Simulation-based inference for rapid Bayesian parameter estimation in epidemiological models: a comparison with MCMC

As infectious disease outbreaks evolve, public health officials require rapid, data-driven forecasts to guide interventions. Traditional Bayesian calibration using Markov chain Monte Carlo (MCMC) is often too computationally expensive for the near-real-time updates needed during a pandemic. This study investigates whether Simulation-Based Inference (SBI)—specifically Neural Posterior Estimation (NPE)—can serve as a faster, scalable alternative for calibrating a mechanistic SECIR epidemiological model using COVID-19 ICU occupancy data.

The researchers compared SBI against a standard MCMC baseline using two distinct scenarios: short 31-day windows representing typical operational updates, and a more complex 201-day reconstruction problem involving multiple transmission change points. The SECIR model, implemented in the MEmilio framework, was used to simulate ICU occupancy. While MCMC relied on explicit likelihood evaluations, SBI was trained to learn a probabilistic mapping from simulated data to model parameters. The performance was evaluated using Wasserstein distances, Kullback-Leibler divergences, and posterior predictive checks to ensure the inferred parameters accurately reproduced observed epidemic trajectories.

SBI demonstrated significant computational advantages over MCMC. For the 31-day inference tasks, SBI achieved results comparable to MCMC in approximately 60–70 seconds on a single GPU, compared to 1,000 seconds for MCMC on CPUs. The performance gap widened significantly in the 201-day reconstruction, where SBI required only 157 seconds versus over 19,000 seconds for MCMC. Despite the speed, SBI successfully recovered posterior distributions that were in strong agreement with MCMC, confirming that the neural approximation preserved the necessary structure for reliable uncertainty quantification and epidemiological interpretation.