A posteriori estimation of correlated jointly gaussian mean vectors

This paper describes the use of maximum a posteriori probability (MAP) techniques to estimate the mean values of features used in statistical pattern classification problems, when these mean feature values from the various decision classes are jointly Gaussian random vectors that are correlated across the decision classes. A set of mathematical formalisms is proposed and used to derive closed-form expressions for the estimates of the class-conditional mean vectors, and for the covariance matrix of the errors of these estimates. Finally, the performance of these algorithms is described for the simple case of a two-class one-feature pattern recognition problem, and compared to the performance of classical estimators that do not exploit the class-to-class correlations of the features' mean values.