Minimizing variable selection criteria by Markov chain Monte Carlo

Regression models with a large number of predictors arise in diverse fields of social sciences and natural sciences. For proper interpretation, we often would like to identify a smaller subset of the variables that shows the strongest information. In such a large size of candidate predictors setting, one would encounter a computationally cumbersome search in practice by optimizing some criteria for selecting variables, such as AIC, (C_{P}) and BIC, through all possible subsets. In this paper, we present two efficient optimization algorithms vis Markov chain Monte Carlo (MCMC) approach for searching the global optimal subset. Simulated examples as well as one real data set exhibit that our proposed MCMC algorithms did find better solutions than other popular search methods in terms of minimizing a given criterion.