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Conditional Independences among Four Random Variables I*

Published online by Cambridge University Press:  12 September 2008

F. Matúš  and
M. Studený
F. Matúš
Affiliation:
Institute of Information Theory and Automation, Pod vodárenskou věží 4, 182 08 Prague, Czech Republic e-mail: matus@utia.cas.cz, studeny@utia.cas.cz
M. Studený
Affiliation:
Institute of Information Theory and Automation, Pod vodárenskou věží 4, 182 08 Prague, Czech Republic e-mail: matus@utia.cas.cz, studeny@utia.cas.cz
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Abstract

The conditional independences within a system of four discrete random variables are studied simultaneously. The problem of where independences can occur at the same time, called the problem of probabilistic representability, is attacked by an analysis of cones of polymatroids. New results on the cone of all polymatroids satisfying Ingleton inequalities imply a substantial reduction of the problem and an explicit description of the remaining open cases.†

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 4 , Issue 3 , September 1995 , pp. 269 - 278
Copyright
Copyright © Cambridge University Press 1995

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