  When performing regression or classification, we are interested in the
conditional probability distribution for an outcome or class variable Y given a
set of explanatoryor input variables X. We consider Bayesian models for this
task. In particular, we examine a special class of models, which we call
Bayesian regression/classification (BRC) models, that can be factored into
independent conditional (y|x) and input (x) models. These models are
convenient, because the conditional model (the portion of the full model that
we care about) can be analyzed by itself. We examine the practice of
transforming arbitrary Bayesian models to BRC models, and argue that this
practice is often inappropriate because it ignores prior knowledge that may be
important for learning. In addition, we examine Bayesian methods for learning
models from data. We discuss two criteria for Bayesian model selection that are
appropriate for repression/classification: one described by Spiegelhalter et
al. (1993), and another by Buntine (1993). We contrast these two criteria using
the prequential framework of Dawid (1984), and give sufficient conditions under
which the criteria agree.
