Bayesian Minimum Mean-Square Error Estimation for Classification Error—Part II: Linear Classification of Gaussian Models

In this paper, Part II of a two-part study, we derive a closed-form analytic representation of the Bayesian minimum mean-square error (MMSE) error estimator for linear classification assuming Gaussian models. This is presented in a general framework permitting a structure on the covariance matrices and a very flexible class of prior parameter distributions with four free parameters. Closed-form solutions are provided for known, scaled identity, and arbitrary covariance matrices. We examine performance in small sample settings via simulations on both synthetic and real genomic data, and demonstrate the robustness of these error estimators to false Gaussian modeling assumptions by applying them to Johnson distributions.