Fast Model Search for Designed Experiments with Complex Aliasing

In screening experiments, run size considerations often necessitate the use of designs with complex aliasing patterns. Such designs provide an opportunity to examine interactions and other higher order terms as possible predictors, as Hamada and Wu (1992) propose. The large number of model terms and the small number of observations mean that many good models may describe the data well. The need for good model search algorithms motivated Chipman, Hamada, and Wu (1997) to propose a Bayesian approach based on the Gibbs sampler. Their stochastic search method was able to identify many promising models, while incorporating preferences for certain models. In this paper, several enhancements to this procedure are outlined. The selection of prior parameters is further explained and simpliied, so that in the absence of strong prior knowledge the methodology may be used to search for promising models. Priors that allow the posterior to be simpliied speed up the search, and eliminate Monte Carlo error in evaluating model probabilities. Several new plots and summaries are introduced to examine models identiied by the procedure. These proposals and methods are illustrated using simulated data in a Plackett-Burman 12-run layout.