Asymptotic behaviour of the posterior distribution in overfitted mixture models

作者：Rousseau Judith^*; Mengersen Kerrie

来源：Journal of the Royal Statistical Society - Series B: Statistical Methodology , 2011, 73(5): 689-710.

DOI：10.1111/j.1467-9868.2011.00781.x

• Asymptotic behaviour
• Bayesian methods
• Mixture models
• Overfitting
• Posterior concentration

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.

• 出版日期2011