A note on Bayesian c- and D-optimal designs in nonlinear regression models

• 成果类型: Article
• 署名作者: Dette, H
• 署名单位: Technische Universitat Dresden
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1032526965
• 发表日期: 1996
• 页码: 1225-1234
• 关键词: theorem; robust

摘要

We present a version of Elfving's theorem for the Bayesian D-optimality criterion in nonlinear regression models. The Bayesian optimal design can be characterized as a design which allows a representation of a (uniquely determined) boundary point of a convex subset of L(2)-integrable functions. A similar characterization is given for the Bayesian c-optimality criterion where a (possible) nonlinear function of the unknown parameters has to be estimated. The results are illustrated in the example of an exponential growth model using a gamma prior distribution.