| Thomas Bayes |
Article Index for Thomas |
Website Links For Thomas |
Information About ™Thomas Bayes |
|
Reverend Thomas Bayes (c. 1702 – April 17 , 1761 ) was a British Mathematician and Presbyterian minister, known for having formulated a special case of Bayes' Theorem , which was published posthumously. BIOGRAPHY Thomas Bayes was born in ), and ''An Introduction to the Doctrine of Fluxions, and a Defence of the Mathematicians Against the Objections of the Author of the Analyst'' (published anonymously in 1736 ), in which he defended the logical foundation of Isaac Newton 's Calculus against the criticism of George Berkeley , author of '' The Analyst ''. It is speculated that Bayes was elected as a Fellow of the Royal Society in 1742 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. Bayes died in Tunbridge Wells , Kent . He is interred in Bunhill Fields Cemetery in London where many Nonconformist s are buried. 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 '' (1833). In addition to the ''Essay Towards Solving a Problem'', a paper on Asymptotic Series was published posthumously. BAYES AND BAYESIANISM Bayesian Probability is the name given to several related interpretations of Probability , which have in common the application of probability to any kind of statement, not just those involving Random Variable s. "Bayesian" has been used in this sense since about 1950. It is not at all clear that Bayes himself would have embraced the very broad interpretation now called Bayesian. It is difficult to assess Bayes' philosophical views on probability, as the only direct evidence is his essay, which does not go into questions of interpretation. In the essay, Bayes defines ''probability'' as follows (Definition 5). The probability of any event is the ratio between the value at which an expectation depending on the happening of the event ought to be computed, and the chance of the thing expected upon it's In modern Utility Theory we would say that expected utility is the probability of an event times the payoff received in case of that event. Rearranging that to solve for the probability, we obtain Bayes' definition. 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". {Some would argue, however, that things can happen without being observable.} Thus it can be argued, as Stigler does, that Bayes intended his results in a rather 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. MODERN APPLICATIONS The Search Engine Google , and the information retrieval company Autonomy Systems , employ Bayesian principles to provide probable results to searches. Microsoft is reported as using Bayesian "probabalistic" mathematics in its future Notification Platform to filter unwanted messages. SEE ALSO REFERENCES
EXTERNAL LINKS
|
|
|