Actuarial Credibility Theory and Bayesian Statistics – The Story of a Special Evolution

Actuarial practitioners and researchers are more open to Bayesian thinking compared to their counterparts in the statistical world. This is evident in the context of credibility theory which adopted Bayesian influences almost from the start and is solidly founded on empirical Bayes philosophy. This chapter focuses on the evolution of credibility theory, the early Bayesian impact, and the current divergence between credibility theory and Bayesian statistics. It traces the early days of credibility theory and the influence of Bayesian thoughts. It describes the empirical Bayes solution to the problem, a solution which has dominated the actuarial profession until today. It then presents approximate Bayesian credibility solutions for special loss distributions.