Practical perfect sampling using composite bounding chains: the Dirichlet-multinomial model

• 成果类型: Article
• 署名作者: Stein, Nathan M.; Meng, Xiao-Li
• 署名单位: Harvard University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ast024
• 发表日期: 2013
• 页码: 817830
• 关键词: simulation; mixtures; distributions

摘要

A discrete data augmentation scheme together with two different parameterizations yields two Gibbs samplers for sampling from the posterior distribution of the hyperparameters of the Dirichlet-multinomial hierarchical model under a default prior distribution. The finite-state space nature of this data augmentation permits us to construct two perfect samplers using bounding chains that take advantage of monotonicity and anti-monotonicity in the target posterior distribution, but both are impractically slow. We demonstrate that a composite algorithm that strategically alternates between the two samplers' updates can be substantially faster than either individually. The speed gains come because the composite algorithm takes a divide-and-conquer approach in which one update quickly shrinks the bounding set for the augmented data, and the other update immediately coalesces on the parameter, once the augmented-data bounding set is a singleton. We theoretically bound the expected time until coalescence for the composite algorithm, and show via simulation that the theoretical bounds can be close to actual performance.