Asymptotic behaviour of the posterior distribution in overfitted mixture models

• 成果类型: Article
• 署名作者: Rousseau, Judith; Mengersen, Kerrie
• 署名单位: Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris; Queensland University of Technology (QUT)
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2011.00781.x
• 发表日期: 2011
• 页码: 689-710
• 关键词: maximum-likelihood; CONVERGENCE; ORDER; rates

摘要

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.