Actuarial credibility

Actuarial credibility describes an approach used by actuaries to improve statistical estimates. Although the approach can be formulated in either a frequentist or Bayesian statistical setting, the latter is often preferred because of the ease of recognizing more that one source of randomness through both "sampling" and "prior" information. In a typical application, the actuary has an estimate X based on a small set of data, and an estimate M based on a larger but less relevant set of data. The credibility estimate is ZX + (1-Z)M, where Z is a number between 0 and 1 (called the "credibility weight" or "credibility factor") calculated to balance the sampling error of X against the possible lack of relevance (and therefore modeling error) of M.

For example, an actuary has accident and payroll historical data for a shoe factory that suggest that the accident rate is 3.1 accidents per million dollars of payroll. She has industry statistics (based on all shoe factories) suggesting that the rate is 7.4 accidents per million. With a credibility, Z, of 30%, she would estimate the rate for the factory as 30%(3.1) + 70%(7.4) = 6.1 accidents per million.

Sources

Whitney, A.W. (1918) The Theory of Experience Rating, Proceedings of the Casualty Actuarial Society, 4, 274-292 [This is one of the original casualty actuarial papers dealing with credibility. It uses Bayesian techniques, although the author uses the now archaic "inverse probability" terminology.]

Longley-Cook, L.H. (1962) An introduction to credibility theory PCAS, 49, 194-221.

http://stats.lse.ac.uk/norberg/links/papers/CRED-eas.pdf