Bayesian mixture labeling by highest posterior density

Journal of the American Statistical Association

Volumn 104, Issue 486, 2009, Pages 758-767

  Yao, Weixin ^a   Lindsay, Bruce G ^b  

^a KANSAS STATE UNIVERSITY   (United States)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Bayesian approach; Label switching; Markov chain Monte Carlo; Mixture model; Posterior modes

Indexed keywords

EID: 66549120967     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/jasa.2009.0237     Document Type: Article

References (35)

1. Böhning, D. (1999), Computer-Assisted Analysis of Mixtures and Applications, Boca Raton, FL: Chapman and Hall/CRC.
2. Celeux, G. (1997), "Discussion of 'On Bayesian Analysis of Mixtures with an Unknown Number of Components,' by S. Richardson and P. J. Green," Journal of the Royal Statistical Society, Ser. A, B59, 775-776.
3. (1998), "Bayesian Inference for Mixtures: The Label Switching Problem," in Compstat 98-Proceedings in Computational Statistics, eds. R. Payne and P. J. Green, Heidelberg: Physica, pp. 227-232.
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. Chung, H., Loken, E., and Schafer, J. L. (2004), "Difficulties in Drawing Inferences with Finite-Mixture Models: A Simple Example with a Simple Solution," The American Statistician, 58, 152-158.
6. Corana, A., Marchesi, M., Martini, C., and Ridella, S. (1987), "Minimizing Multimodal Functions of Continuous Variables with the Simulated Annealing Algorithm," ACM Transactions on Mathematical Software, 13, 262-280.
7. Crawford, S. L. (1994), "An Application of the Laplace Method to Finite Mixture Distributions," Journal of the American Statistical Association, 89, 259-267.
8. Crawford, S. L., Degroot, M. H., Kadane, J. B., and Small, M. J. (1992), "Modeling Lake-Chemistry Distributions: Approximate Bayesian Methods for Estimating a Finite-Mixture Model," Technometrics, 34, 441-453.
9. Davis, L. (ed.) (1991), Handbook of Genetic Algorithms, New York: Van Nostrand Reinhold.
10. Dellaportas, P., Stephens, D. A., Smith, A. F. M., and Guttman, I. (1996), "A Comparative Study of Perinatal Mortality Using a Two-Component Mixture Model," in Bayesian Biostatistics, eds. D. A. Berry and D. K. Stangl, New York: Dekker, pp. 601-616.
11. Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977), "Maximum Likelihood from Incomplete Data via the EM Algorithm" (with discussion), Journal of the Royal Statistical Society, Ser. A, B39, 1-38.
12. Diebolt, J., and Robert, C. P. (1994), "Estimation of Finite Mixture Distributions through Bayesian Sampling," Journal of the Royal Statistical Society, Ser. A, B56, 363-375.
13. Frühwirth-Schnatter, S. (2001), "Markov Chain Monte Carlo Estimation of Classical and Dynamic Switching and Mixture Models," Journal of the American Statistical Association, 96, 194-209.
14. (2006), Finite Mixture and Markov Switching Models, Berlin: Springer.
15. Goldberg, D. E. (1989), Genetic Algorithms in Search, Optimization and Machine Learning, Reading, MA: Addison Wesley.
16. Holland, J. H. (1975), Adaption in Natural and Artifical Systems, Ann Arbor, MI: University of Michigan Press.
17. Hurn, M., Justel, A., and Robert, C. P. (2003), "Estimating Mixtures of Regressions," Journal of Computational and Graphical Statistics, 12, 55-79.
18. Ingber, L., and Rosen, B. (1992), "Genetic Algorithms and Very Fast Simulated Reannealing: A Comparison," Mathematical and Computer Modelling, 16, 87-100.
19. Jasra, A., Holmes, C. C., and Stephens, D. A. (2005), "Markov Chain Monte Carlo Methods and the Label Switching Problem in Bayesian Mixture Modeling," Statistical Science, 20, 50-67.
20. Li, J., Ray, S., and Lindsay, B. G. (2007), "A Nonparametric Statistical Approach to Clustering via Mode Identification," Journal of Machine Learning Research, 8, 1687-1723.
21. Lindsay, B. G. (1995), Mixture Models: Theory, Geometry, and Applications, NSF-CBMS Regional Conference Series in Probability and Statistics v 5, Hayward, CA: Institute of Mathematical Statistics.
22. Marin, J.-M., Mengersen, K. L., and Robert, C. P. (2005), "Bayesian Modelling and Inference on Mixtures of Distributions," in Handbook of Statistics 25, eds. D. Dey and C. R. Rao, Amsterdam: North-Holland, pp. 459-507.
23. McLachlan, G. (1982). "The Classification and Mixture Maximum Likelihood Approaches to Cluster Analysis," in Handbook of Statistics (vol. 2), eds. P. R. Krishnaiah and L. N. Kanal, Amsterdam: North-Holland, pp. 199-208.
24. McLachlan, G. J., and Basford, K. E. (1988), Mixture Models: Inference and Applications to Clustering, New York: Marcel Dekker.
25. McLachlan, G. J., and Peel, D. (2000), Finite Mixture Models, NewYork: Wiley.
26. Meng, X.-L., and Rubin, D. B. (1993), "Maximum Likelihood Estimation via the ECM Algorithm: A General Framework," Biometrika, 80, 267-278.
27. Mengersen, K. (2009), Bayesian Analysis of Mixtures: Foundations and Applications, New York: Wiley.
28. Phillips,D.B., and Smith,A.F.M. (1996), "BayesianModelComparisonvia Jump Diffusion," in Markov Chain Monte Carlo in Practice, eds.,W. R. Gilks, S. T. Richardson, and D. J. Spiegelhalter, London: Chapman and Hall, pp. 215-239.
29. Richardson, S., and Green, P. J. (1997), "On Bayesian Analysis of Mixtures with an Unknown Number of Components" (with discussion), Journal of the Royal Statistical Society, Ser. A, B59, 731-792.
30. Stephens, M. (1997a), "Bayesian Methods for Mixtures of Normal Distributions," Ph.D. dissertation, University of Oxford, Dept. of Statistics.
31. (1997b), "Discussion of 'On Bayesian Analysis of Mixtures with an Unknown Number of Components,' by S. Richardson and P. J. Green," Journal of the Royal Statistical Society, Ser. A, B59, 768-769.
32. (2000), "Dealing with Label Switching in Mixture Models," Journal of the Royal Statistical Society, Ser. A, B62, 795-809.
33. Symons, M. (1981), "Clustering Criteria and Multivariate Normal Mixtures," Biometrics, 37, 35-43.
34. Walker, A. M. (1969), "On the Asymptotic Behaviour of Posterior Distributions," Journal of the Royal Statistical Society, Ser. A, B31, 80-88.
35. Yao,W. (2007), "On Using Mixtures and Modes of Mixtures in Data Analysis," Ph.D. dissertation, The Pennsylvania State University, Dept. of Statistics.