Markov Bases: A 25 Year Update

• 成果类型: Review
• 署名作者: Almendra-Hernandez, Felix; De Loera, Jesus A.; Petrovic, Sonja
• 署名单位: University of California System; University of California Davis; Illinois Institute of Technology
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2024.2310181
• 发表日期: 2024
• 页码: 1671-1686
• 关键词: conditional inference; algebraic statistics; positive margins; tables; MODEL; graph; chain

摘要

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.