Thomas Bayes | |
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 The correct identification of this portrait has been questioned [1] | |
| Born | c. 1702 |
| Died | 17 April 1761 (aged 59) |
| Nationality | English |
| Signature | |
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Thomas Bayes (pronounced: ˈbeɪz) (c. 1702 – 17 April 1761) was an English mathematician and Presbyterian minister, known for having formulated a specific case of the theorem that bears his name: Bayes' theorem, which was published posthumously.
Thomas Bayes was the son of London Presbyterian minister Joshua Bayes [2] and perhaps born in Hertfordshire.[3] In 1719 he enrolled at the University of Edinburgh to study logic and theology. On his return to London around 1722 he assisted his father at the latter's non-conformist chapel in London before moving to Tunbridge Wells, Kent around 1734. There he became minister of the Mount Sion chapel until 1752.[4]
He is known to have published two works in his lifetime, one theological and one mathematical:
It is speculated that Bayes was elected as a Fellow of the Royal Society in 1742 [5] on the strength of the Introduction to the Doctrine of Fluxions, as he is not known to have published any other mathematical works during his lifetime.
In his later years he took a deep interest in probability. Some feel that he became interested in the subject while reviewing a work written in 1755 by Thomas Simpson,[6] but others think he learned mathematics and probability from a book by de Moivre.[7] His work and findings on probability theory were passed in manuscript form to his friend Richard Price after his death.
By 1755 he was ill and in 1761 had died in Tunbridge. He was buried in Bunhill Fields Cemetery in Moorgate, London where many Nonconformists lie.
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Main article: Bayes' theorem |
Bayes' solution to a problem of "inverse probability" was presented in the Essay Towards Solving a Problem in the Doctrine of Chances (1764), published posthumously by his friend Richard Price in the Philosophical Transactions of the Royal Society of London. This essay contains a statement of a special case of Bayes' theorem.
In the first decades of the eighteenth century, many problems concerning the probability of certain events, given specified conditions, were solved. For example, given a specified number of white and black balls in an urn, what is the probability of drawing a black ball? These are sometimes called "forward probability" problems. Attention soon turned to the converse of such a problem: given that one or more balls has been drawn, what can be said about the number of white and black balls in the urn? The Essay of Bayes contains his solution to a similar problem, posed by Abraham de Moivre, author of The Doctrine of Chances (1718).
In addition to the Essay Towards Solving a Problem, a paper on asymptotic series was published posthumously.
Bayesian probability is the name given to several related interpretations of probability, which have in common the notion of probability as something like a partial belief, rather than a frequency. This allows the application of probability to all sorts of propositions rather than just ones that come with a reference class. "Bayesian" has been used in this sense since about 1950.
Bayes himself might not have embraced the broad interpretation now called Bayesian. It is difficult to assess Bayes' philosophical views on probability, since his essay does not go into questions of interpretation. There Bayes defines probability as follows (Definition 5).
In modern utility theory, expected utility can (with qualifications, because buying risk for small amounts or buying security for big amounts also happen) be taken as the probability of an event times the payoff received in case of that event. Rearranging that to solve for the probability, Bayes' definition results. As Stigler (citation below) points out, this is a subjective definition, and does not require repeated events; however, it does require that the event in question be observable, for otherwise it could never be said to have "happened". Stigler argues that Bayes intended his results in a more limited way than modern Bayesians; given Bayes' definition of probability, his result concerning the parameter of a binomial distribution makes sense only to the extent that one can bet on its observable consequences.
