Bayesian model choice for epidemic models with two levels of mixing

This paper considers the problem of choosing between competing models for infectious disease final outcome data in a population that is partitioned into households. The epidemic models are stochastic individual-based transmission models of the susceptible-infective-removed type. The main focus is on various algorithms for the estimation of Bayes factors, of which a path sampling-based algorithm is seen to give the best results. We also explore theoretical properties in the case where the within-model prior distributions become increasingly uninformative, which show the need for caution when using Bayes factors as a model choice tool. A suitable form of deviance information criterion is also considered for comparison. The theory and methods are illustrated with both artificial data, and influenza data from the Tecumseh study of illness.