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An important aspect of Bayesian model selection is how to deal with hugemodel spaces, since exhaustive enumeration of all the models entertained isunfeasible and inferences have to be based on the very small proportion ofmodels visited. This is the case for the variable selection problem, with amoderate to large number of possible explanatory variables being considered inthis paper. We review some of the strategies proposed in the literature andargue that inferences based on empirical frequencies via Markov Chain MonteCarlo sampling of the posterior distribution outperforms recently proposedsearching methods. We give a plausible yet very simple explanation of thiseffect, showing that estimators based on frequencies are unbiased. The resultsobtained in two illustrative examples provide strong evidence in favor of ourarguments.

Inferences in Bayesian variable selection problems with large model spaces