Existing Bayesian model selection procedures require the specification of prior distributions on each of the parameter vectors appearing in every model in the selection set. In practice, this requirement limits the application of Bayesian model selection methodology. To overcome this limitation, we propose a new approach toward Bayesian model selection that uses classical test statistics to compute Bayes factors between possible models. In several test cases, our approach produces results that are similar to previously-proposed Bayesian model selection and model averaging techniques in which prior distributions were carefully chosen. Aside from eliminating the requirement to specify complicated prior distributions, this method also offers important computational and algorithmic advantages over existing simulation-based methods. Finally, because it is easy to evaluate the operating characteristics of this procedure for a given sample size and specified number of covariates, our method facilitates the selection of hyperparameter values through prior-predictive simulation.
Statistical Methodology | Statistical Theory
Hu, Jianhua and Johnson, Valen E., "Bayesian Model Selection Using Test Statistics" (November 2005). UT MD Anderson Cancer Center Department of Biostatistics Working Paper Series. Working Paper 8.