Bayesian hypothesis testing for the distribution of insurance claim counts using the Gibbs sampler

We construct and present a Markov Chain Monte Carlo (MCMC) algorithm for the estimation of posterior odds and probabilities of alternative models used to evaluate competing hypotheses regarding three common discrete distributions involved in the modeling of the outstanding claim counts in actuarial science. The proposed methodology involves advanced statistical techniques of Bayesian modeling which make use of the Gibbs sampling variable selection algorithm. One of the main advantages of this approach over the popular reversible jump algorithm [12] is its straightforward implementation using the MCMC language tool of WINBUGS software [17]. The methodology is applied to a real data set. Directions regarding the implementation in WINBUGS are provided at the Appendix. It is worth noting that although the context of the problem is actuarial, the methodology can be applied to any field of science where the aim is the comparison or selection of discrete distributions of counts.