M. Studeny and P. Bocek:
CI-models arising among 4 random variables.
In Proceedings of the 3rd workshop WUPES, September 11-15, 1994,
Trest, Czech Republic, pp. 268-282.
The paper is a lucid survey (without technicalities) of some
results from the (later published) paper:
- F. Matus and M. Studeny:
Conditional independences among four random variables I.
Combinatorics,
Probability and Computing 4 (1995), n. 3, pp. 267-278.
- Abstract
- Let X(1), X(2), X(3),
X(4) be a system of four finitely-valued random variables.
By the conditional independence model induced by this system
we understand the list of triplets (A,B,C) of disjoint
subsets of {1, 2, 3, 4} such that X(A) is
conditionally independent of X(B) given X(C) (here
X(A) is the random vector composed of random variables
X(i) where i belongs to A). The topic of the
contribution is the question which lists of such triplets are
conditional independence models induced by a system of four
finitely-valued random variables.
These conditional independence models are almost completely
characterized in terms of probabilistically valid inference rules
(= axioms), 24 of them are mentioned. A dual characterization
is based on irreducible models: every conditional independence model
is an intersection of irreducible conditional independency models. The
list of all known irreducible conditional independency models over four
variables together with the corresponding constructions of probability
distributions is given.
- AMS classification 68T30
- Keywords
- conditional independence model
- (probabilistically sound) inference rule
- irreducible model
- submaximal model
- A
pdf copy (converted postscript version) (192kB) is available.