Thomas Bayes

Fixed: Why Personal Finance is Broken and How to Make it Work for Everyone

by John Y. Campbell and Tarun Ramadorai  · 25 Jul 2025

of Experimental Psychology: Human Learning and Memory 4, no. 6 (1978): 551–578. 16. This reasoning is an application of Bayes’ Theorem, first stated by Thomas Bayes, an eighteenth century English mathematician and Presbyterian minister. Bayesian reasoning is at the heart of rational thinking in the face of uncertainty. 17. This is

Everything Is Predictable: How Bayesian Statistics Explain Our World

by Tom Chivers  · 6 May 2024  · 283pp  · 102,484 words

that is the exact opposite question. For quite a long time, the history of probability was about asking the first question. But after the Reverend Thomas Bayes—about whom much more later—started asking the second one, in the eighteenth century, it became known as inverse probability. As you’ll see over

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occasions, be walking from the Tube to the nearby Royal Statistical Society, Bunhill is best known for being the final resting place of the Reverend Thomas Bayes. Bayes was an eighteenth-century Presbyterian minister and a hobbyist mathematician. In his lifetime, he wrote a book about theology and another about Newton’s

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Unitarian. Price in particular was a close friend—when Bayes died, it was Price who reworked and published the famous essay that contained Bayes’ theorem. Thomas Bayes lived in a high-society world. His peers tended to be university-educated, often with doctorates of divinity, and many of them were members of

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to the ratio in the sample. But in that he was wrong; the probabilities can be very different indeed. It was not until the Reverend Thomas Bayes that it was understood how Bernoulli was wrong. DE MOIVRE ON THE NORMAL DISTRIBUTION Abraham de Moivre was a French Protestant who fled persecution by

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the mean of as many observations as possible. The second key point is that one of the reviewers of Simpson’s paper was the Reverend Thomas Bayes of Tunbridge Wells. “By then he was fairly mature in his use of probability,” says Bellhouse, “and he gave some very insightful comments.” The key

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. There exists, stored on the servers of the University of Minnesota, for reasons I don’t fully understand, a “Bayesian songbook,” containing such wonders as: Thomas Bayes’s Army [The Battle Hymn of Las Fuentes] Words: P. R. Freeman and A. O’Hagan Music: Traditional [“The Battle Hymn of the Republic”] Mine

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eyes have seen the glory of the Reverend Thomas Bayes, He is stamping out frequentists and their incoherent ways, He has raised his mighty army at the Hotel Las Fuentes, His troops are marching on

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of the Church of Scotland in 1650, ahead of the Battle of Dunbar.9 Cromwell had the misfortune to die more than forty years before Thomas Bayes was born, but nonetheless he has given his name to an important rule of Bayesian decision theory, Cromwell’s rule. Named by Dennis Lindley, the

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when I say that it is fundamentally Bayesian. Artificial Intelligence: A Modern Approach, the standard textbook for undergraduate AI degrees, even has a picture of Thomas Bayes on the front cover, and says, “Bayes’ rule underlies most modern approaches to uncertain reasoning in AI systems.”20 There is such a thing as

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distribution until I have quite a lot of my probability mass on “All swans are white.” But I never get to total certainty, just as Thomas Bayes gets more confidence in the whereabouts of the white ball as more and more red ones are thrown, without ever being sure. Then, if I

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divorce because you predict it will upset them. There’s nothing mystical about it: that’s just how we work. Humans are prediction machines. And Thomas Bayes showed us the math of how we do it. Acknowledgments I couldn’t have written this book without the help of a lot of people

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a Letter to John Canton, A. M. F. R. S.,” Philosophical Transactions 53, no. 1763 (1683–1775): 370–418. 2. D. R. Bellhouse, “The Reverend Thomas Bayes, FRS: A Biography to Celebrate the Tercentenary of His Birth,” Statistical Science 19, no. 1 (2004): 3–43, https://doi.org/10.1214/088342304000000189. 3

