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FOURTH
INTERNATIONAL SYMPOSIUM ON

IMPRECISE PROBABILITIES AND THEIR APPLICATIONS

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Carnegie Mellon University

Pittsburgh, PA, USA

July 20-23 2005

#
ISIPTA'05 ELECTRONIC PROCEEDINGS

## Jirina Vejnarova, Radim Jirousek, Vladislav Bína

# On an Interval-Valued Solution of the Marginal Problem

### Abstract

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: **

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