A Bayesian Approach to the Design and Analysis of Fractionated Experiments

Specifying a prior distribution for the large number of parameters in the statistical model is a critical step in a Bayesian approach to the design and analysis of experiments. This article shows that the prior distribution can be induced from a functional prior on the underlying transfer function. The functional prior requires specification of only a few hyperparameters and thus can be easily implemented in practice. The usefulness of the approach is demonstrated through the analysis of some experiments. The article also proposes a new class of design criteria and establishes their connections with the minimum aberration criterion.