Journal
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
Volume 73, Issue -, Pages 689-710Publisher
WILEY-BLACKWELL
DOI: 10.1111/j.1467-9868.2011.00781.x
Keywords
Asymptotic behaviour; Bayesian methods; Mixture models; Overfitting; Posterior concentration
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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.
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