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Many researchers use computer simulators as experimental tools, especially when physical experiments are infeasible. When computer codes are computationally intensive, nonparametric predictors can be fitted to training data for detailed exploration of the input-output relationship. The accuracy of such flexible predictors is enhanced by taking training inputs to be "space-filling." If there are inputs that have little or no effect on the response, it is desirable that the design be "noncollapsing" in the sense of having spacefilling lower dimensional projections. This article describes an algorithm for constructing noncollapsing space-filling designs for bounded input regions that are of possibly high dimension. Online supplementary materials provide the code for the algorithm, examples of its use, and show its performance in multiple settings.

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Sophisticated computer codes that implement mathematical models of physical processes can involve large numbers of inputs, and screening to determine the most active inputs is critical for understanding the inputoutput relationship. This article presents a new two-stage group screening methodology for identifying active inputs. In Stage 1, groups of inputs showing low activity are screened out; in Stage 2, individual inputs from the active groups are identified. Inputs are evaluated through their estimated total (effect) sensitivity indices (TSIs), which are compared with a benchmark null TSI distribution created from added low noise inputs. Examples show that, compared with other procedures, the proposed method provides more consistent and accurate results for high-dimensional screening. Additional details and computer code are provided in supplementary materials available online.

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Regular factorial designs with randomization restrictions are widely used in practice. This paper provides a unified approach to the construction of such designs using randomization defining contrast subspaces for the representation of randomization restrictions. We use finite projective geometry to determine the existence of designs with the required structure and develop a systematic approach for their construction. An attractive feature is that commonly used factorial designs with randomization restrictions are special cases of this general representation. Issues related to the use of these designs for particular factorial experiments are also addressed.

Summary This paper extends the results of John and Dean (1975) to asymmetrical factorial experiments, and lists a number of designs.

Summary. One of the main advantages of factorial experiments is the information that they can offer on interactions. When there are many factors to be studied, some or all of this information is often sacri®ced to keep the size of an experiment economically feasible. Two strategies for group screening are presented for a large number of factors, over two stages of experimentation, with particular emphasis on the detection of interactions. One approach estimates only main effects at the ®rst stage (classical group screening), whereas the other new method (interaction group screening) estimates both main effects and key two-factor interactions at the ®rst stage. Three criteria are used to guide the choice of screening technique, and also the size of the groups of factors for study in the ®rst-stage experiment. The criteria seek to minimize the expected total number of observations in the experiment, the probability that the size of the experiment exceeds a prespeci®ed target and the proportion of active individual factorial effects which are not detected. To implement these criteria, results are derived on the relationship between the grouped and individual factorial effects, and the probability distributions of the numbers of grouped factors whose main effects or interactions are declared active at the ®rst stage. Examples are used to illustrate the methodology, and some issues and open questions for the practical implementation of the results are discussed.