Abstract

Due to noisy data and nonlinear dynamics, even simple stochastic epidemic models such as the Susceptible-Infectious-Removed (SIR) present significant challenges to inference. In particular, computing the marginal likelihood of such stochastic processes conditioned on observed endpoints a notoriously difficult task. As a result, likelihood-based inference is typically considered intractable in missing data settings typical of observational data, and practitioners often resort to intensive simulation methods or approximations. We discuss recent contributions that enable "exact" inference, focusing on a perspective that makes use of latent variables to explore configurations of the missing data within a Markov chain Monte Carlo framework. Motivated both by count data from large outbreaks and high-resolution contact data from mobile health studies, we show how our data-augmented approach successfully learns the interpretable epidemic parameters and scales to handle large realistic data settings efficiently.