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College; F.R.S. and F.S.A. (London: P. Vaillant, 1766), quoted in Bellhouse, “The Reverend Thomas Bayes.” 7. G. A. Barnard and T. Bayes, “Studies in the History of Probability and Statistics: IX. Thomas Bayes’s Essay towards Solving a Problem in the Doctrine of Chances,” Biometrika 45, no. 3/4 (1958

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): 293–315, https://doi.org/10.2307/2333180. 8. Letters to Thomas Bayes and John Skinner Smith in Ward’s Latin Correspondence, British Library

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Manuscript, Additional Manuscript 6224, 116. Cited in Bellhouse, “The Reverend Thomas Bayes.” 9. Alexander Gordon, “Peirce, James,” Dictionary of National Biography, 1885–1900, https://en.wikisource.org/wiki/Dictionary_of_National_Biography,_1885-1900/Peirce,_James. 10.

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Respect of Creation and Providence (London: Printed for John Pemberton, at the Buck, over-against St. Dunstan’s Church, Fleetstreet, 1730). 13. Bellhouse, “The Reverend Thomas Bayes,” 10. 14. James Foster, An Essay on Fundamentals in Religion (1720), taken from Unitarian Tracts in Nine Volumes (London: British and Foreign Unitarian Association, 1836

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). 15. D. Coomer, English Dissent under the Early Hanoverians (London: Epworth Press, 1946), quoted in Bellhouse, “The Reverend Thomas Bayes.” 16. Bellhouse, “The Reverend Thomas Bayes,” 12. 17. Ibid., 13. 18. E. Montague, The Letters of Mrs. Elizabeth Montagu, with Some of the Letters of her Correspondents, vols. 1

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–4 (1974; London: T. Cadell and W. Davies, London, 1809–13), quoted in Bellhouse, “The Reverend Thomas Bayes.” 19. Thomas Bayes, An introduction to the doctrine of fluxions, and defence of the mathematicians against the objections of the author of the Analyst, so far as they

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par les Soins de M. J.-A, Serret 3 (1869): 441–76; Serret 5 (1870): 663–84 (Paris: Gauthier-Villars), cited in Bellhouse, “The Reverend Thomas Bayes.” 23. P. Gorroochurn, “The Chevalier de Méré Problem I: The Problem of Dice (1654),” in Classic Problems of Probability, ed., P. Gorroochurn (Hoboken, NJ: John

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the Royal Society of London 49 (1755): 82–93. 43. Stigler, The History of Statistics, 138. 44. David Bellhouse, personal conversation, 2022. 45. Letter from Thomas Bayes to John Canton, undated but likely from 1755, cited in Bellhouse, “The Reverend Thomas Baines,” 20. 46. Thomas Simpson, Miscellaneous Tracts on Some Curious, and

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Problem.” 51. Example taken from Spiegelhalter, The Art of Statistics. 52. Ibid., 325. 53. Stigler, The History of Statistics, 179. 54. From the will of Thomas Bayes, cited in Barnard and Bayes, “Studies in the History of Probability.” 55. Letter to Thomas Jefferson from Richard Price, July 2, 1785, https://founders.archives

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and Richard Price, Dictionary of National Biography, vol. 46 (1896), 335. 58. David Bellhouse, personal conversation. 59. David Bellhouse, “On Some Recently Discovered Manuscripts of Thomas Bayes,” Historia Mathematica 29 (2002): 383–94. 60. Stephen M. Stigler, “Richard Price, the First Bayesian,” Statistical Science 33, no. 1 (February 2018): 117–25. 61

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Meetings on Bayesian Statistics,” ISBA Newsletter, December 1999, https://www.uv.es/bernardo/ValenciaStory.pdf. 109. Ibid. 110. P. R. Freeman and A. O’Hagan, “Thomas Bayes’s Army [The Battle Hymn of Las Fuentes],” in The Bayesian Songbook, ed., Carlin and Bradley, Yumpu, 2006, 37, https://www.yumpu.com/en/document

