Using the bootstrap to select models

The problem of model selection is addressed by the Bayesian methodology and the bootstrap technique. As a rule for choosing the best model from a set of proposed models, the maximum a posteriori principle is used. The evaluation of the maximum a posteriori probability (MAP) of each model amounts to computation of integrals whose integrands may be very peaked functions. We carry out the integration by importance sampling, where the importance function is a multivariate Gaussian whose samples are obtained by the bootstrap technique. The performance of the MAP rule is examined by computer simulations, and comparisons with the widely used AIC (Akaike information criterion) and MDL (minimum description length) rules are made.