A Two-Stage Bayesian Model Selection Strategy for Supersaturated Designs

In early stages of experimentation, one often has many candidate factors of which only few have signiŽ cant in uence on the response. Supersaturated designs can offer important advantages. However, standard regression techniques of Ž tting a prediction line using all candidate variables fail to analyze data from such designs. Stepwise regression may be used but has drawbacks as reported in the literature. A two-stage Bayesian model selection strategy, able to keep all possible models under consideration while providing a level of robustness akin to Bayesian analyses incorporating noninformative priors, is proposed. The strategy is demonstrated on a well-known dataset and compared to competing methods via simulation.