Open Access
October 2010 Trajectory averaging for stochastic approximation MCMC algorithms
Faming Liang
Ann. Statist. 38(5): 2823-2856 (October 2010). DOI: 10.1214/10-AOS807


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.


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Faming Liang. "Trajectory averaging for stochastic approximation MCMC algorithms." Ann. Statist. 38 (5) 2823 - 2856, October 2010.


Published: October 2010
First available in Project Euclid: 20 July 2010

zbMATH: 1218.60064
MathSciNet: MR2722457
Digital Object Identifier: 10.1214/10-AOS807

Primary: 60J22 , 65C05

Keywords: Asymptotic efficiency , convergence , Markov chain Monte Carlo , stochastic approximation Monte Carlo , trajectory averaging

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 5 • October 2010
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