PERFECT TREE-LIKE MARKOVIAN DISTRIBUTIONS
Ann Becker
Dan Geiger
Christopher Meek
Abstract: We show that if a strictly positive joint probability distribution for a set of binary
variables factors according to a tree, then vertex separation represents all and only the
independence relations encoded in the distribution. The same result is shown to hold also for
multivariate nondegenerate normal distributions. Our proof uses a new property of
conditional independence that holds for these two classes of probability distributions.
2000 AMS Mathematics Subject Classification: 60E0S.
Key words and phrases: Conditional independence, graphical models, Markov models.