Local empirical Bayes correction for Bayesian modeling

TL;DR

This paper discusses the limitations of the James-Stein estimator in large-scale data and introduces a local empirical Bayes correction to address selection bias in such contexts.

Contribution

It proposes a local empirical Bayes correction method tailored for large-scale data where traditional estimators like James-Stein are inadequate.

Findings

Addresses bias correction in large-scale data

Improves estimation accuracy over traditional methods

Applicable to differential gene expression analysis

Abstract

The James-Stein estimator has attracted much interest as a shrinkage estimator that yields better estimates than the maximum likelihood estimator. The James-Stein estimator is also very useful as an argument in favor of empirical Bayesian methods. However, for problems involving large-scale data, such as differential gene expression data, the distribution is considered a mixture distribution with different means that cannot be considered sufficiently close. Therefore, it is not appropriate to apply the James-Stein estimator. Efron (2011) proposed a local empirical Bayes correction that attempted to correct a selection bias for large-scale data.