Optimal designs for experiments with a large number of factors. (English) Zbl 0832.62070
Summary: Optimal designs are considered for experiments with many binary factors. In the model, only main effects are considered and responses are normal with equal variances. The design objective is to determine factor settings that give a large expected response after experimentation. Asymptotically optimal designs are obtained using a Bayesian decision theoretic formulation in which factors are independent with finite Fisher information. Both the number of runs and the number of factors tend to infinity in the limit considered. In the derivation, Stein’s identity provides accurate approximations for posterior risks. The optimal number of runs for experiments with many factors is determined.
MSC:
| 62K05 | Optimal statistical designs |
| 62C10 | Bayesian problems; characterization of Bayes procedures |
Keywords:
quality control; two-level designs; asymptotically optimal designs; binary factors; main effects; finite Fisher information; Stein’s identity; posterior risks; optimal number of runsReferences:
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