A Bayesian Approach to Model Robust Designs

In industrial experiments, cost considerations will sometimes make it impractical to design experiments so that effects of all the factors can be estimated simultaneously. Therefore experimental designs are frequently constructed to estimate main effects and a few pre-specified interactions. A criticism frequently associated with the use of many optimality criteria is the specific reliance on an assumed statistical model. One way to deal with such a criticism may be to assume that instead the true model is part of a known set of models. In this paper, we consider a class of Bayesian designs that are robust for change in model specification. This paper is motivated by the belief that appropriate Bayesian approaches may perform well in constructing model robust designs and by the limitation of such ap-proaches in the literature. We introduce an idea that uses the traditional Bayesian design method for parameter estimation and incorporates a discrete prior probability on the set of models of interest. Two-levels orthogonal designs and designs derived from orthogonal starting designs will be used in the examples. Comparisons with de-signs resulting from existing approaches will be provided. Results show that Bayesian models robust designs perform well compared to model robust factorial designs and fractional factorial designs. We also show that the Bayesian model robust criterion is a good alternative to the generalized word length pattern for evaluating 16-run 7-factors orthogonal designs