  Theory refinement is the task of updating a domain theory in the light of new
cases, to be done automatically or with some expert assistance. The problem of
theory refinement under uncertainty is reviewed here in the context of Bayesian
statistics, a theory of belief revision. The problem is reduced to an
incremental learning task as follows: the learning system is initially primed
with a partial theory supplied by a domain expert, and thereafter maintains its
own internal representation of alternative theories which is able to be
interrogated by the domain expert and able to be incrementally refined from
data. Algorithms for refinement of Bayesian networks are presented to
illustrate what is meant by "partial theory", "alternative theory
representation", etc. The algorithms are an incremental variant of batch
learning algorithms from the literature so can work well in batch and
incremental mode.
