  Selecting between competing statistical models is a challenging problem
especially when the competing models are non-nested. In this paper we offer a
simple solution by devising an algorithm which combines MCMC and importance
sampling to obtain computationally efficient estimates of the marginal
likelihood which can then be used to compare the models. The algorithm is
successfully applied to longitudinal epidemic and time series data sets and
shown to outperform existing methods for computing the marginal likelihood.
