An Empirical Bayes Approach to Statistics

@inproceedings{Robbins2005AnEB,
  title={An Empirical Bayes Approach to Statistics},
  author={Herbert Robbins},
  year={2005}
}
Let X be a random variable which for simplicity we shall assume to have discrete values x and which has a probability distribution depending in a known way on an unknown real parameter A, (1) p (xIX) =Pr [X = xIA =X], A-itself being a random variable with a priori distribution function (2) G (X) =Pr [A-< X. The unconditional probability distribution of X is then given by (3) PG(x) =Pr[X=xI =fP(xjX)dG(X), and the expected squared deviation of any estimator of A of the form sp(X) is (4) Ek[o(X… CONTINUE READING
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Contributions to the theory of empirical Bayes procedures in statistics

H. JEFFREYS, Theory of Probability, +36 authors JR.
doctoral thesis at Columbia University (unpublished), 1956. • 1956

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