Confidence Intervals for Nonparametric Empirical Bayes Analysis

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 recov...

Full description

Saved in:
Bibliographic Details
Published in:Journal of the American Statistical Association 2022-09, Vol.117 (539), p.1149-1166
Main Authors: Ignatiadis, Nikolaos, Wager, Stefan
Format: Article
Language:English
Subjects:
Bayesian analysis
Bias-aware inference
Confidence intervals
Empirical analysis
Empirical Bayes
Estimates
Local false sign rate
Mixture models
Nonparametric statistics
Partial identification
Regression analysis
Statistical methods
Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.2021.2008403