Thomas Bayes

Infobox_Scientist
name = Thomas Bayes


image_width = 300px
caption = The correct identification of this portrait has been questioned [ [http://www.york.ac.uk/depts/maths/histstat/bayespic.htm Bayes' portrait ] ]
birth_date = c. 1702
birth_place = London, England
death_date = death date and age|1761|4|17|1702|1|1|df=y
death_place = Tunbridge Wells, Kent, England
residence =
citizenship =
nationality = British
field =
work_institution =
alma_mater =
doctoral_advisor =
doctoral_students =
known_for =
author_abbreviation_bot =
author_abbreviation_zoo =
prizes =
religion = Presbyterian


footnotes =

Thomas Bayes (c. 1702 – 17 April 1761) was a British mathematician and Presbyterian minister, known for having formulated a specific case of the theorem that bears his name: Bayes' theorem, which was published posthumously.

Biography

Thomas Bayes was born in London. In 1719 he enrolled at the University of Edinburgh to study logic and theology.

He is known to have published two works in his lifetime: "Divine Benevolence, or an Attempt to Prove That the Principal End of the Divine Providence and Government is the Happiness of His Creatures" (1731), 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.

Some feel that he became interested in probability while reviewing a work written in 1755 by Thomas Simpson, [cite book|author = Stigler, S. M.| year = 1986| title = The History of Statistics: The Measurement of Uncertainty before 1900.|publisher = Harvard University Press] but others think he learned mathematics and probability while reading a book by de Moivre. [cite journal|author = Barnard, G. A.| title = Thomas Bayes—a biographical note. |journal = Biometrika | year = 1958| volume = 45 | pages=293–295]

Bayes died in Tunbridge Wells, Kent. He is buried in Bunhill Fields Cemetery in London where many Nonconformists 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" (1718).

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 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.

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 value of the thing expected upon its happening

In modern utility theory we would say that expected utility is — sometimes, because buying risk for small amounts or buying security for big amounts also happens — 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.

ee also

* Empirical Bayes

References

* Andrew I. Dale. "Most Honourable Remembrance: The Life and Work of Thomas Bayes". ISBN 0-387-00499-8. Springer, 2003.
* Stephen M. Stigler. [http://links.jstor.org/sici?sici=0035-9238%281982%29145%3A2%3C250%3ATBBI%3E2.0.CO%3B2-W "Thomas Bayes' Bayesian Inference,"] "Journal of the Royal Statistical Society", Series A, 145:250–258, 1982.
* Stephen M. Stigler. "Who Discovered Bayes's Theorem?" "The American Statistician", 37(4):290–296, 1983.
* Michael Kanellos. [http://news.com.com/Old-school+theory+is+a+new+force/2009-1001_3-984695.html "18th-century theory is new force in computing"] CNET News, 18 Feb 2003.

Further reading

* Thomas Bayes, " [http://www.stat.ucla.edu/history/essay.pdf An essay towards solving a Problem in the Doctrine of Chances.] " Bayes's essay in the original notation.
* Thomas Bayes, 1763, " [http://www.york.ac.uk/depts/maths/histstat/letter.pdf A letter to John Canton,] " "Phil. Trans. Royal Society London" 53: 269-71.
* D. R. Bellhouse, " [http://web.archive.org/web/20041106225211/http://www.stats.uwo.ca/faculty/bellhouse/bayesmss.pdf On Some Recently Discovered Manuscripts of Thomas Bayes.] "
* D. R. Bellhouse, 2004, " [http://www.york.ac.uk/depts/maths/histstat/bayesbiog.pdf The Reverend Thomas Bayes, FRS: A Biography to Celebrate the Tercentenary of His Birth,] " "Statistical Science" 19 (1): 3–43.
*Dale, A.I., 2005, "An essay towards solving a problem in the doctrine of chances" in Grattan-Guiness, I., ed., "Landmark Writings in Western Mathematics". Elsevier: 199-207.

External links

* [http://www.bayesian.org/resources/bayes.html Who was The Rev. Thomas Bayes?]
* [http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Bayes.html Biographical sketch of Thomas Bayes]
* [http://yudkowsky.net/bayes/bayes.html An Intuitive Explanation of Bayesian Reasoning] (includes biography)

Persondata
NAME= Bayes, Thomas
ALTERNATIVE NAMES=
SHORT DESCRIPTION= British mathematician
DATE OF BIRTH= 1702
PLACE OF BIRTH= London
DATE OF DEATH= April 17 1761
PLACE OF DEATH= Tunbridge Wells