Computational Methods for Estimating the Evidence and Bayes Factor in SEIR Stochastic Infectious Diseases Models Featuring Asymmetrical Dynamics of Transmission

Abstract

Stochastic epidemic models may offer a vitally essential public health tool for comprehending and regulating disease progression. The best illustration of their importance and usefulness is perhaps the substantial influence that these models have had on the global COVID-19 epidemic. Nonetheless, these models are of limited practical use unless they provide an adequate fit to real-life epidemic outbreaks. In this work, we consider the problem of model selection for epidemic models given temporal observation of a disease outbreak through time. The epidemic models are stochastic individual-based transmission models of the Susceptible–Exposed–Infective–Removed (SEIR) type. The main focus is on the use of model evidence (or marginal likelihood), and hence the Bayes factor is a gold-standard measure of merit for comparing the fits of models to data. Even though the Bayes factor has been discussed in the epidemic modeling literature, little focus has been given to the fundamental issues surrounding its utility and computation. Based on various asymmetrical infection mechanism assumptions, we derive analytical expressions for Bayes factors which offer helpful suggestions for model selection problems. We also explore theoretical aspects that highlight the need for caution when utilizing the Bayes factor as a model selection technique, such as when the within-model prior distributions become more asymmetrical (diffuse or informative). Three computational methods for estimating the marginal likelihood and hence Bayes factor are discussed, which are the arithmetic mean estimator, the harmonic mean estimator, and the power posterior estimator. The theory and methods are illustrated using artificial data.