Exact MSE performance of the Bayesian MMSE estimator for classification error

Biomedicine is faced with difficult high-throughput small-sample classification problems, with classifier errors typically approximated using classical, though heuristically devised, resampling methods. A recently proposed Bayesian error estimator places the problem in a signal estimation framework in the presence of uncertainty, resulting in a minimum-mean-square error solution, where uncertainty is relative to the parameters of the feature-label distribution and conditioned on the observed sample. Here, we present the theoretical sample-conditioned MSE for Bayesian error estimators, demonstrating a unique advantage over resampling methods in that their mathematical framework naturally gives rise to a practical expected measure of performance given a fixed sample.