Marginal problem, statistical estimation, and Möbius formula

Martin Janžura

Kybernetika (2007)

  • Volume: 43, Issue: 5, page 619-631
  • ISSN: 0023-5954

Abstract

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A solution to the marginal problem is obtained in a form of parametric exponential (Gibbs–Markov) distribution, where the unknown parameters are obtained by an optimization procedure that agrees with the maximum likelihood (ML) estimate. With respect to a difficult performance of the method we propose also an alternative approach, providing the original basis of marginals can be appropriately extended. Then the (numerically feasible) solution can be obtained either by the maximum pseudo-likelihood (MPL) estimate, or directly by Möbius formula.

How to cite

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Janžura, Martin. "Marginal problem, statistical estimation, and Möbius formula." Kybernetika 43.5 (2007): 619-631. <http://eudml.org/doc/33884>.

@article{Janžura2007,
abstract = {A solution to the marginal problem is obtained in a form of parametric exponential (Gibbs–Markov) distribution, where the unknown parameters are obtained by an optimization procedure that agrees with the maximum likelihood (ML) estimate. With respect to a difficult performance of the method we propose also an alternative approach, providing the original basis of marginals can be appropriately extended. Then the (numerically feasible) solution can be obtained either by the maximum pseudo-likelihood (MPL) estimate, or directly by Möbius formula.},
author = {Janžura, Martin},
journal = {Kybernetika},
keywords = {Gibbs distributions; maximum entropy; pseudo-likelihood; Möbius formula; Gibbs distributions; maximum entropy; pseudo-likelihood; Möbius formula},
language = {eng},
number = {5},
pages = {619-631},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Marginal problem, statistical estimation, and Möbius formula},
url = {http://eudml.org/doc/33884},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Janžura, Martin
TI - Marginal problem, statistical estimation, and Möbius formula
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 5
SP - 619
EP - 631
AB - A solution to the marginal problem is obtained in a form of parametric exponential (Gibbs–Markov) distribution, where the unknown parameters are obtained by an optimization procedure that agrees with the maximum likelihood (ML) estimate. With respect to a difficult performance of the method we propose also an alternative approach, providing the original basis of marginals can be appropriately extended. Then the (numerically feasible) solution can be obtained either by the maximum pseudo-likelihood (MPL) estimate, or directly by Möbius formula.
LA - eng
KW - Gibbs distributions; maximum entropy; pseudo-likelihood; Möbius formula; Gibbs distributions; maximum entropy; pseudo-likelihood; Möbius formula
UR - http://eudml.org/doc/33884
ER -

References

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  13. Perez A., Studený M., Comparison of two methods for approximation of probability distributions with prescribed marginals, Kybernetika 43 (2007), 5, 591–618 Zbl1144.68379MR2376326
  14. Winkler G., Image Analysis, Random Fields and Dynamic Monte Carlo Methods, Springer–Verlag, Berlin 1995 Zbl0821.68125MR1316400
  15. Younes L., Estimation and annealing for Gibbsian fields, Ann. Inst. H. Poincaré 24 (1988), 2, 269–294 (1988) Zbl0651.62091MR0953120

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