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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 interaction effect might only be considered active if main effects for and 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.

This chapter provides a review of special methods for analyzing data from screening experiments conducted using regular fractional factorial designs. The methods considered are robust to the presence of multiple nonzero effects. Of special interest are methods that try to adapt effectively to the unknown number of nonzero effects. Emphasis is on the development of adaptive methods of analysis of orthogonal saturated designs that rigorously control Type I error rates of tests or confidence levels of confidence intervals under standard linear model assumptions. The robust, adaptive method of Lenth (1989) is used to illustrate the basic problem. Then nonadaptive and adaptive robust methods of testing and confidence interval estimation known to control error rates are introduced and illustrated. Although the focus is on Type I error rates and orthogonal saturated designs, Type II error rates, nonorthogonal designs, and supersaturated designs are also discussed briefly.

Screening in simulation experiments to find the most important factors, from a very large number of factors, is discussed. The method of sequential bifurcation in the presence of random noise is described and is demonstrated through a case study from the mobile telecommunications industry. The case study involves 92 factors and three related, discrete-event simulation models. These models represent three supply chain configurations of varying complexity that were studied for an Ericsson factory in Sweden. Five replicates of observations from 21 combinations of factor levels (or scenarios) are simulated under a particular noise distribution, and a shortlist of the 11 most important factors is identified for the most complex of the three models. Various different assumptions underlying the sequential bifurcation technique are discussed, including the role of first- and second-order polynomial regression models to describe the response, and knowledge of the directions and relative sizes of the factor main effects.

A nexperiment involving a complex computer model or code may have tens or even hundreds of input variables and, hence, the identification of the more important variables (screening) is often crucial. Methods are described for decomposing a complex input—output relationship into effects. Effects are more easily understood because each is due to only one or a small number of input variables. They can be assessed for importance either visually or via a functional analysis of variance. Effects are estimated from flexible approximations to the input—output relationships of the computer model. This allows complex nonlinear and interaction relationships to be identified. The methodology is demonstrated on a computer model of the relationship between environmental policy and the world economy.