Design and analysis of fractional factorial experiments from the viewpoint of computational algebraic statistics

TL;DR

This paper reviews how computational algebraic statistics, including Gr"obner bases, indicator functions, and Markov bases, enhances the design and analysis of fractional factorial experiments, broadening their applicability.

Contribution

It introduces algebraic statistical techniques that unify the treatment of regular and non-regular fractional factorial designs and improve data analysis methods.

Findings

Unified approach to design of fractional factorial experiments

Use of Markov bases for analyzing discrete data

Expansion of fractional factorial design scope

Abstract

We give an expository review of applications of computational algebraic statistics to design and analysis of fractional factorial experiments based on our recent works. For the purpose of design, the techniques of Gr\"obner bases and indicator functions allow us to treat fractional factorial designs without distinction between regular designs and non-regular designs. For the purpose of analysis of data from fractional factorial designs, the techniques of Markov bases allow us to handle discrete observations. Thus the approach of computational algebraic statistics greatly enlarges the scope of fractional factorial designs.