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

TL;DR

This paper enhances the convergence of the SAMC algorithm using smoothing techniques and demonstrates its effectiveness in Bayesian model selection, outperforming existing methods in change-point detection tasks.

Contribution

It introduces a new, generalized SAMC algorithm with smoothing methods, providing convergence proof and improved performance in Bayesian model selection.

Findings

The new algorithm outperforms SAMC and reversible jump MCMC in model selection.

Numerical tests show significant efficiency gains in change-point identification.

Theoretical convergence of the proposed algorithm is rigorously established.

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.