Thomas Bayes

Thomas Bayes (c. 1701–1761) was an English Presbyterian minister and mathematician whose posthumously published work inspired Bayes’ theorem and modern Bayesian statistics.

An Essay towards Solving a Problem in the Doctrine of Chances: A paper published in 1763 that presents an early solution to inverse probability problems and includes a version of Bayes’ theorem. Richard Price edited and published this essay after Bayes’s death, introducing his work to a wider mathematical audience.
John Canton: An English scientist and schoolteacher who investigated claims of spontaneous generation and corresponded with the Royal Society. Canton’s report of Bayes’s probability work helped prompt its presentation to the Royal Society.
Conditional probability: The probability of an event given that another event has occurred. Bayes’s probability problem asks how evidence changes the probability assigned to a hypothesis.
Bayesian statistics: A statistical framework that represents uncertainty with probability distributions and updates them using evidence. Bayes’s name became attached to the inferential tradition built around probability updating.
Richard Price: A Welsh philosopher, minister, and mathematician who edited and published Bayes’s essay on probability in 1763. Price found Bayes’s manuscript and shaped its posthumous publication.
Pierre-Simon Laplace: A French mathematician and astronomer who developed probability methods and used a general form of Bayes’ theorem. Laplace independently developed and applied the inverse-probability approach that Bayes’s essay had anticipated.
Prior probability: A probability assigned to a hypothesis before incorporating a particular new observation. Inverse-probability reasoning combines an initial probability with observed evidence.
Bayesian inference: A method of statistical reasoning that updates probabilities for hypotheses or parameters using observed data. The approach gives a modern form to the inverse reasoning central to Bayes’s legacy.
Bayes’ theorem: A rule for updating the probability of a hypothesis using evidence and prior probabilities. The theorem’s name preserves the connection to the inverse-probability work Bayes inspired.
Harold Jeffreys: A British mathematician and geophysicist who established influential foundations for Bayesian inference in the twentieth century. Jeffreys helped turn Bayes’s legacy into a systematic statistical framework.

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