A number of methods of flare prediction rely on classification of physical characteristics of an active region, in particular optical classification of sunspots, and historical rates of flaring for a given classification. However, these methods largely ignore the number of flares the active region has already produced, in particular the number of small events. The past history of occurrence of flares (of all sizes) is an important indicator of future flare production. We present a Bayesian approach to flare prediction, which uses the flaring record of an active region together with phenomenological rules of flare statistics to refine an initial prediction for the occurrence of a big flare during a subsequent period of time. The initial prediction is assumed to come from one of the extant methods of flare prediction. The theory of the method is outlined, and simulations are presented to show how the refinement step of the method works in practice.