Bayesian analysis of mixture models with an unknown number of components - An alternative to reversible jump methods

• 成果类型: Article
• 署名作者: Stephens, M
• 署名单位: University of Oxford
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1016120364
• 发表日期: 2000
• 页码: 40-74
• 关键词: chain monte-carlo; DENSITY-ESTIMATION; distributions; likelihood; simulation; inference

摘要

Richardson and Green present a method of performing a Bayesian analysis of data from a finite mixture distribution with an unknown number of components. Their method is a Markov Chain Monte Carlo (MCMC) approach, which makes use of the reversible jump methodology described by Green. We describe an alternative MCMC method which views the parameters of the model as a (marked point process, extending methods suggested by Ripley to create a Markov birth-death process with an appropriate stationary distribution. Our method is easy Co implement, even in the case of data in more than one dimension, and we illustrate it on both univariate and bivariate data. There appears to be considerable potential for applying these ideas to other contexts, as an alternative to more general reversible jump methods, and we conclude with a brief discussion of how this might be achieved.