Empirical Bayes: Concepts and Methods
Bradley Efron · 2024
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 , . . . , Θ N ; the Θ i are unobserved, but each one has yielded an observed random variable x i according to a known family of densities f ( x i | Θ i ): 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 "/>