Premium
On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)
Author(s) -
Richardson Sylvia.,
Green Peter J.
Publication year - 1997
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00095
Subject(s) - prior probability , markov chain monte carlo , bayesian probability , reversible jump markov chain monte carlo , univariate , computer science , context (archaeology) , posterior probability , mixture model , joint probability distribution , basis (linear algebra) , mathematics , statistics , artificial intelligence , machine learning , multivariate statistics , paleontology , geometry , biology
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.