  Optimal Bayesian feature filtering (OBF) is a supervised screening method
designed for biomarker discovery. In this article, we prove two major
theoretical properties of OBF. First, optimal Bayesian feature selection under
a general family of Bayesian models reduces to filtering if and only if the
underlying Bayesian model assumes all features are mutually independent.
Therefore, OBF is optimal if and only if one assumes all features are mutually
independent, and OBF is the only filter method that is optimal under at least
one model in the general Bayesian framework. Second, OBF under independent
Gaussian models is consistent under very mild conditions, including cases where
the data is non-Gaussian with correlated features. This result provides
conditions where OBF is guaranteed to identify the correct feature set given
enough data, and it justifies the use of OBF in non-design settings where its
assumptions are invalid.
