Abstract
It is shown that Bayesian inference from data modeled by a mixture distribution can feasibly be performed via Monte Carlo simulation. This method exhibits the true Bayesian predictive distribution, implicitly integrating over the entire underlying parameter space. An infinite number of mixture components can be accommodated without difficulty, using a prior distribution for mixing proportions that selects a reasonable subset of components to explain any finite training set. The need to decide on a “correct” number of components is thereby avoided. The feasibility of the method is shown empirically for a simple classification task.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cheeseman, P., Kelly, J., Self, M., Stutz, J., Taylor, W., and Freeman, D. (1988) ‘AutoClass: A Bayesian classification system’, Proceedings of the Fifth International Conference on Machine Learning.
Everitt, B. S. and Hand, D. J. (1981) Finite Mixture Distributions, London: Chapman and Hall.
Gelfand, A. E. and Smith, A. F. M. (1990) ‘Sampling-based approaches to calculating marginal densities’, Journal of the American Statistical Association, 85, 398–409.
Hanson, R., Stutz, J., and Cheeseman, P. (1991) ‘Bayesian classification with correlation and inheritance’, to be presented at the 12th International Joint Conference on Artificial Intelligence, Sydney, Australia, August 1991.
Kai-Tai, F. and Yao-Ting, Z. (1990) Generalized Multivariate Analysis, Berlin: Springer-Verlag.
Levinson, S. E., Rabiner, L. R., and Sondhi, M. M. (1983) ‘An introduction to the application of the theory of probabilistic functions of a Markov process to automatic speech recognition’, Bell System Technical Journal, 62, 1035–1074.
Neal, R. M. (1991) ‘Bayesian mixture modeling by Monte Carlo simulation’, Technical Report CRG-TR-91–2, Department of Computer Science, University of Toronto.
Titterington, D. M., Smith, A. F. M., and Makov, U. E. (1985) Statistical Analysis of Finite Mixture Distributions, Chichester, New York: Wiley.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Neal, R.M. (1992). Bayesian Mixture Modeling. In: Smith, C.R., Erickson, G.J., Neudorfer, P.O. (eds) Maximum Entropy and Bayesian Methods. Fundamental Theories of Physics, vol 50. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2219-3_14
Download citation
DOI: https://doi.org/10.1007/978-94-017-2219-3_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4220-0
Online ISBN: 978-94-017-2219-3
eBook Packages: Springer Book Archive