A Bayesian approach to calibrate system dynamics models using Hamiltonian Monte Carlo

Model calibration is an essential test that dynamic hypotheses must pass in order to serve as tools for decision-making. In short, it is the search for a match between actual and simulated behaviours using parameter inference. Here, we approach such an inference process from a Bayesian perspective. Under this paradigm, we provide statements about the parameters (viewed as random variables) and data in probabilistic terms. These statements stem from a posterior distribution whose solution is often found via statistical simulation. However, the uptake of these methods within the system dynamics field has been somewhat limited, and state-of-the-art algorithms have not been explored. Therefore, we introduce Hamiltonian Monte Carlo (HMC), an efficient algorithm that outperforms random-walk methods in exploring complex parameter spaces. We apply HMC to calibrate an SEIR model and frame the process within a practical workflow. In doing so, we also recommend visualisation tools that facilitate the communication of results.