An Inductive Inference Rule for Noisy Data and its Proof of Convergence.

When formulating a theory based on observations corrupted by noise or other sources of errors, an exact fit between the theory and the data is impossible. It therefore becomes necessary to decide whether a proposed theory agrees with the data "well enough". A previous paper presented a success criterion for making this judgement for an infinite sequence of observations. In practice, however, one must select a theory based on a finite set of observations. This paper presents a rule for making this selection, along with a proof that the rule enables one to converge on a theory satisfying the success criterion given sufficient number of observations.