Dealing with label switching in mixture models

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 62, Issue 4, 2000, Pages 795-809

  Stephens, Matthew ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Bayesian approach; Classification; Clustering; Identifiability; Markov chain Monte Carlo methods; Mixture model; Multimodal posterior

Indexed keywords

EID: 0034354410     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9868.00265     Document Type: Article

References (19)

1. Carlin, B. P. and Chib, S. (1995) Bayesian model choice via Markov chain Monte Carlo methods. J. R. Statist. Soc. B, 57, 473-484.
2. Celeux, G. (1997) Discussion on 'On Bayesian analysis of mixtures with an unknown number of components' (by S. Richardson and P. J. Green). J. R. Statist. Soc. B, 59, 775-776.
3. - (1998) Bayesian inference for mixtures: the label-switching problem. In COMPSTAT 98 (eds R. Payne and P. Green), pp. 227-232. Heidelberg: Physica.
4. Celeux, G., Chauveau, D. and Diebolt, J. (1996) Stochastic versions of the EM algorithm: an experimental study in the mixture case. J. Statist. Computn Simuln, 55, 287-314.
5. Celeux, G., Hum, M. and Robert, C. P. (2000) Computational and inferential difficulties with mixture posterior distributions. J. Am. Statist. Ass., to be published.
6. Chib, S. (1995) Marginal likelihood from the Gibbs output. J. Am. Statist. Ass., 90, 1313-1321.
7. Crawford, S. L. (1994) An application of the Laplace method to finite mixture distributions. J. Am. Statist. Ass., 89, 259-267.
8. Diebolt, J. and Robert C. P. (1994) Estimation of finite mixture distributions through Bayesian sampling. J. R. Statist. Soc. B, 56, 363-375.
9. Escobar, M. D. and West, M. (1995) Bayesian density estimation and inference using mixtures. J. Am. Statist. Ass., 90, 577-588.
10. Gilks, W. R., Richardson, S. and Spiegelhalter, D. J. (eds) (1996) Markov Chain Monte Carlo in Practice. London: Chapman and Hall.
11. Phillips, D. B. and Smith, A. F. M. (1996) Bayesian model comparison via jump diffusions. In Markov Chain Monte Carlo in Practice (eds W. R. Gilks, S. Richardson and D. J. Spiegelhalter), ch. 13, pp. 215-239. London: Chapman and Hall.
12. Redner, R. A. and Walker, H. F. (1984) Mixture densities, maximum likelihood and the EM algorithm. SIAM Rev., 26, 195-239.
13. Richardson, S. and Green, P. J. (1997) On Bayesian analysis of mixtures with an unknown number of components (with discussion). J. R. Statist. Soc. B, 59, 731-792.
14. Robert, C. P., Rydén, T. and Titterington, D. M. (2000) Bayesian inference in hidden Markov models through the reversible jump Markov chain Monte Carlo method. J. R. Statist. Soc. B, 62, 57-75.
15. Roeder, K. (1990) Density estimation with confidence sets exemplified by superclusters and voids in the galaxies. J. Am. Statist. Ass., 85, 617-624.
16. Stephens, M. (1997a) Discussion on 'On Bayesian analysis of mixtures with an unknown number of components' (by S. Richardson and P. J. Green). J. R. Statist. Soc. B, 59, 768-769.
17. - (1997b) Bayesian methods for mixtures of normal distributions. D Phil Thesis. University of Oxford, Oxford. (Available from http: //www.stats.ox.ac.uk/~stephens.)
18. - (2000) Bayesian analysis of mixture models with an unknown number of components - an alternative to reversible jump methods. Ann. Statist., 28, in the press.
19. Taha, H. A. (1989) Operations Research: an Introduction, 4th edn. New York: Macmillan.