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Conditional Independences among Four Random Variables III: Final Conclusion

Published online by Cambridge University Press:  01 May 1999

Statistik und Informatik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany (e-mail:


The problem of probabilistic representability of semimatroids over a four-element set is solved. In this problem, one looks for all combinations of conditional independences within four random variables which can occur simultaneously. New properties of the stochastic conditional independences are deduced from conditional information inequalities. Examples of four-tuples of random variables are presented to show the probabilistic representability of three non-Ingleton semimatroids.

Research Article
1999 Cambridge University Press

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