A comparative study of simulation-based inference methods for epidemic models with identifiability considerations

Epidemic models help us understand disease transmission and inform public health decisions, but their usefulness depends on how well we can estimate model parameters from data. For complex models, evaluating the likelihood can be difficult or computationally expensive. Simulation-based inference (SBI) offers an alternative by using model simulations to estimate posterior distributions without explicit likelihood evaluation.

In this talk, I will compare four SBI approaches: Approximate Bayesian Computation (ABC), Neural Posterior Estimation (NPE), a neural method with temporal embedding, and Preconditioned Neural Posterior Estimation (PNPE). Using epidemic models of increasing complexity, I will examine how simulation budgets, observational noise, and parameter identifiability affect their performance. Particular attention will be given to whether the observed data contain enough information to distinguish different parameter values.

The results show that neural methods generally improve posterior fidelity and predictive accuracy under limited simulation budgets, but these gains involve trade-offs in computational cost, uncertainty calibration, and reusability across datasets. PNPE performs well in several settings, while temporal embeddings improve inference for complex epidemic dynamics. ABC provides reasonable, often more conservative estimates. I will discuss the practical implications of these findings for choosing inference methods based on model complexity, data quality, identifiability, and available computational resources.