Separation Properties of Sets of Probability Measures
This paper analyzes independence concepts for sets of probability measures associated with directed acyclic graphs. The paper shows that epistemic independence and the standard Markov condition violate desirable separation properties. The adoption of a contraction condition leads to d-separation but still fails to guarantee a belief separation property. To overcome this unsatisfactory situation, a strong Markov condition is proposed, based on epistemic independence. The main result is that the strong Markov condition leads to strong independence and does enforce separation properties; this result implies that (1) separation properties of Bayesian networks do extend to epistemic independence and sets of probability measures, and (2) strong independence has a clear justification based on epistemic independence and the strong Markov condition.
Keywords: Sets of probability measures, independence in graphical models, Markov condition, d-s
PS Link: http://www.cs.cmu.edu/~qbayes/Independence/UAI2000/104.ps.gz
PDF Link: /papers/00/p107-cozman.pdf
AUTHOR = "Fabio Cozman
TITLE = "Separation Properties of Sets of Probability Measures",
BOOKTITLE = "Proceedings of the Sixteenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-00)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "2000",
PAGES = "107--114"