Three-level main-effects designs exploiting prior information about model uncertainty

Pi Wen Tsai, Steven G. Gilmour, Roger Mead

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

To explore the projection efficiency of a design, Tsai, et al [2000. Projective three-level main effects designs robust to model uncertainty. Biometrika 87, 467-475] introduced the Q criterion to compare three-level main-effects designs for quantitative factors that allow the consideration of interactions in addition to main effects. In this paper, we extend their method and focus on the case in which experimenters have some prior knowledge, in advance of running the experiment, about the probabilities of effects being non-negligible. A criterion which incorporates experimenters' prior beliefs about the importance of each effect is introduced to compare orthogonal, or nearly orthogonal, main effects designs with robustness to interactions as a secondary consideration. We show that this criterion, exploiting prior information about model uncertainty, can lead to more appropriate designs reflecting experimenters' prior beliefs.

Original languageEnglish
Pages (from-to)619-627
Number of pages9
JournalJournal of Statistical Planning and Inference
Volume137
Issue number2
DOIs
Publication statusPublished - 2007 Feb 1

Keywords

  • Bayesian optimal designs
  • Factor screening
  • Orthogonal array
  • Prior information
  • Projection

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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