  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.
