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October 2009 Improving SAMC using smoothing methods: Theory and applications to Bayesian model selection problems
Faming Liang
Ann. Statist. 37(5B): 2626-2654 (October 2009). DOI: 10.1214/07-AOS577

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.

Citation

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Faming Liang. "Improving SAMC using smoothing methods: Theory and applications to Bayesian model selection problems." Ann. Statist. 37 (5B) 2626 - 2654, October 2009. https://doi.org/10.1214/07-AOS577

Information

Published: October 2009
First available in Project Euclid: 17 July 2009

zbMATH: 1182.62162
MathSciNet: MR2541441
Digital Object Identifier: 10.1214/07-AOS577

Subjects:
Primary: 60J22, 65C05

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 5B • October 2009
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