Empirical Bayes Rebiasing
Abstract
We study methods for simultaneous analysis of many noisy and biased estimates, each paired with an even noisier estimate of its own bias. The analyst's goal is to construct short calibrated intervals for each parameter. The standard debiasing approach, which subtracts the bias estimate from each biased estimate, inflates variance and yields long intervals. In this paper, we propose an empirical Bayes rebiasing strategy that starts from the fully debiased estimates and learns from data how much bias to reintroduce by estimating the unknown bias distribution. We provide convergence rates for the coverage of our intervals when the bias distribution is estimated using nonparametric maximum likelihood. Furthermore, we demonstrate substantial precision gains in prediction-powered inference, including pairwise LLM win-rate evaluations, as well as for inference of direct genetic effects in family-based GWAS.
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BibTeX
@misc{ling2026empirical,
title = {{Empirical Bayes Rebiasing}},
author = {Wanyi Ling and Sida Li and Junming Guan and Nikolaos Ignatiadis},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2605.08069},
eprint = {2605.08069},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.08069},
}
RIS
TY - UNPB
TI - Empirical Bayes Rebiasing
AU - Wanyi Ling
AU - Sida Li
AU - Junming Guan
AU - Nikolaos Ignatiadis
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2605.08069
UR - https://arxiv.org/abs/2605.08069
AB - We study methods for simultaneous analysis of many noisy and biased estimates, each paired with an even noisier estimate of its own bias. The analyst's goal is to construct short calibrated intervals for each parameter. The standard debiasing approach, which subtracts the bias estimate from each biased estimate, inflates variance and yields long intervals. In this paper, we propose an empirical Bayes rebiasing strategy that starts from the fully debiased estimates and learns from data how much bias to reintroduce by estimating the unknown bias distribution. We provide convergence rates for the coverage of our intervals when the bias distribution is estimated using nonparametric maximum likelihood. Furthermore, we demonstrate substantial precision gains in prediction-powered inference, including pairwise LLM win-rate evaluations, as well as for inference of direct genetic effects in family-based GWAS.
ER -