I did not know Jaynes died. Was it recent? Shannon also died recently.
Since I started this, I will state what I finally did as far as my
definition. To me Milan's noting that not all specified conditionals yield
a probability distribution killed defining Bayes nets in this way.
Furthermore, I still clung to my old reasons for defining them the other
way. Yet the arguments that readers need to immediately know that Bayes
nets are shown as DAGs and conditionals made me essentially do what Dave
Heckerman recommended (in a private post). Here it is (Note the Markov
conditions and the theorems have already been presented by this time.):
We call {G},P)a Bayesian network if {G,P) satisfies the Markov condition.
Owing to Theorem 1.3, P is the product of its conditional distributions in
G, and this is the way P is always represented in a Bayesian network.
Furthermore, owing to Theorem 1.4, if we specify any discrete distribution
and many continuous ones, we obtain a Bayesian network. This is the way
Bayesian networks are constructed in practice.
Sincerely,
Rich
At 01:13 PM 7/29/2001 -0700, David Poole wrote:
>
>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
>
>
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