توماس بـِى‌يز

(تم التحويل من توماس بايز)

توماس بايز (Thomas Bayes؛ /ˈbz/؛ ح. 1701 – 7 أبريل 1761)[2][3][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.[4]

توماس بايز
Thomas Bayes
Thomas Bayes.gif
پورتريه مستخدم لبايز في كتاب من عام 1936،[1] إلا أنه من المشكوك فيه إذا ما كان هذا الپورتريه هو حقاً له.[2] ولا يوجد پورتريه أقدم أو مؤكـَد له.
وُلِدَح. 1701
لندن، إنگلترة
توفي7 أبريل 1761(1761-04-07) (عن عمر 59 عاماً)
آبار تنبردج، كنت، إنگلترة
الجنسيةإنگليزي
اللقبمبرهنة بايز
التوقيع
Bayes sig.svg


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مبرهنة بايز

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.[5] 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.

Bayes's "Essay" contains his solution to a similar problem posed by ابراهام دى مواڤر، مؤلف The Doctrine of Chances (1718).

وبالاضافة لذلك، فقد تم نشر ورقة بحثة من بايز في موضوع asymptotic series بعد وفاته.


البايزيانية

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.[6]

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.[7] 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,[8] 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.

انظر أيضاً

  • List of things named after Thomas Bayes
  • Bayesian inference
  • Laplace
  • Royal Society – Bayes was elected to membership in the Society in 1742; and his nomination letter has been posted with other membership records at the Royal Society website here. Those signing that nomination letter were: Philip Stanhope; Martin Folkes; James Burrow; Cromwell Mortimer; John Eames.
  • الهامش

    1. ^  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[2]

    المراجع

    1. ^ 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.")
    2. ^ أ ب ت Bayes's portrait The IMS Bulletin, Vol. 17 (1988), No. 3, pp. 276–278.
    3. ^ Belhouse, D.R. The Reverend Thomas Bayes FRS: a Biography to Celebrate the Tercentenary of his Birth.
    4. ^ McGrayne, Sharon Bertsch. (2011). The Theory That Would Not Die p. 10., p. 10, في كتب گوگل
    5. ^ 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
    6. ^ Paulos, John Allen. "The Mathematics of Changing Your Mind," New York Times (US). 5 August 2011; retrieved 6 August 2011
    7. ^ Stigler, Stephen M. (1986) The history of statistics., Harvard University press. pp97-98, 131.
    8. ^ خطأ استشهاد: وسم <ref> غير صحيح؛ لا نص تم توفيره للمراجع المسماة stigler86history

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