Empirical Bayes: Concepts and Methods

Abstract

Robbins (1956) coined the name “empirical Bayes” for his method of dealing with the following kind of inferential situation: an unknown probability density g(Θ) (“density” here including the possibility of discrete atoms) has produced a random sample of realizations Θ 1, Θ 2, . . . , ΘN ; the Θi are unobserved, but each one has yielded an observed random variable xi according to a known family of densities f(xi | Θi ): 2.1 https://www.w3.org/1998/Math/MathML" display="block"> Θ i ~ g ( Θ ) and x i ~ f ( x i ∣ Θ i ) https://www.w3.org/1999/xlink" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429341731/7ae177d9-a70d-4244-bda5-0ab0fe307079/content/equ08-01.tif"/>

Topics & Concepts