Markov bases and subbases for bounded contingency tables

DOI10.1007/s10463-010-0289-2zbMath1440.62220arXiv0905.4841OpenAlexW2018962646MaRDI QIDQ2634809

Fabio Rapallo, Ruriko Yoshida

Publication date: 19 February 2016

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.4841

zbMATH Keywords

Markov basisstructural zerosuniversal Gröbner basis

Mathematics Subject Classification ID

Computational methods for problems pertaining to statistics (62-08) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Contingency tables (62H17)

Related Items (6)

Blow-up algebras, determinantal ideals, and Dedekind-Mertens-like formulas ⋮ Goodness of fit for log-linear network models: dynamic Markov bases using hypergraphs ⋮ A characterization of saturated designs for factorial experiments ⋮ Exact inference in contingency tables via stochastic approximation Monte Carlo ⋮ Exact Goodness‐of‐Fit Testing for the Ising Model ⋮ Counting subsets of contingency tables

Uses Software

• CoCoA
• SINGULAR
• 4ti2

Cites Work

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• Markov bases of three-way tables are arbitrarily complicated
• The largest group of invariance for Markov bases and toric ideals
• Sequential importance sampling for multiway tables
• Approximately counting integral flows and cell-bounded contingency tables
• SINGULAR
• Markov chain Monte Carlo exact tests for incomplete two-way contingency tables

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