Bayes' Theorem

Bayes' theorem is a rule for calculating the probability of an event given prior knowledge of conditions related to it, expressing how the probability of a hypothesis should be revised as new evidence arrives. It first appeared in Thomas Bayes' essay An Essay towards Solving a Problem in the Doctrine of Chances, found among his papers after his death and prepared for publication by his friend Richard Price, published in the Philosophical Transactions of the Royal Society of London in 1763. The theorem attracted little attention for more than a century, but in the twentieth century it became the foundation of Bayesian statistics, a school of inference that treats probability as a degree of belief to be updated as evidence accumulates, standing alongside and sometimes in tension with the frequentist methods developed by Fisher, Neyman and Egon Pearson.