Bayes / Frequentist Compromise Rules for Outlier Detection

                                Lynn Eberly
                          Department of Biostatistics 
                           University of Minnesota

Bayesian methods produce substantial inferential advantages over
frequentist approaches when the assumed prior is approximately
correct, but can have poor performance otherwise.  Decision rules that
trade-off Bayes optimality with frequentist robustness have the potential
to perform well in both domains.

We evaluate the Bayes/frequentist trade-off for three families of
estimation rules under a Gaussian sampling distribution, with Bayes
evaluation based on a Gaussian prior.  All rules are of the form 
(1 - B(y))*y, with B(y) taking one of three forms. The first is
motivated by a Gaussian contamination prior, the second approximates the
posterior mean for a t-prior, and the third yields the Limited Translation
Rule. 

Results indicate that for a small increase in Bayes risk we can "purchase"
bounded frequentist risk with an acceptable risk increase over use of, for
example, the MLE. More specifically, when considering the range of the
Gaussian prior variance, the first estimator performs best for small
values, the second performs best for medium values, and the third performs
best for large values. This trend in preferred estimator across the prior
variance corresponds essentially to changes in the power p of y^p within
B(y).

-------joint work with Tom Louis