Neural techniques for simulation-based inference (SBI) have become popular in scientific domains featuring complex simulation models. These methods train neural networks on simulated data to infer unknown parameters; their reliability depends on the simulator faithfully representing reality. In infectious disease modeling, multiple models encoding different hypotheses often provide plausible explanations of observed data. Model selection is a difficult problem when likelihoods are unavailable, as is the case with many common stochastic transmission models. We propose a model criticism methodology designed for SBI, Neural Evidence Estimation (NEE), that integrates model selection and model misspecification detection. NEE learns a model's marginal likelihood (a.k.a. evidence) directly from simulations using normalizing flows, thereby avoiding noisy or complex Monte Carlo estimators. Through synthetic experiments, we demonstrate that NEE reliably selects the correct data generating process among multiple models and flags poorly specified models. We apply NEE to a real-world modeling problem concerning competing mechanisms for influenza reinfection in a multiple wave epidemic. This work argues for the importance of principled model criticism in SBI and infectious disease modeling.

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