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On Bayesian analysis of mixtures with an unknown number of components. (With discussion). (English) Zbl 0891.62020
J. R. Stat. Soc., Ser. B 59, No. 4, 731-792 (1997); corrigendum ibid. 60, No. 3, 661 (1998).
Summary: New methodology for fully Bayesian mixture analysis is developed, making use of reversible jump Markov chain Monte Carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture. A sample from the full joint distribution of all unknown variables is thereby generated, and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution. The methodology is applied here to the analysis of univariate normal mixtures, using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context.

MSC:
62F15 Bayesian inference
65C99 Probabilistic methods, stochastic differential equations
62P99 Applications of statistics
65C05 Monte Carlo methods
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