Conference paper

Vejnarová J., Jiroušek R., Bína V.

Proceedings of the 4th International Symposium on Imprecise Probabilities and Their Applications. (Cozman F. G., Nau R., Seidenfeld T. eds.).

SIPTA

Pittsburg

2005

379-387

Prof. Radim Jiroušek, DrSc. (ÚTIA - Oddělení matematické teorie rozhodování)

On an Interval-Valued Solution of the Marginal Problem [file]

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 improved (tightened).