Optimal experimental design for another’s analysis. (English) Zbl 0792.62062

Etzioni, Ruth; Kadane, Joseph B.

J. Am. Stat. Assoc. 88, No. 424, 1404-1411 (1993).

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

Keywords:

adversarial design; conjugate prior; posterior distribution; predictive distribution; one-prior designs; optimal sample size selection; normal likelihood; constant cost per observation; optimal allocation; given overall sample sizes; squared-error loss; logarithmic utility; asymmetric discrepancy measure; optimal two-prior designs