Mixture Models With a Prior on the Number of Components

• 成果类型: Article
• 署名作者: Miller, Jeffrey W.; Harrison, Matthew T.
• 署名单位: Harvard University; Brown University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2016.1255636
• 发表日期: 2018
• 页码: 340-356
• 关键词: chain-monte-carlo; dirichlet process mixture; product partition models; process hierarchical-models; bayesian density-estimation; microarray expression data; stick-breaking processes; inverse-gaussian priors; label switching problem; reversible-jump MCMC

摘要

A natural Bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with symmetric Dirichlet weights, and put a prior on the number of componentsthat is, to use a mixture of finite mixtures (MFM). The most commonly used method of inference for MFMs is reversible jump Markov chain Monte Carlo, but it can be nontrivial to design good reversible jump moves, especially in high-dimensional spaces. Meanwhile, there are samplers for Dirichlet process mixture (DPM) models that are relatively simple and are easily adapted to new applications. It turns out that, in fact, many of the essential properties of DPMs are also exhibited by MFMsan exchangeable partition distribution, restaurant process, random measure representation, and stick-breaking representationand crucially, the MFM analogues are simple enough that they can be used much like the corresponding DPM properties. Consequently, many of the powerful methods developed for inference in DPMs can be directly applied to MFMs as well; this simplifies the implementation of MFMs and can substantially improve mixing. We illustrate with real and simulated data, including high-dimensional gene expression data used to discriminate cancer subtypes. Supplementary materials for this article are available online.