  Two different approaches to dealing with probabilistic knowledge are examined
-models and inductive inference. Examples of the first are: influence diagrams
[1], Bayesian networks [2], log-linear models [3, 4]. Examples of the second
are: games-against nature [5, 6] varieties of maximum-entropy methods [7, 8,
9], and the author's min-score induction [10]. In the modeling approach, the
basic issue is manageability, with respect to data elicitation and computation.
Thus, it is assumed that the pertinent set of users in some sense knows the
relevant probabilities, and the problem is to format that knowledge in a way
that is convenient to input and store and that allows computation of the
answers to current questions in an expeditious fashion. The basic issue for the
inductive approach appears at first sight to be very different. In this
approach it is presumed that the relevant probabilities are only partially
known, and the problem is to extend that incomplete information in a reasonable
way to answer current questions. Clearly, this approach requires that some form
of induction be invoked. Of course, manageability is an important additional
concern. Despite their seeming differences, the two approaches have a fair
amount in common, especially with respect to the structural framework they
employ. Roughly speaking, this framework involves identifying clusters of
variables which strongly interact, establishing marginal probability
distributions on the clusters, and extending the subdistributions to a more
complete distribution, usually via a product formalism. The product extension
is justified on the modeling approach in terms of assumed conditional
independence; in the inductive approach the product form arises from an
inductive rule.
