The Optimum Classifier and the Performance Evaluation by Bayesian Approach

Abstract This paper deals with the optimum classifier and the performance evaluation by the Bayesian approach. Gaussian population with unknown parameters is assumed. The conditional density given a limited sample of the population has a relationship to the multivariate t-distribution. The mean error rate of the optimum classifier is theoretically evaluated by the quadrature of the conditional density. To verify the optimality of the classifier and the correctness of the mean error calculation, the results of Monte Carlo simulation employing a new sampling procedure are shown. It is also shown by the comparative study that the Bayesian formulas of the mean error rate have the following characteristics. 1) The unknown population parameters are not required in its calculation. 2) The expression is simple and clearly shows the limited sample effect on the mean error rate. 3) The relationship between the prior parameters and the mean error rate is explicitly expressed