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, 301–302 Tetlock, Philip, 250–256, 258–260 “There’s No Theorem Like Bayes’ Theorem,” 111, 325 Thinking Fast and Slow (Kahneman), 119–120, 230 “Thomas Bayes’s Army (The Battle Hymn of Las Fuentes),” 111 tickling, 303–308 Tilburg University, 118 Times (London), 89 Trinity College, Cambridge, 25 Trump, Donald, 237

Frommer's Caribbean 2010

by Christina Paulette Colón, Alexis Lipsitz Flippin, Darwin Porter, Danforth Prince and John Marino  · 2 Jan 1989

Copper Mine Point Copper Mine Bay Virgin Gorda Airport Virgin Gorda Yacht Harbour Devil’s Bay National Park 6 (Spanish Town) Spring Bay ola St Thomas Bay 5 Little Dix Bay Savannah Bay Pond Bay nd ou .S No Gorda Peak . Rd 0 0 0.75 km 3/4 mi N South

The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant From Two Centuries of Controversy

by Sharon Bertsch McGrayne  · 16 May 2011  · 561pp  · 120,899 words

in England in the 1740s: can we make rational conclusions about God based on evidence about the world around us? An amateur mathematician, the Reverend Thomas Bayes, discovered the rule, and we celebrate him today as the iconic father of mathematical decision making. Yet Bayes consigned his discovery to oblivion. In his

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for the errors in this book. part I enlightenment and the anti-bayesian reaction 1. causes in the air Sometime during the 1740s, the Reverend Thomas Bayes made the ingenious discovery that bears his name but then mysteriously abandoned it. It was rediscovered independently by a different and far more renowned man

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hard to imagine Bayes’ editor or his publisher not saying something publicly. Thirty years later Price was still referring to the work as that of Thomas Bayes. Although Bayes’ idea was discussed in Royal Society circles, he himself seems not to have believed in it. Instead of sending it off to the

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, the great French mathematician Pierre Simon Laplace. 2. the man who did everything Just across the English Channel from Tunbridge Wells, about the time that Thomas Bayes was imagining his perfectly smooth table, the mayor of a tiny village in Normandy was celebrating the birth of a son, Pierre Simon Laplace, the

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of Chances, by Abraham de Moivre. The book had appeared in three editions between 1718 and 1756, and Laplace may have read the 1756 version. Thomas Bayes had studied an earlier edition. Reading de Moivre, Laplace became more and more convinced that probability might help him deal with uncertainties in the solar

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with Newton’s sigma sign makes the total probability of all possible causes add up to one. Armed with his principle, Laplace could do everything Thomas Bayes could have done—as long as he accepted the restrictive assumption that all his possible causes or hypotheses were equally likely. Laplace’s goal, however

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probability and statistics for a century. “In my mind,” Glenn Shafer of Rutgers University observed, “Laplace did everything, and we just read stuff back into Thomas Bayes. Laplace put it into modern terms. In a sense, everything is Laplacean.”23 If advancing the world’s knowledge is important, Bayes’ rule should be

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many observations. Eventually, adherents of this frequency-based probability became known as frequentists or sampling theorists. To frequentists Laplace was such a towering target that Thomas Bayes’ existence barely registered. When critics thought of Bayes’ rule, they thought of it as Laplace’s rule and focused their criticism on him and his

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’ theorem and a spectrum of priors: honest priors and improper ones; priors that represented what was known and sometimes not; and in different places both Thomas Bayes’ uniform priors and Laplace’s unequal ones. To deduce the pattern of cams surrounding the wheels of the Tunny-Lorenz machines Turing invented a highly

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health officials will have ideas in advance of the likely sources of infection and will examine them first.”36 Koopman started right off by assigning Thomas Bayes’ 50–50 odds to the presence of a target U-boat inside the 236-mile circle. Then he added data that were as objective as

