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

arXiv: https://arxiv.org/abs/2610.16820 · HTML: https://mlsanity.com/paper/2610.16820/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 43 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Builds on (most cited first, 24 of 24)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [BayesFlow: Learning complex stochastic models with invertible neural networks](https://mlsanity.com/paper/2003.06281/) (2020)
- [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](https://mlsanity.com/paper/1804.06788/) (2018)
- [On Contrastive Learning for Likelihood-free Inference](https://mlsanity.com/paper/2002.03712/) (2020)
- [All-in-one simulation-based inference](https://mlsanity.com/paper/2404.09636/) (2024)
- [Compositional Score Modeling for Simulation-based Inference](https://mlsanity.com/paper/2209.14249/) (2022)
- [Robust Neural Posterior Estimation and Statistical Model Criticism](https://mlsanity.com/paper/2210.06564/) (2022)
- [Truncated proposals for scalable and hassle-free simulation-based inference](https://mlsanity.com/paper/2210.04815/) (2022)
- [A Likelihood-Free Inference Framework for Population Genetic Data using Exchangeable Neural Networks](https://mlsanity.com/paper/1802.06153/) (2018)
- [Diffusion posterior sampling for simulation-based inference in tall data settings](https://mlsanity.com/paper/2404.07593/) (2024)
- [The Statistical Accuracy of Neural Posterior and Likelihood Estimation](https://mlsanity.com/paper/2411.12068/) (2024)
- [Amortized In-Context Bayesian Posterior Estimation](https://mlsanity.com/paper/2502.06601/) (2025)
- [Amortized Bayesian Multilevel Models](https://mlsanity.com/paper/2408.13230/) (2024)
- [Conditional diffusions for amortized neural posterior estimation](https://mlsanity.com/paper/2410.19105/) (2024)
- [Demonstrating the power and flexibility of variational assumptions for amortized neural posterior estimation in environmental applications](https://mlsanity.com/paper/2404.10899/) (2024)
- [Amortized Simulation-Based Inference in Generalized Bayes via Neural Posterior Estimation](https://mlsanity.com/paper/2601.22367/) (2026)

## Abstract (arXiv)

In simulation-based inference (SBI), neural posterior estimators trained on a bounded range of sample sizes can become inaccurate on larger datasets because their parameterizations 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 a statistical 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 and decomposes Gaussian posterior error into shape, mean and covariance contributions. On six regular benchmarks, CE-NPE gives the best reference-posterior agreement of all tested amortized estimators at every out-of-range size, up to five times the largest training size, without retraining; it also fits better within the training range on most of them. 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.