Bayesian approach for the design and analysis of a two level factorial experiment in the presence of dispersion effects

Abstract

With linear dispersion effects, the standard factorial designs are not optimal estimation of a mean model. A sequential two-stage experimental design procedure has been proposed that first estimates the variance structure, and then uses the variance estimates and the variance optimality criterion to develop a second stage design that efficiency estimates the mean model. This procedure has been compared to an equal replicate design analyzed by ordinary least squares, and found to be a superior procedure in many situations. However with small first stage sample sizes the variance estiamtes are not reliable, and hence an alternative procedure could be more beneficial. For this reason a Bayesian modification to the two-stage procedure is proposed which will combine the first stage variance estiamtes with some prior variance information that will produce a more efficient procedure. This Bayesian procedure will be compared to the non-Bayesian twostage procedure and to the two one-stage alternative procedures li...