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of Bayes’ articles with a preface by Bell Telephone’s Edward Molina. Like Molina, Bailey used Laplace’s more complex and precise system instead of Thomas Bayes’. By 1950 Bailey was a vice president of the Kemper Insurance Group in Chicago and a frequent after-dinner speaker at black-tie banquets of

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hooked.”3 Although both Fisher and Neyman lectured on sampling methods at the Graduate School, its director, W. Edwards Deming, was open-minded; he published Thomas Bayes’ essay with an introduction by Edward Molina of Bell Laboratories. Friends referred to Cornfield’s tenure at the Department of Labor as his serious and

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happen. David Hume agreed, arguing that because the sun had risen thousands of times in the past it would continue to do so. It was Thomas Bayes’ friend and editor, Richard Price, who took the contrary view that the highly improbable could still occur. During the nineteenth and early twentieth centuries, Antoine

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H-bomb report, the schism between entrenched frequentists and upstart Bayesians was getting downright noisy. As usual, the bone of contention was the subjectivity of Thomas Bayes’ pesky prior. The idea of importing knowledge that did not originate in the statistical data at hand was anathema to the anti-Bayesian duo Fisher

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involved. In 2008, when the Englishman Dennis Lindley was 85 years old, he said he was now almost convinced that Laplace was more important than Thomas Bayes: “Bayes solved one narrow problem; Laplace solved many, even in probability. . . . My ignorance of the Frenchman’s work may be cultural, since he did not

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have a large impact on many mathematical statisticians and decision theorists, including Raiffa. Until Wald’s book appeared, the word “Bayesian” had referred only to Thomas Bayes’ controversial suggestion about equal priors, not to his theorem for solving inverse probability problems. After Wald died in a plane crash in India in 1950

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1967 about how “the battle of Bayes has raged for more than two centuries, sometimes violently, sometimes almost placidly, . . . a combination of doubt and vigor.” Thomas Bayes had turned his back on his own creation; a quarter century later, Laplace glorified it. During the 1800s it was both employed and undermined. Derided

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50% likely to exist; later Swinburne would figure the probability of Jesus’ resurrection at “something like 97 percent.” These were calculations that neither the Reverend Thomas Bayes nor the Reverend Richard Price had cared to make, and even many nonstatisticians regarded Swinburne’s lack of careful measurement as a black mark against

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computed the probabilities that, in its death throes, the submarine changed course and traveled, for example, another mile in any of several random directions. Using Thomas Bayes’ simplification, Richardson began by considering each of those directions as equally probable. Then, making a point at each new possible location, the computer repeated the

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hierarchical models. Mainstream statisticians and scientists simply did not believe that Bayes could ever be practical. Indicative of their attitude is the fact that while Thomas Bayes’ clerical ancestors were listed in Britain’s Dictionary of National Biography he himself was not. Yet amazingly, amid these academic doubts, a U.S. Air

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, and artificial intelligence. The number of attendees at Bayesian conferences in Valencia quadrupled in 20 years. In 1993, more than two centuries after his death, Thomas Bayes finally joined his clerical relatives in the Dictionary of National Biography. Amid the Bayesian community’s frenzy over MCMC and Gibbs sampling, a generic software

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can often pinpoint the day when Bayes came into their lives, when they dropped these childish frequentist ways (or even “came out”). Clearly the Reverend Thomas Bayes is their spiritual guide and leader, and he even imitated the Christian God by not publishing in his own lifetime (mind you, I have heard

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often called the date of his death. The degraded condition of his vault may have contributed to the confusion. Second, the often-reproduced portrait of Thomas Bayes is almost assuredly of someone else named “T. Bayes.” The sketch first appeared in 1936 in History of Life Insurance in its Formative Years by

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of the Columnar Method developed by Barrett,” and Barrett did not develop his method until 1810, a half-century after the death of “our” Rev. Thomas Bayes. Bellhouse (2004) first noticed that the portrait’s hairstyle is anachronistic. Sharon North, curator of Textiles and Fashion at the Victoria and Albert Museum, London

