An evaluation of Hamiltonian Monte Carlo performance to calibrate age-structured compartmental SEIR models to incidence data

Abstract

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.

Keywords: Hamiltonian Monte Carlo; Nelder–Mead optimisation; SEIR; Stan; WAIFW.