Bayesian Adjustment for Multiplicity in Large Model-Selection Problems
				James Scott
			      Duke University

This talk will focus on some recent theoretical and methodological developments
in Bayesian multiple-hypothesis testing.  I will discuss two classes of
problems: variable selection in linear regression, and graphical model selection
for multivariate-normal data.

Regression modeling often poses multiplicity problems, particularly in cases
where researchers have little reason to believe any model and simply want the
data to flag interesting covariates from a large pool.  I will prove a theorem
that characterizes a surprising discrepancy between fully Bayes and
empirical-Bayes approaches to multiplicity adjustment.  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 empirical-Bayes inference.
Indeed, even at the extreme, when the empirical-Bayes estimate converges
asymptotically to the true parameter value, the potential for a serious
difference remains.

These lessons will then be applied in the context of Gaussian graphical models,
which pose a special kind of variable-selection problem for an ensemble of
related linear regressions.  I will describe a novel default prior for
graphically constrained covariance matrices, and show how this approach leads to
significant improvement in handling the multiplicity issue.