Bayesian Modelling and Inference on Mixtures of Distributions

Handbook of Statistics

Volumn 25, Issue , 2005, Pages 459-507

  Marin, Jean Michel ^a   Mengersen, Kerrie ^a   Robert, Christian P ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33750274518     PISSN: 01697161     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0169-7161(05)25016-2     Document Type: Review

References (123)

1. Aitkin M. Likelihood and Bayesian analysis of mixtures. Statistical Modelling 1 4 (2001) 287-304
2. Archer, G., Titterington, D. (1995). Parameter estimation for hidden Markov chains. J. Statist. Plann. Inference
3. p version of the Hausdorff metric. Nieuw Archief voor Wiskunde 10 (1992) 157-183
4. Barron A., Schervish M., and Wasserman L. The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27 (1999) 536-561
5. Basu S., and Mukhopadhyay S. Bayesian analysis of binary regression using symmetric and asymmetric links. Sankhya, Ser. B 62 2 (2000) 372-387
6. Berger J. Statistical Decision Theory and Bayesian Analysis. second ed (1985), Springer-Verlag
7. Bernardo J.M., and Girón F.J. A Bayesian analysis of simple mixture problems. In: Bernardo J.M., DeGrooh M.H., and Lindley D.V. (Eds). Bayesian Statistics, vol. 3 (1988), Oxford University Press
8. Bertillon J. Cours élémentaire de statistique administrative (1895), SES, Paris
9. Besag J., Green E., Higdon D., and Mengersen K. Bayesian computation and stochastic systems (with discussion). Statist. Sci. 10 (1995) 3-66
10. Brooks S. On Bayesian analyses and finite mixtures for proportions. Statist. Comput. 11 2 (2001) 179-190
11. Brown P., Fearn T., and Vannucci M. Bayesian wavelet regression on curves with application to a spectroscopic calibration problem. J. Amer. Statist. Assoc. 96 454 (2001) 398-408
12. Cappé O., Robert C., and Rydén T. Reversible jump MCMC converging to birth-and-death MCMC and more general continuous time samplers. J. Roy. Statist. Soc., Ser. B 65 3 (2002) 679-700
13. Cappé O., Guillin A., Marin J., and Robert C. Population Monte Carlo. J. Comput. Graph. Statist. 13 (2004) 907-929
14. Cappé O., Moulines E., and Rydén T. Hidden Markov Models (2004), Springer-Verlag
15. Casella G., Mengersen K., Robert C., and Titterington D. Perfect slice samplers for mixtures of distributions. J. Roy. Statist. Soc., Ser. B 64 4 (2002) 777-790
16. Casella, G., Robert, C., Wells, M. (2000). Mixture models, latent variables and partitioned importance sampling. Technical Report 2000-03, CREST, INSEE, Paris
17. Celeux G., and Diebolt J. The SEM algorithm: A probabilistic teacher algorithm derived from the EM algorithm for the mixture problem. Comput. Statist. Quaterly 2 (1985) 73-82
18. Celeux G., Hurn M., and Robert C. Computational and inferential difficulties with mixtures posterior distribution. J. Amer. Statist. Assoc. 95 3 (2000) 957-979
19. Celeux, G., Marin, J.M., Robert, C.P. (2003). Iterated importance sampling in missing data problems. Technical Report, Université Paris Dauphine
20. Chen M.-H., and Dey D. A unified Bayesian approach for analyzing correlated ordinal response data. Rev. Brasil. Probab. Estatist. 14 1 (2000) 87-111
21. Chib S. Marginal likelihood from the Gibbs output. J. Amer. Statist. Assoc. 90 (1995) 1313-1321
22. Chib S., and Hamilton B. Bayesian analysis of cross-section and clustered data treatment models. J. Econometrics 97 1 (2000) 25-50
23. Cho J., Kim D., and Kang S. Nonparametric Bayesian multiple comparisons for the exponential populations. Far East J. Theoret. Statist. 5 2 (2001) 327-336
