Minimal Basis for a Connected Markov Chain over 3 × 3 ×K Contingency Tables with Fixed Two‐Dimensional Marginals

By Satoshi Aoki, Akimichi Takemura. 2003

94 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Computational Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1a71faae1b48a4fbca215f77ce882835164c8120

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Computational Mathematics

In Statistics and Probability

Citations in the corpus

Ideals of adjacent minors (2003, background): “A particular family of statistical models that describe the joint probability distributions of these random variables (the so-called no dway interaction models [8]) gives rise to a toric variety whose set of defining equations may be extremely large and complicated [ 1 , 15].”
Toric fiber products (2006, unknown): “Let φ be the ring homomorphism φ : K[qi1•i3•i5 | i1, i3, i5 ∈ [3]] → K[ai1i2 , bi2i3 , ci3i4 , di4i5 | i1, i3, i5 ∈ [3], i2, i4 ∈ [2]]”
Markov chain Monte Carlo exact tests for incomplete two-way contingency tables (2005, background): “= 2M2(1, 2; 1, 2) + Y ′ Note that there is no cancellation of signs in any cell and the remaining pattern, Y ′ = Y − 2M2(1, 2; 1, 2), is again in F0(S).”
Some characterizations of minimal Markov basis for sampling from discrete conditional distributions (2004, methodology): “For the case of t 0 = (2; 2); (2; 3); (2; 5); (2; 6), there are two elements in F t , but for the case of t 0 = (2; 4) there are three elements in F t as”
Toric Ideals Arising from Contingency Tables (2007, background): “The toric ideal of the configuration A333 is studied in [18], [7] [4] and [2].”
Nonlinear Discrete Optimization (2010, background): “They have been studied extensively for decades, in operations research in the context of high dimensional transportation problems, and in statistics in the context of privacy in statistical databases and disclosure control, see [3], [7], [8], [22], [29], [36], [58], [62], [63], [75], [97], [100], an”