Minimal invariant Markov basis for sampling contingency tables with fixed marginals

DOI10.1007/s10463-006-0089-xzbMath1332.62181OpenAlexW2116088913MaRDI QIDQ1019460

Satoshi Aoki, Akimichi Takemura

Publication date: 2 June 2009

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

Full work available at URL: https://doi.org/10.1007/s10463-006-0089-x

zbMATH Keywords

Markov chain Monte Carloorbitsymmetric grouptransformation grouphierarchical modelsexact tests

Mathematics Subject Classification ID

Numerical analysis or methods applied to Markov chains (65C40) Contingency tables (62H17)

Related Items

Minimal and minimal invariant Markov bases of decomposable models for contingency tables ⋮ Markov basis and Gröbner basis of Segre-Veronese configuration for testing independence in group-wise selections ⋮ Indispensable monomials of toric ideals and Markov bases ⋮ Perturbation method for determining the group of invariance of hierarchical models ⋮ Markov chain Monte Carlo tests for designed experiments ⋮ Fibers of multi-way contingency tables given conditionals: relation to marginals, cell bounds and Markov bases

Uses Software

• 4ti2

Cites Work

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• A Network Algorithm for Performing Fisher's Exact Test in r × c Contingency Tables
• An application of Harnack inequalities to random walk on nilpotent quotients
• Polynomial-time counting and sampling of two-rowed contingency tables
• Use of primal-dual technique in the network algorithm for two-way contingency tables
• Algebraic algorithms for sampling from conditional distributions
• Some characterizations of minimal Markov basis for sampling from discrete conditional distribu\-tions
• Short rational functions for toric algebra and applications
• Minimal Basis for a Connected Markov Chain over 3 x 3 x K Contingency Tables with Fixed Two-Dimensional Marginals
• Performing the Exact Test of Hardy-Weinberg Proportion for Multiple Alleles
• [https://portal.mardi4nfdi.de/wiki/Publication:4705324 Random generation of 2�n contingency tables]
• Generalized Monte Carlo significance tests
• Monte Carlo sampling methods using Markov chains and their applications
• Markov chain Monte Carlo exact tests for incomplete two-way contingency tables