Trajectory averaging for stochastic approximation MCMC algorithms

Handle URI:
http://hdl.handle.net/10754/600054
Title:
Trajectory averaging for stochastic approximation MCMC algorithms
Authors:
Liang, Faming
Abstract:
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 approximationMCMC algorithms, for example, a stochastic approximation MLE algorithm for missing data problems, is also considered in the paper. © Institute of Mathematical Statistics, 2010.
Citation:
Liang 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.
Publisher:
Institute of Mathematical Statistics
Journal:
The Annals of Statistics
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Oct-2010
DOI:
10.1214/10-AOS807
Type:
Article
ISSN:
0090-5364
Sponsors:
Supported 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).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorLiang, Famingen
dc.date.accessioned2016-02-28T06:35:09Zen
dc.date.available2016-02-28T06:35:09Zen
dc.date.issued2010-10en
dc.identifier.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.en
dc.identifier.issn0090-5364en
dc.identifier.doi10.1214/10-AOS807en
dc.identifier.urihttp://hdl.handle.net/10754/600054en
dc.description.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.en
dc.description.sponsorshipSupported 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).en
dc.publisherInstitute of Mathematical Statisticsen
dc.subjectAsymptotic efficiencyen
dc.subjectConvergenceen
dc.subjectMarkov chain Monte Carloen
dc.subjectStochastic approximation Monte Carloen
dc.subjectTrajectory averagingen
dc.titleTrajectory averaging for stochastic approximation MCMC algorithmsen
dc.typeArticleen
dc.identifier.journalThe Annals of Statisticsen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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