Computational and inferential difficulties with mixture posterior distributions.

• 成果类型: Article
• 署名作者: Celeux, G; Hurn, M; Robert, CP
• 署名单位: University of Bath; Institut Polytechnique de Paris; ENSAE Paris
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2669477
• 发表日期: 2000
• 页码: 957-970
• 关键词: bayesian-analysis; unknown number

摘要

This article dears with both exploration and interpretation problems related to posterior distributions for mixture models. The specification of mixture posterior distributions means that the presence of Ic! modes is known immediately. Standard Markov chain Monte Carlo (MCMC) techniques usually have difficulties with well-separated modes such as occur here; the MCMC sampler stays within a neighborhood of a local mode and fails to visit other equally important modes. We show that exploration of these modes can be imposed using tempered transitions. However, if the prior distribution does not distinguish between the different components, then the posterior mixture distribution is symmetric and standard estimators such as posterior means cannot be used. We propose alternatives for Bayesian inference for permutation invariant posteriors, including a clustering device and alternative appropriate loss functions.