Variable selection by a reversible jump MCMC approach

In this paper we address the problem of selecting the best subset of predictors in linear models from a given set of predictors. In computing the posterior probabilities of the various models, we propose to use the method of reversible jump Markov chain Monte Carlo sampling which cyclicly sweeps through the set of possible predictors and includes or removes them from the model one at a time. Special emphasis is given to a scheme that does not require sampling of the model coefficients and is based on predictive densities. Numerical results are provided that show the performance of the proposed approach.