24. Dempster A., Laird N., and Rubin D. Maximum likelihood from incomplete data via the EM algorithm (with discussion). J. Roy. Statist. Soc., Ser. B 39 (1977) 1-38
25. Diaconis P., and Freedman D. On the consistency of Bayes estimates. Ann. Statist. 14 (1986) 1-26
26. Diebolt, J., Robert, C. (1990a). Bayesian estimation of finite mixture distributions, Part i: Theoretical aspects. Technical Report 110, LSTA, Université Paris VI, Paris
27. Diebolt, J., Robert, C. (1990b). Bayesian estimation of finite mixture distributions, Part ii: Sampling implementation. Technical Report 111, LSTA, Université Paris VI, Paris
28. Diebolt J., and Robert C. Estimation des paramètres d'un mélange par échantillonnage bayésien. Notes aux Comptes-Rendus de l'Académie des Sciences I 311 (1990) 653-658
29. Diebolt J., and Robert C. Discussion of Bayesian computations via the Gibbs sampler by A.F.M. Smith and G. Roberts. J. Roy. Statist. Soc., Ser. B 55 (1993) 71-72
30. Diebolt J., and Robert C. Estimation of finite mixture distributions by Bayesian sampling. J. Roy. Statist. Soc., Ser. B 56 (1994) 363-375
31. Doucet A., de Freitas N., and Gordon N. Sequential Monte Carlo Methods in Practice (2001), Springer-Verlag
32. Dunson D. Bayesian latent variable models for clustered mixed outcomes. J. Roy. Statist. Soc., Ser. B 62 2 (2000) 355-366
33. Dunson D., and Dinse G. Distinguishing effects on tumor multiplicity and growth rate in chemoprevention experiments. Biometrics 56 4 (2000) 1068-1075
34. Dunson D., and Weinberg C. Modeling human fertility in the presence of measurement error. Biometrics 56 1 (2000) 288-292
35. Dunson D., and Zhou H. A Bayesian model for fecundability and sterility. J. Amer. Statist. Assoc. 95 452 (2000) 1054-1062
36. Dupuis J., and Robert C. Model choice in qualitative regression models. J. Statist. Plann. Inference 111 (2003) 77-94
37. Escobar M., and West M. Bayesian prediction and density estimation. J. Amer. Statist. Assoc. 90 (1995) 577-588
38. Fan T.-H., and Berger J. Robust Bayesian displays for standard inferences concerning a normal mean. Comput. Statist. Data Anal. 33 1 (2000) 381-399
39. Ferguson T. Prior distributions in spaces of probability measures. Ann. Statist. 2 (1974) 615-629
40. Fernandez C., and Green P. Modelling spatially correlated data via mixtures: A Bayesian approach. J. Roy. Statist. Soc., Ser. B 64 (2002) 805-826
41. Frühwirth-Schnatter S. Markov chain Monte Carlo estimation of classical and dynamic switching and mixture models. J. Amer. Statist. Assoc. 96 453 (2001) 194-209
42. Gelfand A., and Kottas A. A computational approach for full nonparametric Bayesian inference under Dirichlet process mixture models. J. Comput. Graph. Statist. 11 2 (2002) 289-305
43. Gelfand A., and Smith A. Sampling based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85 (1990) 398-409
44. Gerlach R., Carter C., and Kohn R. Efficient Bayesian inference for dynamic mixture models. J. Amer. Statist. Assoc. 95 451 (2000) 819-828
45. Ghosal S. Convergence rates for density estimation with Bernstein polynomials. Ann. Statist. 29 5 (2001) 1264-1280
46. Gordon N., Salmon J., and Smith A. A novel approach to non-linear/non-Gaussian Bayesian state estimation. IEEE Proc. Radar and Signal Process. 140 (1993) 107-113
47. Green P. Reversible jump MCMC computation and Bayesian model determination. Biometrika 82 4 (1995) 711-732
48. Green P., and Richardson S. Modelling heterogeneity with and without the Dirichlet process. Scand. J. Statist. 28 2 (2001) 355-375
49. Green P., and Richardson S. Hidden Markov models and disease mapping. J. Amer. Statist. Assoc. 97 460 (2002) 1055-1070
