Compound random measures and their use in Bayesian non-parametrics

• 成果类型: Article
• 署名作者: Griffin, Jim E.; Leisen, Fabrizio
• 署名单位: University of Kent
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• 发表日期: 2017
• 页码: 525-545
• 关键词: inference

摘要

A new class of dependent random measures which we call compound random measures is proposed and the use of normalized versions of these random measures as priors in Bayesian non-parametric mixture models is considered. Their tractability allows the properties of both compound random measures and normalized compound random measures to be derived. In particular, we show how compound random measures can be constructed with gamma, sigma-stable and generalized gamma process marginals. We also derive several forms of the Laplace exponent and characterize dependence through both the Levy copula and the correlation function. An augmented Polya urn scheme sampler and a slice sampler are described for posterior inference when a normalized compound random measure is used as the mixing measure in a non-parametric mixture model and a data example is discussed.