Dear Rich:
On Wed, 18 Jul 2001, [EMAIL PROTECTED] wrote:
> Dear Colleagues,
>
> In my 1990 book I defined a Bayesian network approximately as follows:
>
> Definition of Markov Condition: Suppose we have a joint probability
> distribution P of the random variables in some set V and a DAG G=(V,E). We
> say that (G,P) satisfies the Markov condition if for each variable X in V,
> {X} is conditionally independent of the set of all its nondescendants given
> the set of all its parents.
>
> Definition of Bayesian Network: Let P be a joint probability distribution
> of the random variables in some set V, and G=(V,E) be a DAG. We call (G,P)
> a Bayesian network if (G,P)satisfies the Markov condition.
>
> The fact that the joint is the product of the conditionals is then an iff
> theorem.
>
Do not give up! You are right.
When I teach Bayesian nets, I always use your definition, precisely for
the reason you outline below!
> I used the same definition in my current
book. However, a reviewer
> commented that this was nonstandard and unintuitive. The reviewer suggested
> I define it as a DAG along with specified conditional distributions (which
> I realize is more often done). My definition would then be an iff theorem.
>
> My reason for defining it the way I did is that I feel `causal' networks
> exist in nature without anyone specifying conditional probability
> distributions. We identify them by noting that the conditional
> independencies exist, not by seeing if the joint is the product of the
> conditionals. So to me the conditional independencies are the more basic
> concept.
>
> However, a researcher, with whom I discussed this, noted that telling a
> person what numbers you plan to store at each node is not provable from my
> definition, yet it should be part of the definition as Bayes Nets are not
> only statistical objects, they are computational objects.
I do not understand this argument. WHat does he or she mean by "telling a
person ... is not provable?"
>
> I am left undecided about which definition seems more appropriate. I would
> appreciate comments from the general community.
>
> Sincerely,
>
> Rich Neapolitan
>
>
Cheers,
Marco
Marco Valtorta Associate Professor
Department of Computer Science and Engineering
University of South Carolina
Columbia, SC 29208, U.S.A. http://www.cse.sc.edu/~mgv/
803.777-4641 fax:-3767 [EMAIL PROTECTED]
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"Probability is not about numbers. It is about the structure of reasoning."
--Glenn Shafer
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