We consider the case of performing Bayesian inference for stochastic epidemic compartment models, using incomplete time course data consisting of incidence counts that are either the number of new infections or removals in time intervals of fixed length. We eschew the most natural Markov jump process representation for reasons of computational efficiency, and focus on a stochastic differential equation representation. This is further approximated to give a tractable Gaussian process, that is, the linear noise approximation (LNA). Unless the observation model linking the LNA to data is both linear and Gaussian, the observed data likelihood remains intractable. It is in this setting that we consider two approaches for marginalising over the latent process: a correlated pseudo-marginal method and analytic marginalisation via a Gaussian approximation of the observation model. We compare and contrast these approaches using synthetic data before applying the best performing method to real data consisting of removal incidence of oak processionary moth nests in Richmond Park, London. Our approach further allows comparison between various competing compartment models.

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