Markov bases and structural zeros

Fabio Rapallo

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we apply the elimination technique to the computation of Markov bases, paying special attention to contingency tables with structural zeros. An algebraic relationship between the Markov basis for a table with structural zeros and the corresponding complete table is proved. In order to find the relevant Markov basis, it is enough to eliminate the indeterminates associated with the structural zeros from the toric ideal for the complete table. Moreover, we use this result for the computation of Markov bases for some classical log-linear models, such as quasi-independence and quasi-symmetry, and computations in the multi-way setting are presented.

Original languageEnglish
Pages (from-to)164-172
Number of pages9
JournalJournal of Symbolic Computation
Volume41
Issue number2
DOIs
Publication statusPublished - Feb 2006
Externally publishedYes

Keywords

  • Contingency tables
  • Diaconis-Sturmfels algorithm
  • Elimination ideal
  • Log-linear models

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