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:针对将流行病学推理扩展到复杂和异质模型的挑战,我们引入了泊松近似似然(PAL)方法。与流行的隔室ODE方法相比,该方法使用大量人口限制来证明确定性模型,而PAL是从有限种群、随机隔室模型的近似滤波方程中导出的,并且大规模人口限制驱动最大PAL估计量的一致性。我们的理论结果似乎是第一个适用于广泛的部分观察到的随机隔室模型并解决大量人口限制的基于似然的参数估计一致性结果。 PAL很简单,只涉及基本的算术操作和没有调整参数,并且快速评估,不需要从模型进行仿真,并且计算成本与人口规模无关。通过例子,我们演示了PAL如何用于:利用Stan中的自动微分适配流感的年龄结构模型;通过将PAL嵌入顺序Monte Carlo来比较轮状病毒模型中的过度离散机制;以及评估麻疹的元人群模型中单位特定参数的作用。