Bayesian methods in insurance

Statistical methods with a Bayesian flavour, in particular credibility theory, have long been used in the insurance industry as part of the process of estimating risks and setting premiums. Typically, however, fully Bayesian analysis has proved computationally infeasible and various approximate solutions have been proposed. The first part of this paper provides a survey of such problems and the kinds of solutions suggested in the actuarial literature. The second part reviews recent advances in Bayesian computational methodology and illustrates how it opens the way to a fully Bayesian treatment of a range of actuarial problems.