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Stochastic approximation Monte Carlo (SAMC) has recently been proposed byLiang, Liu and Carroll [J. Amer. Statist. Assoc. 102 (2007) 305--320] as ageneral simulation and optimization algorithm. In this paper, we propose toimprove its convergence using smoothing methods and discuss the application ofthe new algorithm to Bayesian model selection problems. The new algorithm istested through a change-point identification example. The numerical resultsindicate that the new algorithm can outperform SAMC and reversible jump MCMCsignificantly for the model selection problems. The new algorithm represents ageneral form of the stochastic approximation Markov chain Monte Carloalgorithm. It allows multiple samples to be generated at each iteration, and abias term to be included in the parameter updating step. A rigorous proof forthe convergence of the general algorithm is established under verifiableconditions. This paper also provides a framework on how to improve efficiencyof Monte Carlo simulations by incorporating some nonparametric techniques.

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