  We investigate the behavior of Bayesian model averaging (BMA) for the normal
linear regression model in the presence of influential observations that
contribute to model misfit, and propose remedies to attenuate the potential
negative impacts of such observations on inference and prediction. The
methodology is motivated by the view that well-behaved residuals and good
predictive performance often go hand-in-hand. The study focuses on regression
models that use variants on Zellner's g prior. By studying the impact of
various forms of model misfit on BMA predictions in simple situations we
identify prescriptive guidelines for "tuning" Zellner's g prior to obtain
optimal predictions. The tuning of the prior distribution is obtained by
considering theoretical properties that should be enjoyed by the optimal fits
of the various models in the BMA ensemble. The methodology can be thought of as
an "empirical Bayes" approach to modeling, as the data help to inform the
specification of the prior in an attempt to attenuate the negative impact of
influential cases.
