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：我们考虑针对不完整的时间过程数据进行随机流行病舱室模型的贝叶斯推断，其中数据由固定时间间隔内的新感染或移除数量组成的发病率计数构成。出于计算效率的考量，我们摒弃最自然的马尔可夫跳跃过程表示，转而采用随机微分方程表示。该表示进一步被近似为可处理的髙斯过程，即线性噪声近似（LNA）。除非连接LNA与数据的观测模型同时满足线性与高斯性，否则观测数据似然仍不可解。在此设定下，我们提出了两种对潜在过程进行边缘化的方法：相关伪边缘方法以及通过观测模型高斯近似实现的分析边缘化方法。我们使用合成数据对这两种方法进行对比分析，然后将性能最优的方法应用于真实数据——伦敦里士满公园的橡树列蛾巢穴移除发病率数据。我们的方法进一步支持对不同竞争性舱室模型之间的比较。