Induction of models under uncertainty

This paper outlines a procedure for performing induction under uncertainty. This procedure uses a probabilitic representation and uses Bayes' theorem to decide between alternative hypotheses (theories). This procedure is illustrated by a robot with no prior world experience performing induction on data it has gathered about the world. The particular inductive problem is the formation class descriptions both for the tutored and untutored cases. The resulting class definitions are inherenty probabilistic and so do not have any sharply defined membership criterion. This robot example raises some fundamental problems about induction—particularly it is shown that inductively formed theories are not the best way of making predictions. Another difficulty is the need to provide prior probabilities for the set of possible theories. The main criterion for such priors is a proagmatic one aimed at keeping the theory structure as simple as possible, while still reflecting any structure discovered in the data.