Bayes' theorem

Definition

Bayes' theorem, named after Thomas Bayes, gives a mathematical rule for inverting conditional probabilities, allowing the probability of a cause to be found given its effect. For example, with Bayes' theorem, the probability that a patient has a disease given that they tested positive for that disease can be found using the probability that the test yields a positive result when the disease is present. The theorem was developed in the 18th century by Bayes and independently by Pierre-Simon Laplace.

Related concepts

A Scanner Darkly Adrian Smith (statistician)Alan Turing Among Us An Essay Towards Solving a Problem in the Doctrine of Chances Andrey Kolmogorov Approximate Bayesian computation Axiomatic system Bas van Fraassen Bayes estimator Bayes factor Bayesian epistemology Bayesian estimator Bayesian hierarchical modeling Bayesian inference Bayesian inference in phylogeny Bayesian information criterion Bayesian linear regression Bayesian model averaging Bayesian network Bayesian persuasion Bayesian probability Bayesian statistics Benjamin Franklin Bernstein–von Mises theorem Binomial distribution Biometrika Bletchley Park Boy or Girl paradox Brian Skyrms Cambridge University Press Chain rule (probability)Charles Sanders Peirce Cheryl Misak Christian Robert Christopher A. Fuchs Cipher Coherence (philosophical gambling strategy)Colin Howson Complex number Conditional density Conditional expectation Conditional probability Conjugate prior Contingency table Cox's theorem Credible interval Cromwell's rule Cryptanalysis Daphne Koller Density matrix Domain of a function Edmund F. Robertson Edward Arnold (publisher)Edward N. Zalta Edwin Thompson Jaynes Empirical Bayes method Encyclopædia Britannica Eleventh Edition Enigma machine Event (probability theory)Evidence lower bound Evolutionary biology F. Thomas Bruss False positive rate Frequentist interpretation of probability Function (Mathematics)Genetic disease Genetic testing Genetic variance Genetics Genetics in Medicine Genotype George Casella Harold Jeffreys Hugh Chisholm I. J. Good Ian Hacking Improper prior Inductive probability Integrated nested Laplace approximations James M. Joyce Japanese naval codes Jason Rosenhouse John Wiley & Sons Joint probability distribution Katrina A. B. Goddard Laplace's approximation Law of total probability Likelihood function Likelihood principle Likelihood ratio MIT OpenCourseWare MacTutor History of Mathematics Archive Marginal likelihood Marginal probability Markov chain Monte Carlo Maximum a posteriori estimation Metascience Monty Hall problem Nested sampling algorithm Nicholas Saunderson Nir Friedman Noûs Odds Persi Diaconis Philosophical Transactions Pierre-Simon Laplace Posterior predictive distribution Posterior probability Principle of indifference Principle of maximum entropy Prior probability Probability interpretations Probability kinematics Proportionality (mathematics)Public domain Pythagorean theorem QBism Quantum mechanics Radon–Nikodym theorem Random variable Real line Realization (probability)Recessive gene Regular conditional probability Richard McElreath Richard Price Robert Spekkens Royal Society Sensitivity (tests)Specificity (tests)Stanford Encyclopedia of Philosophy Statistical Rethinking Statistical Science Statistical inference Stephen Stigler Support (mathematics)Thomas Bayes Three Prisoners problem Théorie analytique des probabilités True negative rate True positive rate Two envelopes problem University of St Andrews Variational Bayesian methods Veritasium Vigenère cipher Why Most Published Research Findings Are False Wikifunctions World War II Yale University Press YouTube

17 concepts already in your glossary