A Note on Posterior Probability Estimation for Classifiers

One of the central themes in the classification task is the estimation of class posterior probability at a new point bfx. The vast majority of classifiers output a score for bfx, which is monotonically related to the posterior probability via an unknown relationship. There are many attempts in the literature to estimate this latter relationship. Here, we provide a way to estimate the posterior probability without resorting to using classification scores. Instead, we vary the prior probabilities of classes in order to derive the ratio of pdf's at point bfx, which is directly used to determine class posterior probabilities. We consider here the binary classification problem.