Data Science Institute and School of Computer Science, National University of Ireland Galway, Ireland.
Epidemics. 2020 Dec;33:100415. doi: 10.1016/j.epidem.2020.100415. Epub 2020 Nov 11.
Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo method to estimate unknown quantities through sample generation from a target distribution for which an analytical solution is difficult. The strength of this method lies in its geometrical foundations, which render it efficient for traversing high-dimensional spaces. First, this paper analyses the performance of HMC in calibrating five variants of inputs to an age-structured SEIR model. Four of these variants are related to restriction assumptions that modellers devise to handle high-dimensional parameter spaces. The other one corresponds to the unrestricted symmetric variant. To provide a robust analysis, we compare HMC's performance to that of the Nelder-Mead algorithm (NMS), a common method for non-linear optimisation. Furthermore, the calibration is performed on synthetic data in order to avoid confounding effects from errors in model selection. Then, we explore the variation in the method's performance due to changes in the scale of the problem. Finally, we fit an SEIR model to real data. In all the experiments, the results show that HMC approximates both the synthetic and real data accurately, and provides reliable estimates for the basic reproduction number and the age-dependent transmission rates. HMC's performance is robust in the presence of underreported incidences and high-dimensional complexity. This study suggests that stringent assumptions on age-dependent transmission rates can be lifted in favour of more realistic representations. The supplementary section presents the full set of results.
Hamiltonian Monte Carlo (HMC) 是一种马尔可夫链蒙特卡罗方法，用于通过从目标分布中生成样本来估计未知量，而目标分布的解析解很难得到。该方法的优势在于其几何基础，这使其在遍历高维空间时非常有效。首先，本文分析了 HMC 在对具有结构的 SEIR 模型的五种输入变体进行校准方面的性能。这四个变体与建模者设计的用于处理高维参数空间的限制假设有关。另一个对应于无限制的对称变体。为了进行稳健的分析，我们将 HMC 的性能与常用的非线性优化方法——Nelder-Mead 算法（NMS）的性能进行了比较。此外，校准是在合成数据上进行的，以避免模型选择错误造成的混杂效应。然后，我们探索了方法性能因问题规模变化而产生的变化。最后，我们使用真实数据拟合了 SEIR 模型。在所有实验中，结果表明 HMC 可以准确地近似合成数据和真实数据，并为基本繁殖数和年龄相关传播率提供可靠的估计。即使在报告的发病率低和高维复杂性的情况下，HMC 的性能也很稳健。本研究表明，可以放宽对年龄相关传播率的严格假设，转而采用更现实的表示方法。补充部分提供了完整的结果集。
