The Annals of Statistics

Improving SAMC using smoothing methods: Theory and applications to Bayesian model selection problems

Faming Liang

Full-text: Open access

Abstract

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 on how to improve efficiency of Monte Carlo simulations by incorporating some nonparametric techniques.

Article information

Source
Ann. Statist., Volume 37, Number 5B (2009), 2626-2654.

Dates
First available in Project Euclid: 17 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.aos/1247836663

Digital Object Identifier
doi:10.1214/07-AOS577

Mathematical Reviews number (MathSciNet)
MR2541441

Zentralblatt MATH identifier
1182.62162

Subjects
Primary: 60J22: Computational methods in Markov chains [See also 65C40] 65C05: Monte Carlo methods

Keywords
Model selection Markov chain Monte Carlo reversible jump smoothing stochastic approximation Monte Carlo

Citation

Liang, Faming. Improving SAMC using smoothing methods: Theory and applications to Bayesian model selection problems. Ann. Statist. 37 (2009), no. 5B, 2626--2654. doi:10.1214/07-AOS577. https://projecteuclid.org/euclid.aos/1247836663


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