Comparison between Fisherian and Bayesian approach to classification using two groups

Abstract

Two approaches to discriminant analysis procedure are examined and compared based on their misclassification error rate. The Fisher’s approach tends to find a linear combination of the variables which maximize the ratio of the between group sum of squares to that of the within group sum of squares in achieving a good separation. On the other hand, the Bayesian approach assigns an observed unit to a group with the greatest posterior probability. Fisher’s linear discriminant analysis though is the most widely used method of classification because of its simplicity and optimality properties is normally used for two group cases. However, Bayesian approach is found to be better than Fisher’s approach because of its low misclassification error rate.

Keywords: variance-covariance matrices, centroids, prior probability, mahalanobis distance, probability of misclassification