Bayes-Ball: The Rational Pastime (for Determining Irrelevance and
  Requisite Information in Belief Networks and Influence Diagrams)
  One of the benefits of belief networks and influence diagrams is that so much
knowledge is captured in the graphical structure. In particular, statements of
conditional irrelevance (or independence) can be verified in time linear in the
size of the graph. To resolve a particular inference query or decision problem,
only some of the possible states and probability distributions must be
specified, the "requisite information."
  This paper presents a new, simple, and efficient "Bayes-ball" algorithm which
is well-suited to both new students of belief networks and state of the art
implementations. The Bayes-ball algorithm determines irrelevant sets and
requisite information more efficiently than existing methods, and is linear in
the size of the graph for belief networks and influence diagrams.
