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

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

2009-08-25

arxiv.org/abs/0908.3553v1

Annals of Statistics 2009, Vol. 37, No. 5B, 2626-2654

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-AOS577 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/07-AOS577

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.

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