50. Grenander U., and Miller M. Representations of knowledge in complex systems (with discussion). J. Roy. Statist. Soc., Ser. B 56 (1994) 549-603
51. Gruet M., Philippe A., and Robert C. MCMC control spreadsheets for exponential mixture estimation. J. Comput. Graph. Statist. 8 (1999) 298-317
52. Guillin, A., Marin, J., Robert, C. (2003). Estimation bayésienne approximative par échantillonnage préférentiel. Technical Report 0335, Cahiers du Ceremade, Université Paris Dauphine
53. Hamilton J.D. Rational-expectations econometric analysis of changes in regime: An investigation of the term structure of interest rates. J. Economic Dynamics and Control 12 (1988) 385-423
54. Hamilton J.D. A new approach to the economic analysis of nonstationary time series and the business cycles. Econometrica 57 (1989) 357-384
55. Hastie T., Tibshirani R., and Friedman J.H. The Elements of Statistical Learning: Data Mining, Inference, and Prediction (2001), Springer-Verlag, New York
56. Hesterberg T. Weighted average importance sampling and defensive mixture distributions. Technometrics 37 (1998) 185-194
57. Hobert J., Robert C., and Titterington D. On perfect simulation for some mixtures of distributions. Statist. Comput. 9 4 (1999) 287-298
58. Humphreys, K., Titterington, D. (2000). Approximate Bayesian inference for simple mixtures. In: COMPSTAT - Proceedings in Computational Statistics, pp. 331-336
59. Hurn M., Justel A., and Robert C. Estimating mixtures of regressions. J. Comput. Graph. Statist. 12 (2003) 1-25
60. Iba Y. Population-based Monte Carlo algorithms. Trans. Japan. Soc. Artificial Intelligence 16 2 (2000) 279-286
61. Ishwaran H., James L., and Sun J. Bayesian model selection in finite mixtures by marginal density decompositions. J. Amer. Statist. Assoc. 96 456 (2001) 1316-1332
62. Jordan, M. (2004). Graphical models. Statist. Sci. Submitted for publication
63. Kass R., and Raftery A. Bayes factors. J. Amer. Statist. Assoc. 90 (1995) 773-795
64. Kim S., Shephard N., and Chib S. Stochastic volatility: Likelihood inference and comparison with ARCH models. Rev. Econom. Stud. 65 (1998) 361-393
65. Kvam P., and Miller J. Discrete predictive analysis in probabilistic safety assessment. J. Quality Technology 34 1 (2002) 106-117
66. Lauritzen S., and Jensen F. Stable local computation with conditional Gaussian distributions. Statist. Comput. 11 2 (2001) 191-203
67. Lavine M., and West M. A Bayesian method for classification and discrimination. Canad. J. Statist. 20 (1992) 451-461
68. Leite J., Rodrigues J., and Milan L. A Bayesian analysis for estimating the number of species in a population using nonhomogeneous Poisson process. Statist. Probab. Lett. 48 2 (2000) 153-161
69. Lenk P., and DeSarbo W. Bayesian inference for finite mixtures of generalized linear models with random effects. Psychometrika 65 1 (2000) 93-119
70. Liang F., and Wong W. Real-parameter evolutionary Monte Carlo with applications to Bayesian mixture models. J. Amer. Statist. Assoc. 96 454 (2001) 653-666
71. Lindsay, B. (1995). Mixture Models: Theory, Geometry and Applications. IMS Monographs, Hayward, CA
72. Liu J., Wong W., and Kong A. Covariance structure of the Gibbs sampler with applications to the comparisons of estimators and sampling schemes. Biometrika 81 (1994) 27-40
73. Louzada-Neto F., Mazucheli J., and Achcar J. Mixture hazard models for lifetime data. Biometrical J. 44 1 (2002) 3-14
74. MacLachlan G., and Basford K. Mixture Models: Inference and Applications to Clustering (1988), Marcel Dekker, New York
75. MacLachlan G., and Peel D. Finite Mixture Models (2000), Wiley, New York
