Conservative neural posterior estimation via distributionally robust training

Simulation-based inference (SBI; Cranmer et al., 2020) is a powerful framework for inferring parameters of scientific models whose likelihood functions are unavailable or computationally prohibitive to evaluate, but for which simulating data is straightforward. The use of flexible neural conditional density estimators has substantially expanded the applicability of SBI to challenging problems, especially in fields such as particle physics (Brehmer, 2021), cognitive neuroscience (Fengler et al., 2021), economics (Dyer et al., 2024) and cosmology (Alsing et al., 2018; Jeffrey et al., 2021). Neural SBI methods rely on simulations from the scientific model to approximate intractable quantities such as the posterior, the likelihood, the likelihood-to-evidence ratio, or the score function; see Zammit-Mangion et al. (2024) for a recent review. In this work, we focus on the widely used neural posterior estimation (NPE) method (Papamakarios and Murray, 2016; Radev et al., 2022). A central practical limitation of NPE is the simulation budget required to train the conditional density estimator. As many scientific simulators are expensive to run, generating a sufficiently large training set is often the main computational bottleneck.