| Title:
|
A note on the interval-valued marginal problem and its maximum entropy solution (English) |
| Author:
|
Vejnarová, Jiřina |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
34 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
[17]-26 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
interval-valued marginal problem |
| Keyword:
|
maximum entropy solution |
| MSC:
|
60E99 |
| MSC:
|
94A17 |
| idZBL:
|
Zbl 1274.94025 |
| idMR:
|
MR1619052 |
| . |
| Date available:
|
2009-09-24T19:13:18Z |
| Last updated:
|
2015-03-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135182 |
| . |
| Reference:
|
[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 |
| Reference:
|
[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 MR 0003527, 10.1214/aoms/1177731829 |
| Reference:
|
[3] Gallager R. R.: Information Theory and Reliable Communication.J. Wiley, New York 1968 Zbl 0295.94001 |
| Reference:
|
[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 |
| Reference:
|
[5] Kellerer H. G.: Verteilungsfunktionen mit gegebenem Marginalverteilungen.Z. Wahrsch. verw. Gebiete 3 (1964), 247–270 MR 0175158, 10.1007/BF00534912 |
| Reference:
|
[6] Malvestuto F. M.: Existence of extensions and product extensions for discrete probability distributions.Discrete Math. 69 (1988), 61–77 Zbl 0637.60021, MR 0935028, 10.1016/0012-365X(88)90178-1 |
| Reference:
|
[7] Walley P.: Measures of uncertainty in expert systems.Artificial Intelligence 83 (1996), 1–58 MR 1391510, 10.1016/0004-3702(95)00009-7 |
| . |
