The algebraic method in experimental design
Hugo Maruri-Aguilar, Henry P. Wynn
TL;DR
This paper surveys the use of algebraic methods, especially Gr"obner bases, in experimental design to identify models and analyze aliasing, illustrated through various design examples.
Contribution
It introduces the algebraic fan concept and applies algebraic techniques to diverse experimental designs, enhancing model identification and confounding analysis.
Findings
Algebraic methods effectively analyze design confounding.
Gr"obner bases facilitate model identification in experimental designs.
The algebraic fan provides a new perspective on design structure.
Abstract
The algebraic method provides useful techniques to identify models in designs and to understand aliasing of polynomial models. The present note surveys the topic of Gr\"obner bases in experimental design and then describes the notion of confounding and the algebraic fan of a design. The ideas are illustrated with a variety of design examples ranging from Latin squares to screening designs.
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Taxonomy
TopicsOptimal Experimental Design Methods · graph theory and CDMA systems