A version of a marginal problem considered in this paper was connected, in the 80ies of the last century, with the necessity to cope with a task of knowledge integration in probabilistic expert systems. In practical situations marginal distributions representing pieces of local knowledge were often inconsistent. The present paper introduces an interval-valued solution of a marginal problem, which always exists, even in cases when, because of inconsistencies, one cannot get a solution in a classical sense. The paper shows how famous Iterative Proportional Fitting Procedure, which is often used to get a classical solution of a consistent problem, can be exploited also when constructing an interval-valued solution, and how any solution can be optimized.
Keywords. Multidimensional distributions, marginal problem, consistency, IPFP, imprecise probabilities, coherence
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Authors addresses:
Jirina Vejnarova
Institute if Infrormation Theory and Automation
Academy of Sciences of the Czech Republic
Pod vodarenskou vezi 4
182 08 Prague
Czech Republik
Radim Jirousek
Inst. of Information Theory and Automation
Czech Academy of Sciences
Pod vodarenskou vezi 4
182 08 Praha 8
Czech Republic
Vladislav Bína
Faculty of Management
(University of Economics, Prague)
Jarošovská 1117/II
Jindřichův Hradec
377 01
E-mail addresses:
| Jirina Vejnarova | vejnar@vse.cz |
| Radim Jirousek | radim@utia.cas.cz |
| Vladislav Bína | bina@fm.vse.cz |