Don't Cut Corners: How Training Outside the Prior Makes Simulation-Based Inference More Robust

2026-08-12

AI Summary

This work addresses the poor performance of neural posterior estimation near the boundaries of uniform priors, which leads to inaccurate simulation-based inference at the edges of parameter space. To overcome this limitation, the authors propose a Tailed-Uniform hybrid sampling strategy that systematically introduces a mixture proposal distribution with decaying tails, extending the training data generation region beyond the conventional uniform prior box and thereby relaxing hard truncation constraints. By integrating this approach with neural density estimation, the method substantially improves posterior accuracy in boundary and exterior regions, as demonstrated on both toy models and cosmological matter power spectrum parameter inference tasks. Notably, it exhibits enhanced robustness in high-dimensional settings.

Abstract

Large astrophysical simulation campaigns often generate training data by sampling parameters across a Uniform prior box. Due to the proposal's sharp edge, neural posterior estimators struggle to learn accurate approximations near the boundaries. We propose Tailed-Uniform, a family of hybrid proposal distributions for sampling training simulations for robust simulation-based inference. By padding the original hard-truncated training box with decaying tails, Tailed-Uniform-trained networks yield more accurate posteriors near and beyond the edges. We demonstrate these improvements on a family of tail shapes, including a widened Uniform box as a control. Our results suggest that additional simulations near the prior boundary better constrain the networks as it approaches the edge of the training box, even for Uniform assumed priors. We show these advantages on a toy problem and cosmological parameter inference from the matter power spectrum. These benefits increase in high dimensions, where boundaries dominate parameter space volume.

Problem

• simulation-based inference
• Uniform prior
• boundary effects
• neural posterior estimation
• robustness

Innovation

• simulation-based inference
• Tailed-Uniform
• neural posterior estimation
• prior boundary
• cosmological parameter inference