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The Essay Found After His Death

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The Essay Found After His Death

This article records tradition as it has been passed down and reported. Its sources are not yet part of the atlas's verified catalogue.

Thomas Bayes never published the theorem that carries his name. He was an English Presbyterian minister in Tunbridge Wells who dabbled in mathematics as an amateur interest, well enough to be elected a Fellow of the Royal Society in 1742, but he put out almost nothing under his own name in his lifetime. When he died in 1761, his papers passed to a friend and fellow minister, Richard Price, who found among them an essay working out how to reason backward from an observed effect to the probability of its cause. Price recognized what he was holding, edited it, and in 1763 presented it to the Royal Society as An Essay towards Solving a Problem in the Doctrine of Chances, two years after the man who wrote it had died. The theorem itself answers a question that sounds simple and is not: given how likely some evidence is under a hypothesis, and how likely the hypothesis was thought to be before the evidence arrived, how should that belief in the hypothesis be updated once the evidence is in? Bayes worked out a special case. It was Pierre-Simon Laplace, in 1774, independently and apparently without knowledge of Bayes's essay at all, who derived a substantially more general form of the same idea and did far more than Bayes ever did to develop it into a working method, which is why some historians consider Laplace, not Bayes, the true founder of what is now called Bayesian probability. The name stuck to Bayes regardless, attached by mathematicians writing decades after both men were dead, to an essay its own author never saw into print.

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Sources
Thomas Bayes, Biography (MacTutor History of Mathematics)
MacTutor History of Mathematics Archive, University of St AndrewsBiography: Presbyterian minister at Tunbridge Wells, FRS 1742, died 1761; Price presented his essay to the Royal Society; Bayes's conclusions were accepted by Laplace in a 1781 memoir.View the Source
Laplace's 1774 Memoir on Inverse Probability (Stigler, Statistical Science 1986)
Institute of Mathematical StatisticsAbstract: Laplace's first major article on mathematical statistics, published 1774, "the first widely read presentation of inverse probability" applied to binomial and location estimation.View the Source
MacTutor History of Mathematics Archive
University of St Andrews, School of Mathematics and StatisticsArticle On: Bayes' TheoremView the Source
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