Reversible jump, birth-and-death and more general continuous time Markov chain Monte Carlo samplers

• 成果类型: Article
• 署名作者: Cappé, O; Robert, CP; Rydén, T
• 署名单位: Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/1467-9868.00409
• 发表日期: 2003
• 页码: 679-700
• 关键词: bayesian-inference; unknown number; models; CONVERGENCE; components; mixtures

摘要

Reversible jump methods are the most commonly used Markov chain Monte Carlo tool for exploring variable dimension statistical models. Recently, however, an alternative approach based on birth-and-death processes has been proposed by Stephens for mixtures of distributions. We show that the birth-and-death setting can be generalized to include other types of continuous time jumps like split-and-combine moves in the spirit of Richardson and Green. We illustrate these extensions both for mixtures of distributions and for hidden Markov models. We demonstrate the strong similarity of reversible jump and continuous time methodologies by showing that, on appropriate rescaling of time, the reversible jump chain converges to a limiting continuous time birth-and-death process. A numerical comparison in the setting of mixtures of distributions highlights this similarity.