A Predictive Approach to the Analysis of Designed Experiments

Abstract

Viewing the analysis of designed experiments as a model selection problem, we introduce the use of a predictive Bayesian criterion in this context based on the predictive density of a replicate experiment (PDRE). A calibration of the criterion is provided to assist in the model choice. The relationships of the proposed criterion to other prevalent criteria, such as AIC, BIC, and Mallows's C _p , are given. An information theoretic criterion based on the PDRE's of two competing models is also introduced and compared with the usual F statistic for two nested models. Examples are given to illustrate the proposed methodology.

Key Words:

• Analysis of variance
• Bayesian analysis
• Kullback-Leibler divergence
• Predictive criterion
• Split-plot design
• Variable selection