76. Mengersen K., and Robert C. Testing for mixtures: A Bayesian entropic approach (with discussion). In: Berger J., Bernardo J., Dawid A., Lindley D., and Smith A. (Eds). Bayesian Statistics, vol. 5 (1996), Oxford University Press, Oxford 255-276
77. Mengersen K., Robert C., and Guihenneuc-Jouyaux C. MCMC convergence diagnostics: a "reviewww". In: Berger J., Bernardo J., Dawid A., Lindley D., and Smith A. (Eds). Bayesian Statistics, vol. 6 (1999), Oxford University Press, Oxford 415-440
78. Mira A., Møller J., and Roberts G. Perfect slice samplers. J. Roy. Statist. Soc., Ser. B 63 (2001) 583-606
79. Moreno E., and Liseo B. A default Bayesian test for the number of components in a mixture. J. Statist. Plann. Inference 111 1-2 (2003) 129-142
80. Nair V., Tang B., and Xu L.-A. Bayesian inference for some mixture problems in quality and reliability. J. Quality Technology 33 (2001) 16-28
81. Nobile A., and Green P. Bayesian analysis of factorial experiments by mixture modelling. Biometrika 87 1 (2000) 15-35
82. Pearson K. Contribution to the mathematical theory of evolution. Proc. Trans. Roy. Soc. A 185 (1894) 71-110
83. Pérez J., and Berger J. Expected-posterior prior distributions for model selection. Biometrika 89 3 (2002) 491-512
84. Perron F., and Mengersen K. Bayesian nonparametric modelling using mixtures of triangular distributions. Biometrics 57 (2001) 518-528
85. Petrone S., and Wasserman L. Consistency of Bernstein polynomial posteriors. J. Roy. Statist. Soc., Ser. B 64 (2002) 79-100
86. Phillips D., and Smith A. Bayesian model comparison via jump diffusions. In: Gilks W., Richardson S., and Spiegelhalter D. (Eds). Markov Chain Monte Carlo in Practice (1996), Chapman and Hall 215-240
87. Pievatolo A., and Rotondi R. Analysing the interevent time distribution to identify seismicity phases: A Bayesian nonparametric approach to the multiple-changepoint problem. Appl. Statist. 49 4 (2000) 543-562
88. Qu P., and Qu Y. A Bayesian approach to finite mixture models in bioassay via data augmentation and Gibbs sampling and its application to insecticide resistance. Biometrics 56 4 (2000) 1249-1255
89. Redner R.A., and Walker H.F. Mixture densities, maximum likelihood and the EM algorithm. SIAM Review 26 2 (1984) 195-239
90. Richardson S., and Green P. On Bayesian analysis of mixtures with an unknown number of components (with discussion). J. Roy. Statist. Soc., Ser. B 59 (1997) 731-792
91. Ripley B. Stochastic Simulation (1987), Wiley, New York
92. Robert C. Discretization and MCMC Convergence Assessment. Lecture Notes in Statistics vol. 135 (1998), Springer-Verlag
93. Robert C. MCMC specifics for latent variable models. In: Payne R., and Green P. (Eds). COMPSTAT 1998 (1998), Physica-Verlag, Heidelberg 101-112
94. Robert C. The Bayesian Choice. second ed (2001), Springer-Verlag
95. Robert C., and Casella G. Monte Carlo Statistical Methods. second ed (2004), Springer-Verlag, New York
96. Robert C., and Mengersen K. Reparametrization issues in mixture estimation and their bearings on the Gibbs sampler. Comput. Statist. Data Anal. 29 (1999) 325-343
97. Robert C., Rousseau, J. (2002). A mixture approach to Bayesian goodness of fit. Technical Report, Cahiers du CEREMADE, Université Paris Dauphine
98. Robert C., and Titterington M. Reparameterisation strategies for hidden Markov models and Bayesian approaches to maximum likelihood estimation. Statist. Comput. 8 2 (1998) 145-158
99. Robert C., Rydén T., and Titterington D. Convergence controls for MCMC algorithms, with applications to hidden Markov chains. J. Statist. Comput. Simulation 64 (1999) 327-355
