies for the label switching problem in Bayesian mixture models. Statistics and Computing, 20, 357-366.
31. Spezia, L. (2009) Reversible jump and the label switching problem in hidden Markov models. Journal of Statistical Planning and Inference, 139, 2305-2315.
32. Stephens, M. (1997) Bayesian methods for mixtures of normal distributions. DPhil Thesis, University of Oxford.
33. Stephens, M. (2000a) Bayesian analysis of mixture models with an unknown number of components - an alternative to reversible jump methods. Annals of Statistics, 28, 40-74.
34. Stephens, M. (2000b) Dealing with label switching in mixture models. Journal of the Royal Statistical Society, Series B, 62, 795-809.
35. Titterington, D. M., Smith, A. F. M. and Makov, U. E. (1985) Statistical Analysis of Finite Mixture Distributions. John Wiley & Sons, Ltd.
36. Yau, C. and Holmes, C. (2010) Hierarchical Bayesian nonparametric mixture models for clustering with variable relevance determination. Technical Report, Department of Statistics, University of Oxford.