Exact Bayesian inference for fitting stochastic epidemic models to partially observed incidence data

Stochastic epidemic models provide an interpretable probabilistic description of the spread of a disease through a population. Yet fitting these models to partially observed data can be a difficult task due to intractability of the marginal likelihood, even for classic Markovian models. To remedy this issue, this article introduces a novel data-augmented Markov chain Monte Carlo sampler for exact Bayesian inference under the stochastic susceptible-infectious-removed model, given only discretely observed counts of infections. In a Metropolis–Hastings step, the latent data are jointly proposed from a surrogate process carefully designed to closely resemble the target process and from which we can efficiently generate epidemics consistent with the observed data. This yields a method that explores the high-dimensional latent space efficiently and easily scales to outbreaks with thousands of infections. We prove that our sampler is uniformly ergodic and find empirically that it mixes much faster than existing single-site samplers. We apply the algorithm to fit a semi-Markov susceptible-infectious-removed model to the 2013–2015 outbreak of Ebola Haemorrhagic Fever in Guéckédou, Guinea.