Geodesic
A note on the interval-valued marginal problem and its maximum entropy solution
Kybernetika, Tome 34 (1998) no. 1, pp. 17-26
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

This contribution introduces the marginal problem, where marginals are not given precisely, but belong to some convex sets given by systems of intervals. Conditions, under which the maximum entropy solution of this problem can be obtained via classical methods using maximum entropy representatives of these convex sets, are presented. Two counterexamples illustrate the fact, that this property is not generally satisfied. Some ideas of an alternative approach are presented at the end of the paper.
This contribution introduces the marginal problem, where marginals are not given precisely, but belong to some convex sets given by systems of intervals. Conditions, under which the maximum entropy solution of this problem can be obtained via classical methods using maximum entropy representatives of these convex sets, are presented. Two counterexamples illustrate the fact, that this property is not generally satisfied. Some ideas of an alternative approach are presented at the end of the paper.
Classification : 60E99, 94A17
Keywords: interval-valued marginal problem; maximum entropy solution 
@article{KYB_1998_34_1_a2,
     author = {Vejnarov\'a, Ji\v{r}ina},
     title = {A note on the interval-valued marginal problem and its maximum entropy solution},
     journal = {Kybernetika},
     pages = {17--26},
     year = {1998},
     volume = {34},
     number = {1},
     mrnumber = {1619052},
     zbl = {1274.94025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1998_34_1_a2/}
}
TY  - JOUR
AU  - Vejnarová, Jiřina
TI  - A note on the interval-valued marginal problem and its maximum entropy solution
JO  - Kybernetika
PY  - 1998
SP  - 17
EP  - 26
VL  - 34
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/KYB_1998_34_1_a2/
LA  - en
ID  - KYB_1998_34_1_a2
ER  - 
%0 Journal Article
%A Vejnarová, Jiřina
%T A note on the interval-valued marginal problem and its maximum entropy solution
%J Kybernetika
%D 1998
%P 17-26
%V 34
%N 1
%U http://geodesic.mathdoc.fr/item/KYB_1998_34_1_a2/
%G en
%F KYB_1998_34_1_a2
Vejnarová, Jiřina. A note on the interval-valued marginal problem and its maximum entropy solution. Kybernetika, Tome 34 (1998) no. 1, pp. 17-26. http://geodesic.mathdoc.fr/item/KYB_1998_34_1_a2/

[1] Cheeseman P.: A method of computing generalized Bayesian probability values for expert systems. In: Proc. 6th Internat. Joint Conference on Artificial Intelligence (IJCAI–83), Karlsruhe 1983, pp. 198–202

[2] Deming W. E., Stephan F. F.: On a least square adjustment of a sampled frequency table when marginal totals are known. Ann. Math. Statist. 11 (1940), 427–444 | DOI | MR

[3] Gallager R. R.: Information Theory and Reliable Communication. J. Wiley, New York 1968 | Zbl

[4] Jiroušek R., Perez A.: A partial solution of the marginal problem. In: Trans. of the 10th Prague Conference on Inform. Theory, vol. B, Academia, Prague 1987, pp. 11–19

[5] Kellerer H. G.: Verteilungsfunktionen mit gegebenem Marginalverteilungen. Z. Wahrsch. verw. Gebiete 3 (1964), 247–270 | DOI | MR

[6] Malvestuto F. M.: Existence of extensions and product extensions for discrete probability distributions. Discrete Math. 69 (1988), 61–77 | DOI | MR | Zbl

[7] Walley P.: Measures of uncertainty in expert systems. Artificial Intelligence 83 (1996), 1–58 | DOI | MR