An Axiomatic Approach to Prove the Converse of Bayes’ Theorem in Probability

Abstract

The converse of Bayes' theorem, have been proved using axiomatic approach to probability. This approach to probability utilizes the relations and theorems of set theory. Simply presentation of the converse of Bayes' theorem has been possible due to the correspondence theorem in set theory. This theorem is seen to be more applicable in the proof of Bayes' theorem and its converse. So at first, the correspondence theorem of set theory with its proof has been presented here and then has been applied to prove the Bayes' theorem and its converse. Some important applications of correspondence theorem for set theory have also been presented in this article. The use of correspondence theorem in proving Bayes' theorem and its converse makes the proof easily understandable and reduces the steps proving them. After this work, the statement of Baye's theorem can be stated with conditions necessary and sufficient both.