Coverage Properties of Empirical Bayes Intervals
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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.
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