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Bayesian Probability ○𓆪｜Definition｜1st｜20251122123847-00-⌔

Bayesian probability - Wikipedia

Bayesian probability

Bayesian probability (/ˈbeɪziən/BAY-zee-ən or/ˈbeɪʒən/BAY-zhən)1 is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation2 representing a state of knowledge3 or as quantification of a personal belief.4

The Bayesian interpretation of probability can be seen as an extension of propositional logic that enables reasoning with hypotheses;56 that is, with propositions whose truth or falsity is unknown. In the Bayesian view, a probability is assigned to a hypothesis, whereas under frequentist inference, a hypothesis is typically tested without being assigned a probability.

Bayesian probability belongs to the category of evidential probabilities; to evaluate the probability of a hypothesis, the Bayesian probabilist specifies a prior probability. This, in turn, is then updated to a posterior probability in the light of new, relevant data (evidence).7 The Bayesian interpretation provides a standard set of procedures and formulae to perform this calculation.

The term Bayesian derives from the 18th-century English mathematician and theologian Thomas Bayes, who provided the first mathematical treatment of a non-trivial problem of statistical data analysis using what is now known as Bayesian inference.8 Mathematician Pierre-Simon Laplace pioneered and popularized what is now called Bayesian probability.8

Printed 2026-06-28.

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Footnotes

  1. “Bayesian”. Merriam-Webster.com Dictionary. Merriam-Webster. OCLC 1032680871. ↩

  2. Cox, R.T. (1946). “Probability, Frequency, and Reasonable Expectation”. American Journal of Physics. 14 (1): 1–10. Bibcode:1946AmJPh..14…1C. doi:10.1119/1.1990764. ↩

  3. Jaynes, E.T. (1986). “Bayesian Methods: General Background”. In Justice, J. H. (ed.). Maximum-Entropy and Bayesian Methods in Applied Statistics. Cambridge: Cambridge University Press. Bibcode:1986mebm.conf…J. CiteSeerX 10.1.1.41.1055. ↩

  4. de Finetti, Bruno (2017). Theory of Probability: A critical introductory treatment. Chichester: John Wiley & Sons Ltd. ISBN 9781119286370. ↩

  5. Hailperin, Theodore (1996). Sentential Probability Logic: Origins, Development, Current Status, and Technical Applications. London: Associated University Presses. ISBN 0934223459. ↩

  6. Howson, Colin (2001). “The Logic of Bayesian Probability”. In Corfield, D.; Williamson, J. (eds.). Foundations of Bayesianism. Dordrecht: Kluwer. pp. 137–159. ISBN 1-4020-0223-8. ↩

  7. Paulos, John Allen (5 August 2011). “The Mathematics of Changing Your Mind [by Sharon Bertsch McGrayne]”. Book Review. New York Times. Archived from the original on 2022-01-01. Retrieved 2011-08-06. ↩

  8. Stigler, Stephen M. (March 1990). The history of statistics. Harvard University Press. ISBN 9780674403413. ↩ ↩2

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