A PREDICTIVE APPROACH TO THE ANALYSIS OF DESIGNED EXPERIMENTS

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