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Conditional Independences among Four Random Variables II

Published online by Cambridge University Press:  12 September 2008

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

Numerous new properties of stochastic conditional independence are introduced. They are aimed, together with two surprisingly trivial examples, at a further reduction of the problem of probabilistic representability for four-element sets, i.e. of the problem which conditional independences within a system of four random variables can occur simultaneously. Proofs are based on fundamental properties of conditional independence and, in the discrete case, on the use of I-divergence and algebraic manipulations with marginal probabilities. A duality question is answered in the negative.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 4 , Issue 4 , December 1995 , pp. 407 - 417
Copyright
Copyright © Cambridge University Press 1995

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