Bayes factors for partially observed stochastic epidemic models

TL;DR

This paper develops methods for computing Bayes factors in partially observed stochastic epidemic models, providing practical guidelines and extending existing techniques to handle missing data, with applications to real and simulated outbreaks.

Contribution

It derives analytic Bayes factor expressions for complete data and extends the power posterior method to partially observed data, enhancing model comparison in epidemic modeling.

Findings

Analytic Bayes factors for complete epidemic data

Extended power posterior method for missing data

Comparison with deviance information criterion

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 extend 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.