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Perfect tree-like Markovian distributions. (English) Zbl 1122.60013
Summary: 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.

MSC:
60E05 Probability distributions: general theory
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