Markov bases for two-way subtable sum problems

Abstract

It has been well-known that for two-way contingency tables with fixed row sums and column sums the set of square-free moves of degree two forms a Markov basis. However when we impose an additional constraint that the sum of a subtable is also fixed, then these moves do not necessarily form a Markov basis. Thus, in this paper, we show a necessary and sufficient condition on a subtable so that the set of square-free moves of degree two forms a Markov basis.

23 pages

References in corpus (3)

• On the toric algebra of graphical models
• Indispensable monomials of toric ideals and Markov bases
• Two way subtable sum problems and quadratic Groebner bases

Cited by in corpus (8)

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• Minimal and minimal invariant Markov bases of decomposable models for contingency tables
• Hierarchical subspace models for contingency tables
• Equivariant lattice generators and Markov bases
• Betti numbers of Stanley-Reisner rings determine hierarchical Markov degrees
• Toric ideals with linear components: an algebraic interpretation of clustering the cells of a contingency table
• Markov Bases for Typical Block Effect Models of Two-way Contingency Tables
• Outliers and patterns of outliers in contingency tables with Algebraic Statistics