Abstract
We consider the problem of model choice for stochastic epidemic models given partial observation of a disease outbreak through time. Our main focus is on the use of Bayes factors. Although Bayes factors have appeared in the epidemic modelling literature before, they can be hard to compute and little attention has been given to fundamental questions concerning their utility. In this paper we derive analytic expressions for Bayes factors given complete observation through time, which suggest practical guidelines for model choice problems. We adapt the power posterior method for computing Bayes factors so as to account for missing data and apply this approach to partially observed epidemics. For comparison, we also explore the use of a deviance information criterion for missing data scenarios. The methods are illustrated via examples involving both simulated and real data.
Highlights
This paper is concerned with the problem of choosing between a small number of competing infectious disease transmission models, given partial observation of an epidemic outbreak through time
The outbreak was very severe, as every one of 188 individuals deemed to be susceptible became infected, these individuals all being children. These data have been considered by a number of authors, and were analysed in a model choice context in Neal and Roberts (2004), where the authors used reversible-jump Markov chain Monte Carlo (MCMC) methods to evaluate Bayes factors for a number of competing models
We have described a method for computing Bayes factors for epidemic models, by utilising an adaption of the power posterior method to accommodate missing data of a certain kind
Summary
This paper is concerned with the problem of choosing between a small number of competing infectious disease transmission models, given partial observation of an epidemic outbreak through time. In this paper we adapt the power posterior method for calculating Bayes factors (Friel and Pettitt, 2008; Friel et al, 2014) to a missing-data situation that commonly occurs in epidemic modelling. In addition to this computational method, we derive analytic expressions for Bayes factors in the setting where an epidemic outbreak is completely observed. Such detailed observation is not that common in practice, our results are of theoretical interest and provide practical insight into the choice and influence of prior distributions for parameters of the competing models.
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