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Markov Bases: A 25 Year Update

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  • Félix Almendra-Hernández
  • Jesús A. De Loera
  • Sonja Petrović

Abstract

In this article, we evaluate the challenges and best practices associated with the Markov bases approach to sampling from conditional distributions. We provide insights and clarifications after 25 years of the publication of the Fundamental theorem for Markov bases by Diaconis and Sturmfels. In addition to a literature review, we prove three new results on the complexity of Markov bases in hierarchical models, relaxations of the fibers in log-linear models, and limitations of partial sets of moves in providing an irreducible Markov chain. Supplementary materials for this article are available online.

Suggested Citation

  • Félix Almendra-Hernández & Jesús A. De Loera & Sonja Petrović, 2024. "Markov Bases: A 25 Year Update," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(546), pages 1671-1686, April.
    • Handle: RePEc:taf:jnlasa:v:119:y:2024:i:546:p:1671-1686
    DOI: 10.1080/01621459.2024.2310181
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