CoLT: The conditional localization test for assessing the accuracy of neural posterior estimates

We consider the problem of validating whether a neural posterior estimate ( q(θ mid x) ) is an accurate approximation to the true, unknown true posterior ( p(θ mid x) ). Existing methods for evaluating the quality of an NPE estimate are largely derived from classifier-based tests or divergence measures, but these suffer from several practical drawbacks. As an alternative, we introduce the Conditional Localization Test (CoLT), a principled method designed to detect discrepancies between ( p(θ mid x) ) and ( q(θ mid x) ) across the full range of conditioning inputs. Rather than relying on exhaustive comparisons or density estimation at every ( x ), CoLT learns a localization function that adaptively selects points θl(x) where the neural posterior q deviates most strongly from the true posterior p for that x. This approach is particularly advantageous in typical simulation-based inference settings, where only a single draw ( θ ~ p(θ mid x) ) from the true posterior is observed for each conditioning input, but where the neural posterior ( q(θ mid x) ) can be sampled an arbitrary number of times. Our theoretical results establish necessary and sufficient conditions for assessing distributional equality across all ( x ), offering both rigorous guarantees and practical scalability. Empirically, we demonstrate that CoLT not only performs better than existing methods at comparing p and q, but also pinpoints regions of significant divergence, providing actionable insights for model refinement. These properties position CoLT as a state-of-the-art solution for validating neural posterior estimates.