Sample-Size Extrapolation in Simulation-Based Inference via Statistical Scaling

In simulation-based inference (SBI), neural posterior estimators trained on a bounded range of sample sizes can become inaccurate on larger datasets as their parameterisations do not specify how posterior location, uncertainty, and shape must change as observations accumulate. We propose center-estimated NPE (CE-NPE), which combines a statistical center with an explicit contraction rate and learns a local center correction and residual densities in posterior-scale coordinates. The center is an estimate, such as a closed-form statistic or a simulator-based moment match, which does not require an evaluable likelihood. Our analysis explains how contraction amplifies center error, decomposes Gaussian posterior error into shape, mean, and covariance contributions, and gives a conditional transfer bound that retains training-boundary error. Across regular benchmarks, CE-NPE improves reference-posterior agreement over the tested free-conditioning baselines at five times the largest training size, without retraining. Matched controls and nonregular examples characterize the scope of these gains and identify the conditions on which they depend: an appropriate contraction rate, an accurate center, and a stable residual representation.