The Empirical Bayes Approach to Statistical Decision Problems

The empirical Bayes approach to statistical decision problems is applicable when the same decision problem presents itself repeatedly and independently with a fixed but unknown a priori distribution of the parameter. Not all decision problems in practice come to us imbedded in such a sequence, but when they do the empirical Bayes approach offers certain advantages over any approach which ignores the fact that the parameter is itself a random variable, as well as over any approach which assumes a personal or a conventional distribution of the parameter not subject to change with experience. My own interest in the empirical Bayes approach was renewed by recent work of E. Samuel 10, 11 and J. Neyman 6, to both of whom I am very much indebted. In keeping with the purpose of the Rietz Lecture I shall not confine myself to presenting new results and shall try to make the argument explicit at the risk of being tedious. In the current controversy between the Bayesian school and their opponents it is obvious that any theory of statistical inference will find itself in and out of fashion as the winds of doctrine blow. Here, then, are some remarks and references for further reading which I hope will interest my audience in thinking the matter through for themselves. Considerations of space have confined mention of the non-parametric case, and of the closely related “compound” approach in which no a priori distribution of the parameter is assumed, to the references at the end of the article.