Bayesian Statistical Variable Selection: A Review

From a Bayesian viewpoint, the answer (in theory, at least) to the general model selection problem is known. However, the formalization of the selection problem does not realistically match the iterative process that occurs when selecting a model in practice. In addition, computational restrictions limit the applicability of the solution in general. In the multiple linear regression variable selection setting, however, the Bayesian approach offers some practical procedures that can be used to at least reduce the possible number of models under consideration. 'Semi-automatic' methods for Bayesian variable selection have recently been developed by Mitchell and Beauchamp (1988) and George and McCulloch (1993) using relatively uniformative prior distributions for the unknown regression coefficients and variance parameter. In particular, their choices enable the computation of the general solution to be feasible.