A Characterization of Saturated Designs for Factorial Experiments

TL;DR

This paper introduces a combinatorial criterion for identifying saturated fractions in factorial experiments and demonstrates how to generate such fractions using algebraic and Markov basis methods.

Contribution

It provides a new combinatorial criterion for saturation and a method to generate random saturated fractions with specified projections.

Findings

The criterion effectively identifies saturated fractions.

The method allows for generating random saturated fractions.

Applications in factorial experiment design are demonstrated.

Abstract

In this paper we study saturated fractions of factorial designs under the perspective of Algebraic Statistics. We define a criterion to check whether a fraction is saturated or not with respect to a given model. The proposed criterion is based purely on combinatorial objects. Our technique is particularly useful when several fractions are needed. We also show how to generate random saturated fractions with given projections, by applying the theory of Markov bases for contingency tables.