Perfect Tree-Like Markovian Distributions

@inproceedings{Becker2000PerfectTM,
  title={Perfect Tree-Like Markovian Distributions},
  author={Ann Becker and Dan Geiger and Christopher Meek},
  booktitle={UAI},
  year={2000}
}
We show that if a strictly positive joint prob­ ability distribution for a set of binary random variables factors according to a tree, then ver­ tex separation represents all and only the in­ dependence relations encoded in the distribu­ tion. The same result is shown to hold also for multivariate strictly positive normal dis­ tributions. Our proof uses a new property of conditional independence that holds for these two classes of probability distributions. 
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