Asymptotic behaviour of the posterior distribution in overfitted mixture models
Rousseau, Judith; Mengersen, Kerrie (2011), Asymptotic behaviour of the posterior distribution in overfitted mixture models, Journal of the Royal Statistical Society. Series B, Statistical Methodology, 73, 5, p. 689-710. http://dx.doi.org/10.1111/j.1467-9868.2011.00781.x
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00641475
Journal nameJournal of the Royal Statistical Society. Series B, Statistical Methodology
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Abstract (EN)We study the asymptotic behaviour of the posterior distribution in a mixture model when the number of components in the mixture is larger than the true number of components: a situation which is commonly referred to as an overfitted mixture. We prove in particular that quite generally the posterior distribution has a stable and interesting behaviour, since it tends to empty the extra components. This stability is achieved under some restriction on the prior, which can be used as a guideline for choosing the prior. Some simulations are presented to illustrate this behaviour.
Subjects / KeywordsAsymptotic; Bayesian; mixture models; overfitting; posterior concentration
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