A computationally efficient Bayesian variable selection method is presented for linear and nonlinear effects in regression models using the Laplace approximation of the marginal likelihood via Bayesian Information Criteria (BIC).

The proposed method can be used to evaluate the inclusion of variables as either linear or nonlinear predictors in the model, as well as to identify redundant variables for removal. The best subset of variables is selected by comparing the posterior probabilities of the possible models. In case of large number number of candidate variables, MCMC model search method that only visits models with high posterior probabilities is adopted for fast computation, and multiplicity is controlled by setting a Dirichlet prior on the probabilities of observing each effect type. The performance of the proposed method is investigated using several simulation studies and two real data examples. The R code used in this study and for applying the proposed method is provided.