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.
