Credibility Theory

Credibility theory answers a practical question: how much should we trust this policyholder, class, or group's own data when it is noisy or limited?

A basic credibility estimate has the form Z x individual experience + (1-Z) x collective mean, where Z is the credibility weight.

Credibility is shrinkage. Buhlmann credibility is actuarial empirical Bayes: noisy group estimates are pulled toward a shared mean based on how much signal they contain.