Population SAMC vs SAMC: Convergence and Applications to Gene Selection Problems

Abstract

The Bayesian model selection approach has been adopted by more and more people when analyzing a large data. However, it is known that the reversible jump MCMC (RJMCMC) algorithm, which is perhaps the most popular MCMC algorithm for Bayesian model selection, is prone to get trapped into local modes when the model space is complex. The stochastic approximation Monte Carlo (SAMC) algorithm essentially overcomes the local trap problem suffered by conventional MCMC algorithms by introducing a self-adjusting mechanism based on the past samples. In this paper, we propose a population SAMC (Pop-SAMC) algorithm, which works on a population of SAMC chains and can make use of crossover operators from genetic algorithms to further improve its efficiency. Under mild conditions, we show the convergence of this algorithm. Comparing to the single chain SAMC algorithm, Pop-SAMC provides a more efficient self-adjusting mechanism and thus can converge faster. The effectiveness of Pop-SAMC for Bayesian model selection problems is examined through a change-point identification problem and a gene selection problem. The numerical results indicate that Pop-SAMC significantly outperforms both the single chain SAMC and RJMCMC.