Richard and others
As I have been travelling for some time, I first now
have noticed the interesting discussion on the
definition of Bayesian networks.
When writing my new book, "Bayesian networks and
Decision Graphs" (which by the way is out this month -
Springer-Verlag, New York) I had the same kind of
problems. I tried to do it in a way requiring as little
mathematical/theoretical sophistication as possible. I
have not yet had the time to study the discussion, so
my input may be out of line, but here is what I ended
up doing in my book:
Define a Bayesian network (over discrete variables) as
a DAG with conditional probabilities attached (node
given parents). State a theorem "Bayesian networks
admit d-separation". Give hints and exercises
indicating what a proof for this theorem could look
like. Prove that the product of the potentials attached
is the joint distribution for the universe. This prove
only requires that a leaf node is indepenent of the
rest given its parents.
/Finn
