Addressing the challenge of scaling-up epidemiological inference to complex and heterogeneous models, we introduce Poisson Approximate Likelihood (PAL) methods. In contrast to the popular ODE approach to compartmental modelling, in which a large population limit is used to motivate a deterministic model, PALs are derived from approximate filtering equations for finite-population, stochastic compartmental models, and the large population limit drives consistency of maximum PAL estimators. Our theoretical results appear to be the first likelihood-based parameter estimation consistency results which apply to a broad class of partially observed stochastic compartmental models and address the large population limit. PALs are simple to implement, involving only elementary arithmetic operations and no tuning parameters, and fast to evaluate, requiring no simulation from the model and having computational cost independent of population size. Through examples we demonstrate how PALs can be used to: fit an age-structured model of influenza, taking advantage of automatic differentiation in Stan; compare over-dispersion mechanisms in a model of rotavirus by embedding PALs within sequential Monte Carlo; and evaluate the role of unit-specific parameters in a meta-population model of measles.

翻译：针对将流行病学推断扩展至复杂异质性模型所面临的挑战，我们提出泊松近似似然（PAL）方法。与流行的常微分方程房室建模方法（通过大群体极限推导确定性模型）不同，PAL源于有限群体随机房室模型的近似滤波方程，且大群体极限保证了最大PAL估计量的一致性。我们的理论结果首次为广泛类的部分观测随机房室模型提供了基于似然的参数估计一致性理论，并阐明了大群体极限的作用。PAL方法实现简单，仅需基本算术运算且无需调参；计算快速，无需模型模拟且计算成本与群体规模无关。通过案例我们展示PAL的应用：利用Stan中的自动微分拟合年龄结构流感模型；通过将PAL嵌入序贯蒙特卡洛方法比较轮状病毒模型的过度离散机制；以及在麻疹元群体模型中评估单位特定参数的作用。