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Abstract:
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Stochastic epidemic models provide an interpretable description of disease outbreaks. Yet, fitting these models in missing data settings is difficult since the likelihood is intractable when the epidemic process is only partially observed. To remedy this issue, we introduce a data-augmented MCMC algorithm for fast and exact likelihood-based inference for the stochastic SIR model given discretely observed infection incidence counts. In a Metropolis-Hastings step, new event times of the latent data are jointly proposed from a process that closely resembles the SIR, and from which we can efficiently generate an epidemic that matches the observed data. The DA-MCMC algorithm is fast and, since the latent data are generated from a faithful approximation of the target model, a large portion of the latent data can be updated per iteration while maintaining a high acceptance rate, thereby exploring the high-dimensional latent space efficiently. Furthermore, the algorithm is uniformly ergodic and requires only a slight modification to fit non-Markovian models. We validate its performance via thorough simulation experiments and a case study on the $2014$ Ebola outbreak in Western Africa.
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