On Bayesian analysis of mixtures with an unknown number of components
On Bayesian analysis of mixtures with an unknown number of components,
with discussion,
by Sylvia Richardson (INSERM, France) and Peter Green (Bristol, UK).
Journal of the Royal Statistical Society, B, 59, 731-792 (1997).
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.
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