Comment on: “Confidence Intervals for Nonparametric Empirical Bayes Analysis” by Ignatiadis and Wager

I want to congratulate Nikolaos Ignatiadis and Stefan Wager on a very stimulating paper on a timely and important topic. They discuss empirical Bayes procedures and propose new methods for constructing robust confidence intervals. The proposed procedures seem to perform well, and the intuition provided further supports the case the authors make that these methods should be widely used. It is remarkable that such procedures had not been developed previously given their importance. As a nondogmatic Bayesian I am very happy to see the attention devoted to empirical Bayes procedures. In this comment I want to raise two issues. First I want to point out additional, currently very active, research areas where empirical Bayes procedures are being found to be useful. In these cases getting accurate confidence intervals is of first order importance, and the methods Ignatiadis and Wager develop are likely to be useful. Second I want to suggest more general problems where the same issues that Ignatiadis and Wager analyze may arise.