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Confidence Intervals for Nonparametric Empirical Bayes Analysis

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  • Nikolaos Ignatiadis
  • Stefan Wager

Abstract

In an empirical Bayes analysis, we use data from repeated sampling to imitate inferences made by an oracle Bayesian with extensive knowledge of the data-generating distribution. Existing results provide a comprehensive characterization of when and why empirical Bayes point estimates accurately recover oracle Bayes behavior. In this paper, we develop flexible and practical confidence intervals that provide asymptotic frequentist coverage of empirical Bayes estimands, such as the posterior mean or the local false sign rate. The coverage statements hold even when the estimands are only partially identified or when empirical Bayes point estimates converge very slowly. Supplementary materials for this article are available online.

Suggested Citation

  • Nikolaos Ignatiadis & Stefan Wager, 2022. "Confidence Intervals for Nonparametric Empirical Bayes Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(539), pages 1149-1166, September.
    • Handle: RePEc:taf:jnlasa:v:117:y:2022:i:539:p:1149-1166
    DOI: 10.1080/01621459.2021.2008403
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    Cited by:

    1. Christoph Breunig & Ruixuan Liu & Zhengfei Yu, 2022. "Double Robust Bayesian Inference on Average Treatment Effects," Papers 2211.16298, arXiv.org, revised Feb 2024.

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