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The behavior of Bayesian model averaging (BMA) for the normal linearregression model in the presence of influential observations that contribute tomodel misfit is investigated. Remedies to attenuate the potential negativeimpacts of such observations on inference and prediction are proposed. Themethodology is motivated by the view that well-behaved residuals and goodpredictive performance often go hand-in-hand. Focus is placed on regressionmodels that use variants on Zellner's g prior. Studying the impact of variousforms of model misfit on BMA predictions in simple situations points toprescriptive guidelines for "tuning" Zellner's g prior to obtain optimalpredictions. The tuning of the prior distribution is obtained by consideringtheoretical properties that should be enjoyed by the optimal fits of thevarious models in the BMA ensemble. The methodology can be thought of as an"empirical Bayes" approach to modeling, as the data help to inform thespecification of the prior in an attempt to attenuate the negative impact ofinfluential cases.

Empirical Bayes Model Averaging with Influential Observations: Tuning Zellner's g Prior for Predictive Robustness