Model comparison with missing data using MCMC and importance sampling

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.