توماس بايز (Thomas Bayes؛ //؛ ح. 1701 – 7 أبريل 1761)[note a] كان إحصائياً وفيلسوفاً وقساً مشيخياً إنگليزياً، عُرف بصياغته حالة محددة من المبرهنة التي تحمل اسمه: مبرهنة بايز. ولم ينشر بايز قط ما سوف يُعتبر لاحقاً أشهر انجازاته؛ ولكن بعد وفاته حرر ونشر ملاحظاته رتشارد پرايس.
|توفي||7 أبريل 1761 (عن عمر 59 عاماً)|
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Bayes's solution to a problem of inverse probability was presented in "An Essay towards solving a Problem in the Doctrine of Chances" which was read to the Royal Society in 1763 after Bayes' death. رتشارد پرايس shepherded the work through this presentation and its publication in the Philosophical Transactions of the Royal Society of London the following year. This was an argument for using a uniform prior distribution for a binomial parameter and not merely a general postulate. This essay contains a statement of a special case of مبرهنة بايز.
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? Or the converse: given that one or more balls has been drawn, what can be said about the number of white and black balls in the urn? These are sometimes called "inverse probability" problems.
وبالاضافة لذلك، فقد تم نشر ورقة بحثة من بايز في موضوع asymptotic series بعد وفاته.
الاحتمالات البايزية 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. Since its rebirth in the 1950s, advancements in computing technology have allowed scientists from many disciplines to pair traditional Bayesian statistics with random walk techniques. The use of the Bayes theorem has been extended in science and in other fields.
Bayes himself might not have embraced the broad interpretation now called Bayesian. Mathematician Pierre-Simon Laplace pioneered and popularised what is now called Bayesian probability. It is difficult to assess Bayes's philosophical views on probability, since his essay does not go into questions of interpretation. There 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, 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's definition results. As Stigler 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's 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.
- ^ Bayes's tombstone says he died at 59 years of age on 7 April 1761, so he was born in either 1701 or 1702. Some sources erroneously write the death date as 17 April, but these sources all seem to stem from a clerical error duplicated; no evidence argues in favour of a 17 April death date. The birth date is unknown likely due to the fact he was baptised in a Dissenting church, which either did not keep or was unable to preserve its baptismal records; accord Royal Society Library and Archive catalogue, Thomas Bayes (1701–1761)[dead link] Thomas Bayes (1701–1761)قالب:Updated link
- ^ Terence O'Donnell, History of Life Insurance in Its Formative Years (Chicago: American Conservation Co:, 1936), p. 335 (caption "Rev. T. Bayes: Improver of the Columnar Method developed by Barrett.")
- ^ أ ب ت Bayes's portrait The IMS Bulletin, Vol. 17 (1988), No. 3, pp. 276–278.
- ^ Belhouse, D.R. The Reverend Thomas Bayes FRS: a Biography to Celebrate the Tercentenary of his Birth.
- ^ McGrayne, Sharon Bertsch. (2011). The Theory That Would Not Die p. 10., p. 10, في كتب گوگل
- ^ Edwards, A. W. G. "Commentary on the Arguments of Thomas Bayes," Scandinavian Journal of Statistics, Vol. 5, No. 2 (1978), pp. 116–118; retrieved 6 August 2011
- ^ Paulos, John Allen. "The Mathematics of Changing Your Mind," New York Times (US). 5 August 2011; retrieved 6 August 2011
- ^ Stigler, Stephen M. (1986) The history of statistics., Harvard University press. pp97-98, 131.
- ^ خطأ استشهاد: وسم
<ref>غير صحيح؛ لا نص تم توفيره للمراجع المسماة
- Thomas Bayes, "An essay towards solving a Problem in the Doctrine of Chances." Bayes's essay in the original notation.
- Thomas Bayes, 1763, "An essay towards solving a Problem in the Doctrine of Chances." Bayes's essay as published in the Philosophical Transactions of the Royal Society of London, Vol. 53, p. 370, on Google Books.
- Thomas Bayes, 1763, "A letter to John Canton," Phil. Trans. Royal Society London 53: 269–71.
- D. R. Bellhouse, "On Some Recently Discovered Manuscripts of Thomas Bayes" at the Internet Archive.
- D. R. Bellhouse, 2004, "The Reverend Thomas Bayes, FRS: A Biography to Celebrate the Tercentenary of His Birth," Statistical Science 19 (1): 3–43.
- F. Thomas Bruss (2013), "250 years of 'An Essay towards solving a Problem in the Doctrine of Chance. By the late Rev. Mr. Bayes, communicated by Mr. Price, in a letter to John Canton, A. M. F. R. S.' ", DOI 10.1365/s13291-013-0077-z, Jahresbericht der Deutschen Mathematiker-Vereinigung, Springer Verlag, Vol. 115, Issue 3–4 (2013), 129–133.
- Dale, Andrew I. (2003.) "Most Honourable Remembrance: The Life and Work of Thomas Bayes". ISBN 0-387-00499-8. Springer, 2003.
- ____________. "An essay towards solving a problem in the doctrine of chances" in Grattan-Guinness, I., ed., Landmark Writings in Western Mathematics. Elsevier: 199–207. (2005).
- Michael Kanellos. "18th-century theory is new force in computing" CNET News, 18 February 2003.
- McGrayne, Sharon Bertsch. (2011). The Theory That Would Not Die: How Bayes's Rule Cracked The Enigma Code, Hunted Down Russian Submarines, & Emerged Triumphant from Two Centuries of Controversy. New Haven: Yale University Press. ISBN 9780300169690 OCLC 670481486
- Stigler, Stephen M. "Thomas Bayes's Bayesian Inference," Journal of the Royal Statistical Society, Series A, 145:250–258, 1982.
- ____________. "Who Discovered Bayes's Theorem?" The American Statistician, 37(4):290–296, 1983.