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Seminar: Eitan Greenshtein

Statistics Seminar
November 1, 2007
All Day
209 W. Eighteenth Ave. (EA), Room 170

Title

Empirical Bayes and high dimensional inference

Speaker

Eitan Greenshtein, Duke University

Abstract

We discuss the relevance of Empirical Bayes to high dimensional inference, especially inference that follows model selection. Empirical Bayes techniques are useful in correcting the selection bias. The usefulness of Empirical Bayes is demonstrated in the classical problem of estimating the vector of normal means under a squared error loss, and also through the following problem. Let Yi ∼ N(µi, 1), i = 1, ..., n, be independent normally distributed random variables and let C be a constant. We study the problem of estimating the quantity S = P {i|C<Yi} µi. The case where n is large, the vector (µ1, ..., µn) is sparse, and the value of C is large, is emphasized. We use a non-parametric empirical Bayes approach, where µi are assumed to be independent identically distributed with unknown distribution function.

The talk combines a collaboration with Larry Brown and a collaboration with Junyong Park and Ya’acov Ritov.

Meet the speaker in Room 212 Cockins Hall at 4:30 p.m. Refreshments will be served.