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Optimal experimental design for another’s analysis. (English) Zbl 0792.62062
Summary: We consider the optimal design of experiments in which estimation and design are performed by different parties. The parties are assumed to share similar goals, as reflected by a common loss function, but they may have different prior beliefs. After presenting a few motivating examples, we examine the problem of optimal sample size selection under a normal likelihood with constant cost per observation. We also consider the problem of optimal allocation for given overall sample sizes. We present results under both squared-error loss and a logarithmic utility, paying attention to the differences between one- and two-prior optimal designs. As asymmetric discrepancy measure features repeatedly in our development, and we question the extent of its role in optimal two-prior designs.

MSC:
62K05 Optimal statistical designs
62F15 Bayesian inference
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