# Empirical Bayes When Estimation Precision Predicts Parameters

arXiv: https://arxiv.org/abs/2212.14444 · HTML: https://mlsanity.com/paper/2212.14444/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Dec 2022.

## Built on by (most cited first, 3 of 3)

- [Estimating the Value of Evidence-Based Decision Making](https://mlsanity.com/paper/2306.13681/) (2023)
- [Empirical Bayes for correlated Gaussian sequence model](https://mlsanity.com/paper/2607.03596/) (2026)
- [Polylogarithmic Sparsity of Randomly Reweighted NPMLEs for Gaussian Mixtures](https://mlsanity.com/paper/2610.01088/) (2026)

## Abstract (arXiv)

Gaussian empirical Bayes methods usually maintain a precision independence assumption: The unknown parameters of interest are independent from the known standard errors of the estimates. This assumption is often theoretically questionable and empirically rejected. This paper proposes to model the conditional distribution of the parameter given the standard errors as a flexibly parametrized location-scale family of distributions, leading to a family of methods that we call CLOSE. The CLOSE framework unifies and generalizes several proposals under precision dependence. We argue that the most flexible member of the CLOSE family is a minimalist and computationally efficient default for accounting for precision dependence. We analyze this method and show that it is competitive in terms of the regret of subsequent decisions rules. Empirically, using CLOSE leads to sizable gains for selecting high-mobility Census tracts.