Emulation‐based inference for spatial infectious disease transmission models incorporating event time uncertainty

Mechanistic models of infectious disease spread are key to inferring spatiotemporal infectious disease transmission dynamics. Ideally, covariate data and the infection status of individuals over time would be used to parameterize such models. However, in reality, complete data are rarely available; for example, infection times are almost never observed. Bayesian data‐augmented Markov chain Monte Carlo (MCMC) methods are commonly used to allow us to infer such missing or censored data. However, for large disease systems, these methods can be highly computationally expensive. In this paper, we propose two methods of approximate inference for such situations based on so‐called emulation techniques. Here, both methods are set in a Bayesian MCMC framework but replace the computationally expensive likelihood function by a Gaussian process‐based likelihood approximation. In the first method, we build an emulator of the discrepancy between summary statistics of simulated and observed epidemic data. In the second method, we develop an emulator of an importance sampling‐based likelihood approximation. We show how both methods offer substantial computational efficiency gains over standard Bayesian MCMC‐based method, and can be used to infer the transmission of complex infectious disease systems. We also show that importance sampling‐based methods tend to perform more satisfactorily.