Markov chain Monte Carlo methods for the regular two-level fractional factorial designs and cut ideals

TL;DR

This paper explores the connection between cut ideals and Markov bases in the context of regular two-level fractional factorial designs, providing new methods for constructing Markov bases using algebraic tools.

Contribution

It introduces a novel application of cut ideals to derive Markov bases for certain factorial designs, especially those with at most two relations.

Findings

Markov basis of degree 2 for specific designs

Connection between cut ideals and Markov bases in factorial designs

Explicit construction of Markov bases for designs with limited relations

Abstract

It is known that a Markov basis of the binary graph model of a graph $G$ corresponds to a set of binomial generators of cut ideals $I_{\widehat{G}}$ of the suspension $\widehat{G}$ of $G$. In this paper, we give another application of cut ideals to statistics. We show that a set of binomial generators of cut ideals is a Markov basis of some regular two-level fractional factorial design. As application, we give a Markov basis of degree 2 for designs defined by at most two relations.