# Compound decisions and empirical Bayes via Bayesian nonparametrics

arXiv: https://arxiv.org/abs/2602.20115 · HTML: https://mlsanity.com/paper/2602.20115/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Feb 2026.

## Built on by (most cited first, 2 of 2)

- [Empirical Bayes for correlated Gaussian sequence model](https://mlsanity.com/paper/2607.03596/) (2026)
- [Adaptive Mean Estimation by In-Context Learning: A Gradient-Flow Analysis](https://mlsanity.com/paper/2610.07804/) (2026)

## Abstract (arXiv)

We study compound decision theory from a nonparametric Bayesian perspective, with particular emphasis on their relationship to empirical Bayes (EB) procedures. Motivated by the sharp risk guarantees available for EB procedures based on the nonparametric maximum likelihood estimator (NPMLE), we investigate whether analogous guarantees can be established for fully Bayesian decision rules. In a class of Gaussian compound decision problems, we show that the fully Bayesian posterior mean achieves near-optimal risk. Moreover, it is admissible as a genuine Bayes rule, whereas the corresponding NPMLE plug-in rule is inadmissible. Simulations illustrate the performance of nonparametric Bayes procedures relative to common alternatives. As an application, we apply our methodology to Census tract-level estimates of economic mobility from the Opportunity Atlas.