# Amortized Data Borrowing with Exchangeability-Aware Neural Posterior Estimation

arXiv: https://arxiv.org/abs/2609.38902 · HTML: https://mlsanity.com/paper/2609.38902/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 39 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 10 of 10)

- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [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)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [BayesFlow: Learning complex stochastic models with invertible neural networks](https://mlsanity.com/paper/2003.06281/) (2020)
- [Balancing Covariates via Propensity Score Weighting](https://mlsanity.com/paper/1609.07494/) (2016)
- [Generalizing causal inferences from individuals in randomized trials to all trial-eligible individuals](https://mlsanity.com/paper/1709.04589/) (2017)
- [Normalized Power Prior Bayesian Analysis](https://mlsanity.com/paper/2204.05615/) (2022)
- [Conflict Diagnostics in Directed Acyclic Graphs, with Applications in Bayesian Evidence Synthesis](https://mlsanity.com/paper/1310.0628/) (2013)

## Abstract (arXiv)

Augmenting small concurrent studies with external or historical cohorts is attractive in drug development, where enrollment is slow, follow-up is expensive, and closely related trial or real-world data are often already available. Bayesian dynamic borrowing (BDB) provides a principled framework for adaptively controlling the influence of external data, but classical implementations often depend on hand-specified priors and MCMC-based inference, which can be computationally expensive and not generalizable. In this work, we study amortized neural posterior estimation (NPE) as a flexible alternative. A single network is pretrained on simulated current/external dataset pairs spanning covariate shift, outcome drift, and joint non-exchangeability, and then returns an approximate posterior for a scalar current-study target in a single forward pass. Through simulation studies, we find that NPE is most useful under outcome drift and joint mismatch: in the harder outcome-drift regimes, it gives up to about five-fold lower absolute bias than the best classical baseline and keeps Type I error close to nominal. After pretraining, posterior summaries are obtained in about 8 ms per dataset, roughly 103× faster than MCMC-based borrowing baselines in our timing experiment. We further analyze Alzheimer's Disease Neuroimaging Initiative (ADNI) data and show that, when mild cognitive impairment outcomes differ across cohorts, the NPE formulation recovers the later-cohort risk level in this example without claiming greater precision. Code is available at https://github.com/ChinHungScott/NPE-for-Bayesian-Dynamic-Borrowing-MLHC-.