Credibility Procedures - La Place's Generalization of Bayes' Rule and the Combination of Collateral Knowledge with Observed Data

The casualty insurance business has used credibility formulas or procedures for many years in making rates or in experience rating plans. These formulas have been used to determine the weight to be given to the indications of actual observations in a combination of such indications with a priori expectations which were based either on other actual data, on prior knowledge or on reasonable assumptions made before actual observations were available. Such formulas have invariably provided that the weight to be given to actual observations increase as the volume of such observations increases.