  In this paper we examine the claims reserving problem using Tweedie's
compound Poisson model. We develop the maximum likelihood and Bayesian Markov
chain Monte Carlo simulation approaches to fit the model and then compare the
estimated models under different scenarios. The key point we demonstrate
relates to the comparison of reserving quantities with and without model
uncertainty incorporated into the prediction. We consider both the model
selection problem and the model averaging solutions for the predicted reserves.
As a part of this process we also consider the sub problem of variable
selection to obtain a parsimonious representation of the model being fitted.
