Trajectory averaging for stochastic approximation MCMC algorithms
KAUST Grant NumberKUS-C1-016-04
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AbstractThe 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 approximationMCMC algorithms, for example, a stochastic approximation MLE algorithm for missing data problems, is also considered in the paper. © Institute of Mathematical Statistics, 2010.
CitationLiang F (2010) Trajectory averaging for stochastic approximation MCMC algorithms. The Annals of Statistics 38: 2823–2856. Available: http://dx.doi.org/10.1214/10-AOS807.
SponsorsSupported in part by NSF Grants DMS-06-07755, CMMI-0926803 and the Award KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).
PublisherInstitute of Mathematical Statistics
JournalThe Annals of Statistics