Seeing no one else has replied, I thought I would put in my 2 cents
worth.
> 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.
A belief network (Bayesian network) is *model*. What dependencies exist
in a model may be different from the dependencies in the world. The
simplest example is the Markov chain which is a simple belief network.
It is arguable that the world is Markovian; the past can only influence
the future by affecting the present. (Whether this is true or not is
presumably an empirical fact of physics; I have no idea what the current
state of thinking of this is in physics. But it is definitely true in
the common sense world). But this does not mean that our models of the
world have to be Markovian. We may not be modelling all the variables
that make the other variables Markovian; thus k-Markovian models are
often useful and appropriate. At the other extremes if we are predicting
the outcome of two-up (or matching pennies; where someone wins if two
coins match their heads) if we are only modeling one of the pennies, who
wins is independent of the the value of the coin toss we are modelling.
In response to your query, to specify the model you have to specify the
variables, the domains, the parents (i.e., the DAG structure) and the
conditional probabilities. That's all. So I would say that these form
the belief network.
But a diversity of ways of explaining the same concepts is definitely
useful to the community. If you want to know what you should do, I
suggest that you run some pilot studies testing different explanations
and seeing what explanations are the most natural to the people who are
the target audience for your book. I, for one, would be interested in
the results of such experiments.
David
-- David Poole, Office: +1 (604) 822-6254 Professor, Fax: +1 (604) 822-5485 Department of Computer Science, poole@cs.ubc.ca University of British Columbia, http://www.cs.ubc.ca/spider/poole Vancouver, B.C., Canada V6T 1Z4 ftp://ftp.cs.ubc.ca/ftp/local/poole
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