Likelihood and Bayesian analysis of mixtures

Statistical Modeling

Volumn 1, Issue 4, 2001, Pages 287-304

  Aitkin, Murray ^a  

^a NEWCASTLE UNIVERSITY   (United Kingdom)

Author keywords

Bayes; galaxy data; inference; Markov chain Monte Carlo; maximum likelihood; mixture model

Indexed keywords

EID: 85010934744     PISSN: 1471082X     EISSN: None     Source Type: Journal    
DOI: 10.1177/1471082X0100100404     Document Type: Article

References (21)

1. Aitkin M. (1996) A general maximum likelihood analysis of overdispersion in generalized linear models. Statistics and Computing, 6, 251-262.
2. Aitkin M., Anderson D.A., Hinde J.P. (1981) Statistical modelling of data on teaching styles (with Discussion). Journal of the Royal Statistical Society A, 144, 419-461.
3. Aitkin M., Francis B.J. (1995) Fitting overdispersed generalized linear models by nonparametric maximum likelihood. The GLIM Newsletter, 25, 37-45.
4. Böhning D. (1999) Computer-assisted analysis of mixtures and applications. Boca Raton, FL: Chapman and Hall/CRC.
5. Carlin B.P., Chib S. (1995) Bayesian model choice via Markov Chain Monte Carlo methods. Journal of the Royal Statistical Society B, 57, 473-484.
6. Escobar M.D., West M. (1995) Bayesian density estimation and inference using mixtures. Journal of the American Statistical Association, 90, 577-588.
7. Kiefer J., Wolfowitz J. (1956) Consistency of the maximum likelihood estimator in the presence of infinitely many nuisance parameters. Annals of Mathematical Statistics, 27, 887-906.
8. Laird N.M. (1978) Nonparametric maximum likelihood estimation of a mixing distribution. Journal of the American Statistical Association, 73, 805-811.
9. Lindsay B.G. (1983 a) The geometry of mixture likelihoods, part I: A general theory. Annals of Statistics, 11, 86-94.
10. Lindsay B.G. (1983 b) The geometry of mixture likelihoods, part II: The exponential family. Annals of Statistics, 11, 783-792.
11. Lindsay B.G. (1995) Mixture models: theory, geometry and applications. Hayward Calif.: Institute of Mathematical Statistics.
12. McLachlan G.J. (1987) On bootstrapping the likelihood ratio test statistic for the number of components in a normal mixture. Applied Statistics, 36, 318-324.
13. McLachlan G., Peel D. (2000) Finite mixture models. New York: John Wiley.
14. Noé M. (1972) The calculations of distributions of two-sided Kolmogorov-Smirnov type statistics. Annals of Mathematical Statistics, 43, 58-64.
15. Owen A.B. (1995) Nonparametric likelihood confidence bounds for a distribution function. Journal of the American Statistical Association, 90, 516-521.
16. Phillips D.B., Smith A.F.M. (1996) Bayesian model comparison via jump diffusions. In Gilks W.R., Richardson S., and Spiegelhalter D.J. eds. Markov chain Monte Carlo in practice. London: Chapman and Hall.
17. Postman M., Huchra J.P., Geller M.J. (1986) Probes of large-scale structures in the Corona Borealis region. The Astronomical Journal, 92, 1238-1247.
18. Richardson S., Green P.J. (1997) On Bayesian analysis of mixtures with an unknown number of components (with Discussion). Journal of the Royal Statistical Society B, 59, 731-792.
19. Roeder K. (1990) Density estimation with confidence sets exemplified by superclusters and voids in the galaxies. Journal of the American Statistical Association, 85, 617-624.
20. Roeder K., Wasserman L. (1997) Practical Bayesian density estimation using mixtures of normals. Journal of the American Statistical Association, 92, 894-902.
21. Titterington D.M., Smith A.F.M., Makov U.E. (1985) Statistical analysis of finite mixture distributions. Chichester: John Wiley.