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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