A Simple Monte Carlo Approach to Bayesian Graduation

The problem of graduating a sequence of data values can be cast as a statistical estimation problem. In particular, the Bayesian approach is attractive due to its ability to formally incorporate known ordering and smoothness conditions for the graduated values into the estimation structure. However, this approach has not been widely adopted in practice, primarily because of the arduousness of specifying the prior distributions for the graduated values and carrying out the necessary numerical integrations. This paper presents simple Bayesian graduation models that substantially ease the prior elicitation burden; it also describes a Monte Carlo integration approach that greatly reduces the computational load. The method is presented in generality and subsequently illustrated with two examples, one from the realm of health insurance and the other from the more traditional graduation context of mortality table construction. It is hoped that the method will stimulate greater use of the Bayesian paradigm within the actuarial community.