Bayesian Error Analysis for Feature Selection in Biomarker Discovery

We present a novel Bayesian validation paradigm with several validation metrics tailored to biomarker discovery, including moments (the mean and variance) of the number of false discoveries, the number of missed discoveries, and the false discovery rate. All of these validation metrics can be used with a variety of Bayesian variable selection methods already available in the literature. When used in conjunction with Bayesian models with independent Gaussian features, we call these validation metrics optimal Bayesian feature filtering moments (OBFMs). We find closed-form expressions for OBFMs and show that they are asymptotically Gaussian and consistent even when the modeling assumptions are violated. In both synthetic simulations and real data analysis, OBFMs perform very well in biomarker discovery relative to other methods from the literature.