Statistical Science

Bayes, Oracle Bayes and Empirical Bayes

Bradley Efron

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Abstract

This article concerns the Bayes and frequentist aspects of empirical Bayes inference. Some of the ideas explored go back to Robbins in the 1950s, while others are current. Several examples are discussed, real and artificial, illustrating the two faces of empirical Bayes methodology: “oracle Bayes” shows empirical Bayes in its most frequentist mode, while “finite Bayes inference” is a fundamentally Bayesian application. In either case, modern theory and computation allow us to present a sharp finite-sample picture of what is at stake in an empirical Bayes analysis.

Article information

Source
Statist. Sci., Volume 34, Number 2 (2019), 177-201.

Dates
First available in Project Euclid: 19 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.ss/1563501631

Digital Object Identifier
doi:10.1214/18-STS674

Mathematical Reviews number (MathSciNet)
MR3983318

Keywords
Finite Bayes inference $g$-modeling relevance empirical Bayes regret

Citation

Efron, Bradley. Bayes, Oracle Bayes and Empirical Bayes. Statist. Sci. 34 (2019), no. 2, 177--201. doi:10.1214/18-STS674. https://projecteuclid.org/euclid.ss/1563501631


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