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Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem

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In this talk, I will present a theorem that characterizes a surprising discrepancy between fully Bayes and empirical-Bayes approaches to multiplicity adjustment in linear regression. This discrepancy arises from a different source than the failure to account for uncertainty in the empirical-Bayes estimate, which is the usual issue in such problems. Indeed, I will show that even at the extreme, when the empirical-Bayes estimate converges asymptotically to the true parameter value, the potential for a serious difference remains.

I will also highlight some interesting examples of Bayesian multiplicity adjustment on large data sets, with particular attention to a business application that involves large-scale screening of functional data.

This talk is part of the Statistics series.

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