Estimating mixtures of regressions

Journal of Computational and Graphical Statistics

Volumn 12, Issue 1, 2003, Pages 55-79

  Hurn, Merrilee ^a   Justel, Ana ^b   Robert, Christian P ^c  

^a UNIVERSITY OF BATH   (United Kingdom)

^b UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

^c UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

Bayesian inference; Birth and death process; Label switching; Logistic regression; Loss functions; MCMC algorithms; Poisson regression; Switching regression

Indexed keywords

EID: 0037353170     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/1061860031329     Document Type: Article

References (27)

1. Altaleb, A. (1999), "Contributions à la Théorie des Algorithmes MCMC," unpublished Ph.D. thesis, Université de Rouen.
2. Bar-Shalom, Y. (1978), "Tracking Methods in a Multi-Target Environment," IEEE Transactions on Automatic Control, 23, 618-626.
3. Bernardo, J. M., and Smith, A. F. M. (1994), Bayesian Theory, New York: Wiley.
4. Billio, M., Monfort, A., and Robert, C. P. (1999), "Bayesian Estimation of Switching ARMA Models," Journal of Econometrics, 93, 229-255.
5. Brenac, T. (1994), "Accidents en Carrefour sur Routes Nationales, Modélisation du Nombre d'Accidents Prédictible sur un Carrefour et Exemples d'Applications," Rapport 185, INRETS, Arcueil.
6. Cappé, O., and Robert, C. P. (2000), "Markov Chain Monte Carlo: Ten Years and Still Running!" Journal of the American Statistical Association, 95, 1282-1286.
7. Cappé, O., Robert, C. P., and Rydén, T. (in press), "Reversible Jump, Birth-and-Death, and More General Continuous Time MCMC Samplers," Journal of the Royal Statistical Society, Ser. B.
8. 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.
9. Damien, P., Wakefield, J., and Walker, S. (1999), "Gibbs Sampling for Bayesian Non-conjugate and Hierarchical Models by Using Auxiliary Variables," Journal of the Royal Statistical Society, Ser. B, 61, 331-344.
10. Diebolt, J., and Robert, C. P. (1994), "Estimation of Finite Mixture Distributions by Bayesian Sampling," Journal of the Royal Statistical Society, Ser. B, 56, 363-375.
11. Dupuis, J., and Robert, C. P. (2001), "Bayesian Variable Selection in Qualitative Models by Kullback-Leibler Projections," Journal of Statistical Planning and Inference, 111, 77-94.
12. Fan, J., and Chen, J. (1999), "One-Step Local Quasi-Likelihood Estimation," Journal of the Royal Statistical Society, Ser. B, 61, 927-943.
13. Goldfeld, S. M., and Quandt, R. E. (1976), "A Markov Model for Switching Regression," Journal of Econometrics, 1, 3-16.
14. Hamilton, J. D. (1989), "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, 57, 357-384.
15. Hurvich, C. M., Simonoff, J. S., and Tsai, C.-L. (1998), "Smoothing Parameter Selection in Nonparametric Regression Using an Improved Akaike Information Criterion," Journal of the Royal Statistical Society, Ser. B, 60, 271-294.
16. Lenk, P. (1999), "Bayesian Inference for Semiparametric Regression Using a Fourier Representation," Journal of the Royal Statistical Society, Ser. B, 61, 863-879.
17. Kiefer, N. (1980), "A Note on Switching Regression and Logistic Discrimination," Econometrica, 48, 1065-1069.
18. Quandt, R. E., and Ramsey, J. B. (1978), "Estimating Mixtures of Normal Distributions and Switching Regressions" (with discussion), Journal of the American Statistical Association, 73, 730-752.
19. 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. B, 59, 731-792.
20. Robert, C. P. (1996), "Inference in Mixture Models," in Markov Chain Monte Carlo in Practice, W. R. Gilks, S. Richardson, and D. J. Spiegelhalter (eds.), London: Chapman and Hall, pp. 441-464.
21. _ (1997), Discussion of "On Bayesian Analysis of Mixtures with an unknown Number of Components" by S. Richardson and P. Green, Journal of the Royal Statistical Society, Ser. B, 59, 758-764.
22. Robert, C. P., and Casella, G. (1999), Monte Carlo Statistical Methods, New York: Springer-Verlag.
23. Rue, H. (1995), "New Loss Functions in Bayesian Imaging," Journal of the American Statistical Association, 90, 900-908.
24. Shumway, R. H., and Stoffer, D. S. (1991), "Dynamic Linear Models with Switching," Journal of the American Statistical Association, 81, 763-769.
25. Stephens, M. (2000a), "Bayesian Methods for Mixtures of Normal Distributions - An Alternative to Reversible Jump Methods," The Annals of Statistics, 28, 40-74.
26. _ (2000b), "Dealing With Label Switching in Mixture Models," Journal of the Royal Statistical Society, Ser. B, 62, 795-810.
27. Viallefont, V., Richardson, S., and Green, P. J. (2002), "Bayesian Estimation of Poisson Mixtures," Journal of Nonparametric Statistics, 14, 181-202.