Positive margins and primary decomposition

DOI10.1216/JCA-2014-6-2-173zbMath1375.13047arXiv1201.2591OpenAlexW3102976302WikidataQ57442342 ScholiaQ57442342MaRDI QIDQ405381

Johannes Rauh, Thomas Kahle, Seth Sullivant

Publication date: 5 September 2014

Published in: Journal of Commutative Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.2591

zbMATH Keywords

algebraic statisticsMarkov basisbinomial primary decompositionconnectivity of fibers

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Generalized linear models (logistic models) (62J12) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Lattice points in specified regions (11P21) Random walks on graphs (05C81) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

Related Items (7)

The geometry of Gaussian double Markovian distributions ⋮ From Polynomial Invariants to Linear Loops ⋮ Lifting Markov bases and higher codimension toric fiber products ⋮ Multigraded commutative algebra of graph decompositions ⋮ Parity binomial edge ideals ⋮ Detecting binomiality ⋮ Rapid Mixing and Markov Bases

Uses Software

• Macaulay2
• 4ti2
• Binomials.m2
• Polyhedra
• GitHub
• GraphBinomials

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Decompositions of commutative monoid congruences and binomial ideals.
• Lectures on algebraic statistics
• Binomial edge ideals and conditional independence statements
• Markov bases of binary graph models
• Algebraic algorithms for sampling from conditional distributions
• Gröbner bases of toric varieties
• Binomial ideals
• Generalized binomial edge ideals
• Multigraded commutative algebra of graph decompositions
• Polyhedra: a package for computations with convex polyhedral objects
• Minimal primes of ideals arising from conditional independence statements
• Markov bases of three-way tables are arbitrarily complicated
• Toric fiber products
• Sequential importance sampling for multiway tables
• On the toric algebra of graphical models
• Decompositions of binomial ideals

This page was built for publication: Positive margins and primary decomposition