CP4SBI: local conformal calibration of credible sets in simulation-based inference

Current experimental scientists have been increasingly relying on simulation-based inference (SBI) to invert complex nonlinear models with intractable likelihoods. However, posterior approximations obtained with SBI are often miscalibrated, causing credible regions to undercover true parameters. We develop CP4SBI, a model-agnostic conformal calibration framework that constructs credible sets with local Bayesian coverage. Our two proposed variants, namely local calibration via regression trees and cumulative distribution function CDF-based calibration, enable finite-sample local coverage guarantees for any scoring function, including highest posterior density (HPD), symmetric and quantile-based regions. Experiments on widely used SBI benchmarks demonstrate that our approach improves the quality of uncertainty quantification for neural posterior estimators (NPEs) using both normalizing flows and score-diffusion modelling. This article is part of the theme issue 'Advancing uncertainty quantification in AI systems'.