100. Roeder K. Density estimation with confidence sets exemplified by superclusters and voids in galaxies. J. Amer. Statist. Assoc. 85 (1992) 617-624
101. Roeder K., and Wasserman L. Practical Bayesian density estimation using mixtures of normals. J. Amer. Statist. Assoc. 92 (1997) 894-902
102. Sahu S., and Cheng R. A fast distance based approach for determining the number of components in mixtures. Canad. J. Statist. 31 (2003) 3-22
103. Sebastiani P., and Wynn H. Maximum entropy sampling and optimal Bayesian experimental design. J. Roy. Statist. Soc., Ser. B 62 1 (2000) 145-157
104. Shephard N. Statistical aspects of ARCH and stochastic volatility. In: Cox D.R., Barndorff-Nielsen O.E., and Hinkley D.V. (Eds). Time Series Models in Econometrics, Finance and Other Fieds (1996), Chapman and Hall
105. Shephard N., and Pitt M. Likelihood analysis of non-Gaussian measurement time series. Biometrika 84 (1997) 653-668
106. Silverman B. Density Estimation for Statistics and Data Analysis (1986), Chapman and Hall
107. Skates S., Pauler D., and Jacobs I. Screening based on the risk of cancer calculation from Bayesian hierarchical changepoint and mixture models of longitudinal markers. J. Amer. Statist. Assoc. 96 454 (2001) 429-439
108. Stephens, M. (1997). Bayesian methods for mixtures of normal distributions. Ph.D. thesis, University of Oxford
109. Stephens M. Bayesian analysis of mixture models with an unknown number of components - an alternative to reversible jump methods. Ann. Statist. 28 (2000) 40-74
110. Stephens M. Dealing with label switching in mixture models. J. Roy. Statist. Soc., Ser. B 62 4 (2000) 795-809
111. Stroud J., Müller P., and Sansó B. Dynamic models for spatiotemporal data. J. Roy. Statist. Soc., Ser. B 63 4 (2001) 673-689
112. Tanner M., and Wong W. The calculation of posterior distributions by data augmentation. J. Amer. Statist. Assoc. 82 (1987) 528-550
113. Titterington D., Smith A., and Makov U. Statistical Analysis of Finite Mixture Distributions (1985), Wiley, New York
114. Tsionas E. Bayesian analysis of finite mixtures of Weibull distributions. Comm. Statist. Part A - Theory and Methods 31 1 (2002) 37-48
115. Verdinelli I., and Wasserman L. Bayesian analysis of outliers problems using the Gibbs sampler. Statist. Comput. 1 (1992) 105-117
116. Verdinelli I., and Wasserman L. Bayesian goodness-of-fit testing using infinite-dimensional exponential families. aos 26 (1998) 1215-1241
117. Walshaw D. Modelling extreme wind speeds in regions prone to hurricanes. Appl. Statist. 49 1 (2000) 51-62
118. Warnes, G. (2001). The Normal kernel coupler: An adaptive Markov Chain Monte Carlo method for efficiently sampling from multi-modal distributions. Technical Report 395, University of Washington
119. Wasserman L. Asymptotic inference for mixture models using data dependent priors. J. Roy. Statist. Soc., Ser. B 62 (2000) 159-180
120. Watanabe T. A Bayesian analysis of dynamic bivariate mixture models: Can they explain the behavior of returns and trading volume?. J. Business and Economic Statistics 18 2 (2000) 199-210
121. Wiper M., Insua D., and Ruggeri F. Mixtures of Gamma distributions with applications. J. Comput. Graph. Statist. 10 3 (2001) 440-454
122. Wruck E., Achcar J., and Mazucheli J. Classification and discrimination for populations with mixture of multivariate normal distributions. Rev. Mat. Estatist. 19 (2001) 383-396
123. Zhu H.-T., and Lee S.-Y. A Bayesian analysis of finite mixtures in the LISREL model. Psychometrika 66 1 (2001) 133-152