Markov bases of conditional independence models for permutations

Villő Csiszár

Kybernetika (2009)

  • Volume: 45, Issue: 2, page 249-260
  • ISSN: 0023-5954

Abstract

top
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.

How to cite

top

Csiszár, Villő. "Markov bases of conditional independence models for permutations." Kybernetika 45.2 (2009): 249-260. <http://eudml.org/doc/37731>.

@article{Csiszár2009,
abstract = {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.},
author = {Csiszár, Villő},
journal = {Kybernetika},
keywords = {conditional independence; Markov basis; closure of exponential family; permutation; L-decomposable; conditional independence; Markov basis; closure of exponential family; permutation; L-decomposable},
language = {eng},
number = {2},
pages = {249-260},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Markov bases of conditional independence models for permutations},
url = {http://eudml.org/doc/37731},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Csiszár, Villő
TI - Markov bases of conditional independence models for permutations
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 2
SP - 249
EP - 260
AB - 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.
LA - eng
KW - conditional independence; Markov basis; closure of exponential family; permutation; L-decomposable; conditional independence; Markov basis; closure of exponential family; permutation; L-decomposable
UR - http://eudml.org/doc/37731
ER -

References

top
  1. Ideals, Varieties, and Algorithms, Springer, New York 1992. MR1189133
  2. Probability models on rankings, J. Math. Psych. 35 (1991), 294–318. MR1128236
  3. Conditional independence relations and log-linear models for random matchings, Acta Math. Hungar. (2008), Online First. MR2487466
  4. Markov bases for noncommutative Fourier analysis of ranked data, J. Symbolic Comput. 41 (2006), 173–181. MR2197153
  5. Algebraic algorithms for sampling from conditional distributions, Ann. Statist. 26 (1998), 363–397. MR1608156
  6. Markov bases for decomposable graphical models, Bernoulli 9 (2003), 1093–1108. Zbl1053.62072MR2046819
  7. Probability Models and Statistical Analyses for Ranking Data, Springer, New York 1993. MR1237197
  8. 4ti2 – A software package for algebraic, geometric and combinatorial problems on linear spaces, Available at www.4ti2.de. 
  9. On the toric algebra of graphical models, Ann. Statist. 34 (2006), 1463–1492. MR2278364
  10. Individual Choice Behavior, Wiley, New York 1959. Zbl0093.31708MR0108411
  11. Analyzing and Modelling Rank Data, Chapman and Hall, London 1995. MR1346107
  12. Algebraic Statistics, Chapman and Hall/CRC, Bocan Raton 2000. MR2332740
  13. Toric statistical models: parametric and binomial representations, Ann. Inst. Statist. Math. 59 (2007), 727–740. Zbl1133.62343MR2397736
  14. Gröbner bases and convex polytopes, Amer. Math. Soc., Providence RI 1996. Zbl0856.13020MR1363949
  15. Toric Ideals in Algebraic Statistics, Ph.D. Thesis, University of California, Berkeley 2005. MR2623019
  16. Some characterizations of minimal Markov basis for sampling from discrete conditional distributions, Ann. Inst. Statist. Math. 56 (2004), 1–17. MR2053726

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.