A very special event: the Sobel Lecture
Prof. Brad Efron (Stanford University)

Title: TWEEDIE'S FORMULA AND SELECTION BIAS

Abstract: Suppose the statistician observes some large number of estimates z[i], each of which is unbiased for its unobserved true mean mu[i]. The largest say 10 of the z[i]'s are likely to substantially overestimate their corresponding mu[i]'s, this being "selection bias", or "regression to the mean". Tweedie's formula, first reported by Robbins in 1956, offers a simple empirical Bayes approach for correcting selection bias. I will discuss its merits and limitations, in terms of some examples and a little bit of theory relating to the James-Stein estimator.