Bayes's Theorem

Bayes's theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian [Page 66]approaches to statistics, epistemology, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes's theorem is central to these paradigms because it simplifies the calculation of conditional probabilities and clarifies significant features of the subjectivist position.

This entry begins with a brief history of Thomas Bayes and the publication of his theorem. Next, the entry focuses on probability and its role in Bayes's theorem. Last, the entry explores modern applications of Bayes's theorem.