Simulation-based inference of epidemiological and phylodynamic models via Neural Posterior Estimation

Mathematical models play a central role in understanding and forecasting infectious disease dynamics, but parameter inference is often difficult when likelihoods are intractable. Simulation-based inference (SBI) circumvents this limitation by relying on model simulations. Traditional SBI methods, such as Approximate Bayesian Computation, typically depend on handcrafted summary statistics and scale poorly in high-dimensional settings. Recent advances address these challenges by using flexible statistical and machine-learning surrogates to approximate likelihoods or posterior distributions. Neural Posterior Estimation (NPE) directly learns the posterior from simulated data using neural density estimators, automatically extracting informative representations without ad-hoc summaries. Despite its potential, NPE has been rarely applied in infectious disease epidemiology and phylodynamics. Here, we evaluate NPE for parameter inference in mechanistic models using data from the 2014 Ebola outbreak in Sierra Leone. We consider two case studies: a compartmental transmission model fitted to case and death time series, and a birth–death phylodynamic model fitted to an early Ebola phylogeny. In both settings, NPE yields accurate and reliable posterior estimates. Its amortized nature further enables efficient model calibration and criticism. We conclude that NPE is a flexible and scalable tool for epidemiological and phylodynamic inference, and provide detailed online tutorials illustrating the workflow.