TRAJECTORY AVERAGING FOR STOCHASTIC APPROXIMATION MCMC ALGORITHMS

• 成果类型: Article
• 署名作者: Lang, 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: 10.1214/10-AOS807
• 发表日期: 2010
• 页码: 2823-2856
• 关键词: chain monte-carlo; wang-landau algorithm; CONVERGENCE; EFFICIENCY

摘要

The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400-407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems and for general simulation and optimizations. In this paper, we first show that the trajectory averaging estimator is asymptotically efficient for the stochastic approximation MCMC (SAMCMC) algorithm under mild conditions, and then apply this result to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximation MCMC algorithms, for example, a stochastic approximation MLE algorithm for missing data problems, is also considered in the paper.