Bayes' theorem

Abstract

Bayes’ Theorem is a simple mathematical formula used for calculatingconditional probabilities. It figures prominently insubjectivist or Bayesian approaches to epistemology,statistics, and inductive logic. Subjectivists, who maintain thatrational belief is governed by the laws of probability, lean heavilyon conditional probabilities in their theories of evidence and theirmodels of empirical learning. Bayes’ Theorem is central to theseenterprises both because it simplifies the calculation of conditionalprobabilities and because it clarifies significant features ofsubjectivist position. Indeed, the Theorem’s central insight —that a hypothesis is confirmed by any body of data that its truthrenders probable — is the cornerstone of all subjectivistmethodology.