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Title: Markov bases of conditional independence models for permutations (English)
Author: Csiszár, Villő
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 45
Issue: 2
Year: 2009
Pages: 249-260
Summary lang: English
Category: math
Summary: The L-decomposable and the bi-decomposable models are two families of distributions on the set $S_n$ of all permutations of the first $n$ positive integers. Both of these models are characterized by collections of conditional independence relations. We first compute a Markov basis for the L-decomposable model, then give partial results about the Markov basis of the bi-decomposable model. Using these Markov bases, we show that not all bi-decomposable distributions can be approximated arbitrarily well by strictly positive bi-decomposable distributions. (English)
Keyword: conditional independence
Keyword: Markov basis
Keyword: closure of exponential family
Keyword: permutation
Keyword: L-decomposable
MSC: 60C05
MSC: 60J99
MSC: 62E10
MSC: 62H05
idZBL: Zbl 1165.62007
idMR: MR2518150
Date available: 2010-06-02T18:29:33Z
Last updated: 2013-09-21
Stable URL:
Reference: [1] D. Cox, J. Little, and D. O’Shea: Ideals, Varieties, and Algorithms.Springer, New York 1992. MR 1189133
Reference: [2] D. E. Critchlow, M. A. Fligner, and J. S. Verducci: Probability models on rankings.J. Math. Psych. 35 (1991), 294–318. MR 1128236
Reference: [3] V. Csiszár: Conditional independence relations and log-linear models for random matchings.Acta Math. Hungar. (2008), Online First. MR 2487466
Reference: [4] P. Diaconis and N. Eriksson: Markov bases for noncommutative Fourier analysis of ranked data.J. Symbolic Comput. 41 (2006), 173–181. MR 2197153
Reference: [5] P. Diaconis and B. Sturmfels: Algebraic algorithms for sampling from conditional distributions.Ann. Statist. 26 (1998), 363–397. MR 1608156
Reference: [6] A. Dobra: Markov bases for decomposable graphical models.Bernoulli 9 (2003), 1093–1108. Zbl 1053.62072, MR 2046819
Reference: [7] M. A. Fligner and J. S. Verducci (eds.): Probability Models and Statistical Analyses for Ranking Data.Springer, New York 1993. MR 1237197
Reference: [8] 4ti2 team: 4ti2 – A software package for algebraic, geometric and combinatorial problems on linear spaces.Available at
Reference: [9] D. Geiger, C. Meek, and B. Sturmfels: On the toric algebra of graphical models.Ann. Statist. 34 (2006), 1463–1492. MR 2278364
Reference: [10] R. D. Luce: Individual Choice Behavior.Wiley, New York 1959. Zbl 0093.31708, MR 0108411
Reference: [11] J. I. Marden: Analyzing and Modelling Rank Data.Chapman and Hall, London 1995. MR 1346107
Reference: [12] G. Pistone, E. Riccomagno, and H. P. Wynn: Algebraic Statistics.Chapman and Hall/CRC, Bocan Raton 2000. MR 2332740
Reference: [13] F. Rapallo: Toric statistical models: parametric and binomial representations.Ann. Inst. Statist. Math. 59 (2007), 727–740. Zbl 1133.62343, MR 2397736
Reference: [14] B. Sturmfels: Gröbner bases and convex polytopes.Amer. Math. Soc., Providence RI 1996. Zbl 0856.13020, MR 1363949
Reference: [15] S. Sullivant: Toric Ideals in Algebraic Statistics.Ph.D. Thesis, University of California, Berkeley 2005. MR 2623019
Reference: [16] A. Takemura and S. Aoki: Some characterizations of minimal Markov basis for sampling from discrete conditional distributions.Ann. Inst. Statist. Math. 56 (2004), 1–17. MR 2053726


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