  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.
