IMPROVING SAMC USING SMOOTHING METHODS: THEORY AND APPLICATIONS TO BAYESIAN MODEL SELECTION PROBLEMS

• 成果类型: Article
• 署名作者: Liang, Faming
• 署名单位: Texas A&M University System; Texas A&M University College Station
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS577
• 发表日期: 2009
• 页码: 2626-2654
• 关键词: chain monte-carlo; stochastic-approximation; algorithm; CONVERGENCE; regression

摘要

Stochastic approximation Monte Carlo (SAMC) has recently been proposed by Liang, Liu and Carroll [J. Amer Statist. Assoc. 102 (2007) 305-320] as a general simulation and optimization algorithm. In this paper, we propose to improve its convergence using smoothing methods and discuss the application of the new algorithm to Bayesian model selection problems. The new algorithm is tested through a change-point identification example. The numerical results indicate that the new algorithm can outperform SAMC and reversible jump MCMC significantly for the model selection problems. The new algorithm represents a general form of the stochastic approximation Markov chain Monte Carlo algorithm. It allows multiple samples to be generated at each iteration, and a bias term to be included in the parameter updating step. A rigorous proof for the convergence of the general algorithm is established under verifiable conditions. This paper also provides a framework oil how to improve efficiency of Monte Carlo simulations by incorporating some nonparametric techniques.