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Asymptotic behaviour of the posterior distribution in overfitted mixture models
Author(s) -
Rousseau Judith,
Mengersen Kerrie
Publication year - 2011
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/j.1467-9868.2011.00781.x
Subject(s) - posterior probability , distribution (mathematics) , stability (learning theory) , computer science , mixture model , mixture distribution , mathematics , statistics , probability density function , machine learning , bayesian probability , mathematical analysis
Summary. 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.