Introduction to Robbins (1955) An Empirical Bayes Approach to Statistics

Abstract

Important ideas are liable to be overlooked unless they are named. The Empirical Bayes (EB) method, in its original form, was well named and well developed by Robbins and was given a further boost by the approval of Neyman (1962). The name was all the more appealing for seeming at first like an oxymoron. After 1962, there was a burgeoning of literature on the topic, helped along by Robbins, his graduate students, their graduate students, and so on, in a scholastic genealogical tree. There were 308 papers with "empirical Bayes" or "empirical Bayesian" in the title or as a keyword listed in Current Index to Statistics for the years 1975-1988, but as explained below, many of these papers do not deal with empirical Bayes as originally defined by Robbins. The literature is too vast to be comprehensively surveyed even in a short book, and I shall concentrate mainly on one example, the "Poisson case" defined below. This was the first case considered by Robbins and the main theme of his paper becomes clear when this case is well understood.