Bayesian Inference for High-Dimensional ODE Models with Time-Varying Parameters via Relaxation

Ordinary differential equation (ODE) models are widely used to analyze real-world data. However, they can be challenging to apply to high-dimensional problems with time-varying parameters. This paper introduces a relaxation technique for Bayesian inference of a high-dimensional ODE model resulting from incorporating time-varying parameters. The relaxation technique ensures reliable parameter estimation by enhancing efficiency and computational speed of the associated Bayesian inference algorithm. We demonstrate our developed methodology for the SEIRV (Susceptible-Exposed-Infected-Recovered-Vaccinated) epidemic model using Malaysian COVID-19 data. Since the SEIRV model is analytically intractable, Bayesian inference entails the development of a computational algorithm for obtaining samples from the posterior distribution on unknown parameters. The maximum-a-posteriori (MAP) estimate is shown to perform particularly well in terms of matching the observed disease trajectories. Furthermore, we develop model validation via predictive distributions and highlight the advantages of a data-driven strategy for optimizing prior hyperparameters.