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：针对复杂异质模型流行病学推断的规模化挑战，我们提出泊松近似似然（Poisson Approximate Likelihood, PAL）方法。与流行的大种群极限驱动确定性模型的常微分方程（ODE）分区建模方法不同，PAL源自有限种群随机分区模型的近似滤波方程，其大种群极限确保了最大PAL估计量的一致性。本文的理论成果首次为广义部分观测随机分区模型提供了基于似然的参数估计一致性结论，并探讨了大种群极限问题。PAL方法实现简洁，仅需基本算术运算且无需调参，评估快速——无需模型仿真且计算成本与种群规模无关。通过实例展示PAL的应用：利用Stan自动微分拟合年龄结构流感模型；通过嵌入式序贯蒙特卡洛方法比较轮状病毒模型中的过离散机制；评估麻疹荟萃种群模型中单元特异性参数的作用。