title: Bayesian model choice for epidemic models with two levels of mixing.
abstract: 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.
authors.affiliation: School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK.
authors.forename: Edward S
authors.initials: ES
authors.lastname: Knock
authors.forename: Philip D
authors.initials: PD
authors.lastname: O'Neill
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D003141:Communicable Diseases / Q000453:epidemiology / Q000635:transmission*; D058872:Epidemics; D005191:Family Characteristics; D006801:Humans; D007251:Influenza, Human / Q000453:epidemiology; D008390:Markov Chains; D015233:Models, Statistical; D009010:Monte Carlo Method; D013269:Stochastic Processes
keywords: Bayes factors; Bayesian inference; Deviance information criterion; Epidemic model; Model choice; Path sampling