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, F.R.S. Communicated by Mr. Price, in a letter to John Canton, A.M.F.R.S. A letter from the late Reverend Mr. Thomas Bayes, F.R.S., to John Canton, M.A. and F.R.S. Author(s): Mr. Bayes and Mr. Price. Philosophical Transactions (1683–1775) (53) 370

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) Nonconformity and Social and Economic Life 1660–1800. London: Epworth Press. Bellhouse, David R. (2002) On some recently discovered manuscripts of Thomas Bayes. Historia Mathematica (29) 383–94. ———. (2007a) The Reverend Thomas Bayes, FRS: A biography to celebrate the tercentenary of his birth. Statistical Science (19:1) 3–43. With Dale (2003) the main

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source for Bayes’ life. ———. (2007b) Lord Stanhope’s papers on the Doctrine of Chances. Historia Mathematica (34) 173–86. Bru, Bernard. (1987) Preface in Thomas Bayes. Essai en vue de résoudre un problème de la doctrine des chances, trans. and ed., J-P Cléro. Paris. ———. (1988) Estimations laplaciennes. Un exemple: La

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I. (1988) On Bayes’ theorem and the inverse Bernoulli theorem. Historia Mathematica (15) 348–60. ———. (1991) Thomas Bayes’s work on infinite series. Historia Mathematica (18) 312–27. ———. (1999) A History of Inverse Probability from Thomas Bayes to Karl Pearson. 2d ed. Springer. One of the foundational works in the history of probability. ———. (2003

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) Most Honourable Remembrance: The Life and Work of Thomas Bayes. Springer. With Bellhouse, the main source for Bayes’ life. Daston, Lorraine. (1988) Classical Probability in the Enlightenment. Princeton University Press. Deming WE, ed. (1940) Facsimiles

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Quarterly (37:147) 166–86. Stanhope G, Gooch GP. (1914) The Life of Charles Third Earl Stanhope. Longmans, Green. Statistical Science (2004) Issue devoted to Thomas Bayes. (19:1) Many useful articles. Stigler, Stephen M. (1983). Who discovered Bayes’s Theorem? American Statistician 37 290–96. ———. (1986). The History of Statistics: The

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Measurement of Uncertainty before 1900. Belknap Press of Harvard University Press. A classic and the place to start for Thomas Bayes. ———. (1999). Statistics on the Table: The History of Statistical Concepts and Methods. Harvard University Press. Thomas, DO. (1977) The Honest Mind: The Thought and Work

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. Dale, Andrew I. (1995) Pierre-Simon Laplace: Philosophical Essay on Probabilities. Trans. and notes by Dale. Springer-Verlag. ———. (1999) A History of Inverse Probability from Thomas Bayes to Karl Pearson. 2d ed. Springer. One of the foundational works in the history of probability. Daston, Lorraine. (1979) D’Alembert’s critique of probability

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. (1975) Napoleonic statistics: The work of Laplace. Biometrika (62:2) 503–17. ———. (1978). Laplace’s early work: Chronology and citations. Isis (69) 234–54. ———. (1982) Thomas Bayes’s Bayesian Inference. JRSS, A. (145) Part 2, 250–58. Bayes’ article with modern mathematical notation and Stigler’s commentary. The starting place for anyone

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) 302–33. Crépel, Pierre. (1993) Henri et la droite de Henry. MATAPLI (36) 19–22. Dale, Andrew I. (1999) A History of Inverse Probability from Thomas Bayes to Karl Pearson. 2d ed. Springer. One of the foundational works in the history of probability. Daston, Lorraine J. (1987) The domestication of risk: mathematical

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single top quarks via t c g and tug flavor-changing-neutral-current couplings. Physical Review Letters (99) 191802. Anderson, Philip W. (1992) The Reverend Thomas Bayes, needles in haystacks, and the fifth force. Physics Today (45:1) 9, 11. Aoki, Masanao. (1967) The Optimization of Stochastic Systems. Academic Press. Berger JO

