Connecting tables with zero-one entries by a subset of a Markov basis

TL;DR

This paper investigates conditions under which subsets of the Graver basis, including minimal Markov bases, can connect zero-one tables, providing theoretical insights into their connectivity in statistical models.

Contribution

It offers theoretical results on the connectivity of zero-one tables using subsets of the Graver basis, focusing on minimal Markov bases.

Findings

Conditions for subset connectivity of zero-one tables

Minimal Markov bases may not always connect zero-one tables

Theoretical characterization of connectivity in common models

Abstract

We discuss connecting tables with zero-one entries by a subset of a Markov basis. In this paper, as a Markov basis we consider the Graver basis, which corresponds to the unique minimal Markov basis for the Lawrence lifting of the original configuration. Since the Graver basis tends to be large, it is of interest to clarify conditions such that a subset of the Graver basis, in particular a minimal Markov basis itself, connects tables with zero-one entries. We give some theoretical results on the connectivity of tables with zero-one entries. We also study some common models, where a minimal Markov basis for tables without the zero-one restriction does not connect tables with zero-one entries.