Bayesian approaches to model robust and model discrimination 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 an approximation of an unknown element of a known set of models. In this thesis, we consider a class of designs that are robust for change in model specification.; This thesis is motivated by the belief that appropriate Bayesian approaches may also perform well in constructing model robust designs and by the limitation of such approaches 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. We also introduce some model discrimination approaches that maximize the capability of the design for discriminating among competing models. Two-levels orthogonal designs and designs derived from orthogonal starting designs were used in the examples. Our model discrimination approaches could be seen as extensions of the approach developed by Atkinson and Federov (1975), and Jones, Li, Nachtsheim and Ye (2006). Comparisons with designs resulting from existing approaches and under similar conditions will be provided.