Markov Bases: A 25 Year Update

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Maximum likelihood estimation in the \(\beta\)-model
Positive margins and primary decomposition
Running Markov chain without Markov basis
Unimodular binary hierarchical models
The Graver complexity of integer programming
A finiteness theorem for Markov bases of hierarchical models
Lifting Markov bases and higher codimension toric fiber products
Indispensable monomials of toric ideals and Markov bases
\(N\)-fold integer programming
Markov bases of binary graph models of \(K_{4}\)-minor free graphs
Markov bases for decomposable graphical models
A divide-and-conquer algorithm for generating Markov bases of multi-way tables
Hybrid schemes for exact conditional inference in discrete exponential families
Algebraic algorithms for sampling from conditional distributions
Graver basis for an undirected graph and its application to testing the beta model of random graphs
Hit and run as a unifying device
Multigraded commutative algebra of graph decompositions
Betti numbers of Stanley-Reisner rings determine hierarchical Markov degrees
Goodness of fit for log-linear network models: dynamic Markov bases using hypergraphs
Heat-bath random walks with Markov bases
Markov bases of three-way tables are arbitrarily complicated
Markov bases for noncommutative Fourier analysis of ranked data
On the toric algebra of graphical models
Markov bases and subbases for bounded contingency tables
Open problems on connectivity of fibers with positive margins in multi-dimensional contingency tables
Rapid mixing and Markov bases
Exact goodness-of-fit tests for Markov chains
Unimodular hierarchical models and their Graver bases
Connecting tables with zero-one entries by a subset of a Markov basis
Algebraic statistics for a directed random graph model with reciprocation
Minimal Basis for a Connected Markov Chain over 3 x 3 x K Contingency Tables with Fixed Two-Dimensional Marginals
Generalized Monte Carlo significance tests
A Parameterized Strongly Polynomial Algorithm for Block Structured Integer Programs
Geometrically aware dynamic Markov bases for statistical linear inverse problems
Tight Complexity Lower Bounds for Integer Linear Programming with Few Constraints
On the relative size of toric bases
A Survey of Statistical Network Models
Ideals, Varieties, and Algorithms
Sampling for Conditional Inference on Network Data
Sampling from a Manifold
Exact Goodness‐of‐Fit Testing for the Ising Model
All Linear and Integer Programs Are Slim 3‐Way Transportation Programs
Approximate exchangeability and de Finetti priors in 2022
De Finetti priors using Markov chain Monte Carlo computations
Discussion of ``Coauthorship and citation networks for statisticians
Sampling lattice points in a polytope: a Bayesian biased algorithm with random updates