Prior Distributions for Bayesian Analysis of Screening Experiments

When many effects are under consideration in a screening experiment, it may be necessary to use designs with complex aliasing patterns, especially when interactions and higher-order effects exist. In this situation, the selection of subsets of active effects is a challenging problem. This chapter describes Bayesian methods for subset selection, with emphasis on the choice of prior distributions and the impact of this choice on subset selection, computation, and practical analysis. Attention is focused on experiments where a linear regression model with Gaussian errors describes the response. Ideas are illustrated through an experiment in clinical laboratory testing and through an example with simulated data. Advantages of the Bayesian approach are stressed, such as the ability to incorporate useful information about which subsets of effects are likely to be active. For example, an AB interaction effect might only be considered active if main effects for A and B are also likely to be active. When such information is combined with a stochastic search for promising subsets of active effects, a powerful subset selection tool results. The techniques may also be applied to designs without complex aliasing as a way of quantifying uncertainty in subset selection.