Learning at the Edge: Tailed-Uniform Sampling for Robust Simulation-Based Inference

We introduce the Tailed-Uniform proposal distribution for generating training simulations in simulation-based inference. Instead of sampling parameters uniformly within bounded regions, we extend the distribution beyond prior boundaries with smooth Gaussian tails. This eliminates sharp transitions that cause neural posterior estimators to fail when the posterior distribution intersects or extends beyond the prior bounds. We show these benefits on a toy problem and cosmological parameter inference from the matter power spectrum. Such an advantage grows in high dimensions, where boundaries dominate parameter space volume. All code is publicly available on Github at https://github.com/chaipattira/tailed-uniform-sbi.