# Simulation-Based Empirical Bayes

arXiv: https://arxiv.org/abs/2607.21843 · HTML: https://mlsanity.com/paper/2607.21843/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 41 references that are in the map.
- First posted on arXiv 23 Jul 2026.

## Builds on (most cited first, 15 of 15)

- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [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)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [Flow Matching for Scalable Simulation-Based Inference](https://mlsanity.com/paper/2305.17161/) (2023)
- [Simulation-Based Inference: A Practical Guide](https://mlsanity.com/paper/2508.12939/) (2025)
- [Amortized Variational Inference: When and Why?](https://mlsanity.com/paper/2307.11018/) (2023)
- [Neural Empirical Bayes: Source Distribution Estimation and its Applications to Simulation-Based Inference](https://mlsanity.com/paper/2011.05836/) (2020)
- [Two Modeling Strategies for Empirical Bayes Estimation](https://mlsanity.com/paper/1409.2677/) (2014)
- [Sourcerer: Sample-based Maximum Entropy Source Distribution Estimation](https://mlsanity.com/paper/2402.07808/) (2024)
- [Overview of Approximate Bayesian Computation](https://mlsanity.com/paper/1802.09720/) (2018)
- [Multilevel neural simulation-based inference](https://mlsanity.com/paper/2506.06087/) (2025)
- [Statistical Inference for Partially Observed Markov Processes via the R Package pomp](https://mlsanity.com/paper/1509.00503/) (2015)

## Built on by (most cited first, 1 of 1)

- [Source Distribution Estimation by Posterior Averaging](https://mlsanity.com/paper/2609.02622/) (2026)

## Abstract (arXiv)

Empirical Bayes (EB) performs simultaneous inference across many related latent variables. Classical EB assumes that the likelihood p(x | z) is tractable. In many scientific applications, however, the likelihood is available only through a simulator. This paper develops EB for such implicit likelihoods. We introduce simulation-based empirical Bayes (SBEB), which connects nonparametric EB to simulation-based inference (SBI). SBEB computes EB estimates without an explicit density by using the observed data, simulator samples, and an amortized inference network. SBEB iteratively refines the fitted EB prior toward the population prior. With several scientific simulators and real-world data, we demonstrate that SBEB improves accuracy over SBI with a fixed prior.