Re: [UAI] Definition of Bayesian network

[David Poole]

I am reminded of the following quote from the late E.T. Jaynes:

"Infinite set paradoxing has become a morbid infection that is today
spreading in a way that threatens the very life of probability theory,
and requires immediate surgical removal. In our system, after this
surgery, such paradoxes are avoided automatically; they cannot arise
from correct application of our basic rules, because those rules admit
only finite sets and infinite sets that arise as well-defined and
well-behaved limits of finite sets.  The paradoxing was caused by (1)
jumping directly into an infinite set without specifying any limiting
process to define its properties; and then (2) asking questions whose
answers depend on how the limit was approached."

     E.E. Jaynes,
     "Probability Theory: The Logic Of Science", page xi
     http://bayes.wustl.edu/etj/prob.html

This, unfortuantely unfinished, book contains lots of thought-provoking
material.

David