Two polynomial representations of experimental design

TL;DR

This paper compares two polynomial representations of experimental designs—Groebner bases and indicator functions—explaining their use in analysis and planning, with examples like factorial and mixture designs.

Contribution

It provides a clear description of both polynomial representations and details how to switch between them in the context of algebraic statistics.

Findings

Describes how to use Groebner bases and indicator functions in design analysis.

Provides methods to switch between the two polynomial representations.

Includes practical examples like factorial and mixture experiments.

Abstract

In the context of algebraic statistics an experimental design is described by a set of polynomials called the design ideal. This, in turn, is generated by finite sets of polynomials. Two types of generating sets are mostly used in the literature: Groebner bases and indicator functions. We briefly describe them both, how they are used in the analysis and planning of a design and how to switch between them. Examples include fractions of full factorial designs and designs for mixture experiments.