BAYES OPTIMAL DESIGNS FOR 2-LEVEL AND 3-LEVEL FACTORIAL-EXPERIMENTS

• 成果类型: Article
• 署名作者: TOMAN, B
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2290919
• 发表日期: 1994
• 页码: 937-946
• 关键词: linear-models

摘要

Two- and three-level factorial designs are often used for exploratory experiments with many independent variables. The purpose of such experiments is to estimate the effects of all active independent variables and their interactions. For reasons of economy or other constraints, only a fraction of the full number of experimental settings of the independent variables may be run, precluding the separate data-based estimation of all the effects. In this situation of relatively sparse data and many unknown parameters, the benefits of reliable prior information, used in the estimation and experimental design, can be especially significant. In this article, exact Bayes-optimal designs of two- and three-level fractional factorial experiments and of blocked two- and three-level factorial experiments are derived. The optimality criteria used in this process are versions of the Bayes psi criterion introduced by Duncan and DeGroot. It is shown that the classical fractional factorial designs for the 2(k) experiment are usually optimal, whereas those for the 3(k) experiment are not. Further, the classical blocked 2(k) and 3(k) designs are Bayes psi optimal.