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A predictive approach to the analysis of designed experiments. (English) Zbl 0791.62080

Summary: 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’ \(C_ p\), 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.

MSC:

62K99 Design of statistical experiments
62J05 Linear regression; mixed models
62F15 Bayesian inference
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