Coverage Properties of Empirical Bayes Intervals

TL;DR

This paper discusses the coverage properties of empirical Bayes intervals, emphasizing the importance of group-specific coverage control over traditional across-group methods for more precise inferences.

Contribution

It highlights the distinction between across-group and group-specific inference, advocating for confidence intervals that prioritize group-specific coverage in empirical Bayes analysis.

Findings

Standard empirical Bayes intervals focus on average coverage.

Group-specific coverage control can improve inference accuracy.

Discussion clarifies goals of empirical Bayes methods.

Abstract

This note is an invited discussion of the article "Confidence Intervals for Nonparametric Empirical Bayes Analysis" by Ignatiadis and Wager. In this discussion, I review some goals of empirical Bayes data analysis and the contribution of Ignatiadis and Wager. Differences between across-group inference and group-specific inference are discussed. Standard empirical Bayes interval procedures focus on controlling the across-group average coverage rate. However, if group-specific inferences are of primary interest, confidence intervals with group-specific coverage control may be preferable.