📜 Theorem, law or theory

Bayes theorem

Teorema de Bayes

Date: 1763 · confidence medium
Place: Tunbridge Wells, England
Credited to: Thomas Bayes (published posthumously by Richard Price); general form by Laplace (1774)
People: 👤 Thomas Bayes1702–1761
Field: Knowledge & symbols

⚠️ Disputed: the sources disagree.

What was discovered

A rule for updating the probability of a hypothesis in the light of new evidence, by inverting conditional probabilities. It is the basis of probabilistic inference.

Laplace independently rediscovered and generalised the result in 1774 and was the one who applied it systematically.

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What it led to

Bayesian statistics
machine learning
spam and Kalman filters
evidence-based medicine

Built on

Pascal-Fermat probability
Ars Conjectandi

Made possible

Enigma decryption (Turing, Bayesian)
probabilistic artificial intelligence

📄 Original publication

LII. An essay towards solving a problem in the doctrine of chances. By the late Rev. Mr. Bayes, F. R. S. communicated by Mr. Price, in a letter to John Canton, A. M. F. R. SThomas Bayes · Philosophical Transactions of the Royal Society of London · 1763