A Bayesian Analysis of Unreplicated Two-Level Factorials Using Effects Sparsity, Hierarchy, and Heredity

This article proposes a Bayesian procedure to calculate posterior probabilities of active effects for unreplicated two-level factorials. The results from a literature survey are used to specify individual prior probabilities for the activity of effects and the posterior probabilities are then calculated in a three-step procedure where the principles of effects sparsity, hierarchy, and heredity are successively considered. We illustrate our approach by reanalyzing experiments found in the literature.