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.

翻译：本文考虑利用不完整的时间过程数据（即固定时间间隔内新感染或移除病例数的发病计数）对随机流行病房室模型进行贝叶斯推断的情形。为提升计算效率，我们摒弃了最自然的马尔可夫跳变过程表示，转而采用随机微分方程表示。该表示进一步近似为可解的 Gaussian 过程，即线性噪声近似（LNA）。若联接 LNA 与数据的观测模型既非线性也非 Gaussian，则观测数据似然仍不可解。在此设定下，我们针对潜变量过程的边缘化提出两种方法：相关伪边际方法，以及通过观测模型 Gaussian 近似实现的分析边缘化方法。我们利用合成数据比较这两类方法，随后将最优方法应用于伦敦里士满公园栎列蛾巢穴移除病例的真实数据。本文方法还支持对多种竞争性房室模型进行比较评估。