RATES OF CONVERGENCE FOR GIBBS SAMPLING FOR VARIANCE COMPONENT MODELS

• 成果类型: Article
• 署名作者: ROSENTHAL, JS
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176324619
• 发表日期: 1995
• 页码: 740-761
• 关键词: markov-chains; distributions; restoration

摘要

This paper analyzes the Gibbs sampler applied to a standard variance component model, and considers the question of how many iterations are required for convergence. It is proved that for K location parameters, with J observations each, the number of iterations required for convergence (for large K and J) is a constant times (1 + log K/log J). This is one of the first rigorous, a priori results about time to convergence for the Gibbs sampler. A quantitative version of the theory of Harris recurrence (for Markov chains) is developed and applied.