  Optimal Bayesian feature selection (OBFS) is a multivariate supervised
screening method designed from the ground up for biomarker discovery. In this
work, we prove that Gaussian OBFS is strongly consistent under mild conditions,
and provide rates of convergence for key posteriors in the framework. These
results are of enormous importance, since they identify precisely what features
are selected by OBFS asymptotically, characterize the relative rates of
convergence for posteriors on different types of features, provide conditions
that guarantee convergence, justify the use of OBFS when its internal
assumptions are invalid, and set the stage for understanding the asymptotic
behavior of other algorithms based on the OBFS framework.
