Bayesian model choice via mixture distributions with application to epidemics and population process models

We describe a new method for evaluating Bayes factors. The key idea is to introduce a hypermodel in which the competing models are components of a mixture distribution. Inference for the mixing probabilities then yields estimates of the Bayes factors. Our motivation is the setting where the observed data are a partially observed realisation of a stochastic population process, although the methods have far wider applicability. The methods allow for missing data and for parameters to be shared between models. Illustrative examples including epidemics, population processes and regression models are given, showing that the methods are competitive compared to existing approaches.