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Bailey, Helen, 91 Bailey, Robert A., 95 Bailey, William O., 174 Banburismus 66–72, 75, 80 Barnard George A., 69, 132 Barnett, Otto, 135 Bayes, Thomas: Bayes’ rule discovered by, ix, 3, 6–10, 22, 130 in dictionary, 215, 225 life and death of, 3–5 portrait of, 259 life and death

Artificial Intelligence: A Modern Approach

by Stuart Russell and Peter Norvig  · 14 Jul 2019  · 2,466pp  · 668,761 words

measurements and incomplete theories. Jacob Bernoulli (1654–1705, uncle of Daniel), Pierre Laplace (1749–1827), and others advanced the theory and introduced new statistical methods. Thomas Bayes (1702–1761) proposed a rule for updating probabilities in the light of new evidence; Bayes’ rule is a crucial tool for AI systems. The formalization

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’s original formulation. Horn (2003) shows how to patch up the difficulties. Jaynes (2003) has a similar argument that is easier to read. The Rev. Thomas Bayes (1702-1761) introduced the rule for reasoning about conditional probabilities that was posthumously named after him (Bayes, 1763). Bayes only considered the case of uniform

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priors forBayesian networks was discussed by Spiegelhalter et al. (1993). The beta distribution as a conjugate prior for a Bernoulli variable was first derived by Thomas (Bayes, 1763) and later reintroduced by Karl Pearson (1895) as a model for skewed data; for many years it was known as a “Pearson Type I

The Signal and the Noise: Why So Many Predictions Fail-But Some Don't

by Nate Silver  · 31 Aug 2012  · 829pp  · 186,976 words

a given game, there is a particular type of thought process that helps govern his decisions. It is called Bayesian reasoning. The Improbable Legacy of Thomas Bayes Thomas Bayes was an English minister who was probably born in 1701—although it may have been 1702. Very little is certain about Bayes’s life, even

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that these researchers are applying. FIGURE 8-6: A GRAPHICAL REPRESENTATION OF FALSE POSITIVES When Statistics Backtracked from Bayes Perhaps the chief intellectual rival to Thomas Bayes—although he was born in 1890, almost 120 years after Bayes’s death—was an English statistician and biologist named Ronald Aylmer (R. A.) Fisher

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.7 The Bayesian Invisible Hand In fact, free-market capitalism and Bayes’ theorem come out of something of the same intellectual tradition. Adam Smith and Thomas Bayes were contemporaries, and both were educated in Scotland and were heavily influenced by the philosopher David Hume. Smith’s “invisible hand” might be thought of

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five times per season. That works out to 150 such streaks per season between the thirty NBA teams combined. 19. D. R. Bellhouse, “The Reverend Thomas Bayes FRS: A Biography to Celebrate the Tercentenary of His Birth,” Statistical Science, 19, 1, pp. 3–43; 2004. http://www2.isye.gatech.edu/~brani/isyebayes

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who regarded Jesus Christ as the divine son of God rather than (as most Christians then and now believe) a direct manifestation of God. 21. Thomas Bayes, “Divine Benevolence: Or an Attempt to Prove That the Principal End of the Divine Providence and Government Is the Happiness of His Creatures.” http://archive

Life Is Simple: How Occam's Razor Set Science Free and Shapes the Universe

by Johnjoe McFadden  · 27 Sep 2021

Einstein, Richard Price (1723–91), the non-conformist Protestant minister, moral philosopher and mathematician, examined the unpublished papers of his recently deceased friend and mathematician Thomas Bayes (1702–61). Bayes had been a modestly successful scientist. Thirty years earlier, he had rushed to the defence of Isaac Newton’s mathematical method known

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his own book on statistical approaches to actuarial calculations. However, in 1761, he had never seen anything like the statistics described in Bayes’s paper. Thomas Bayes is one of the most elusive heroes of our story. We hardly know him any better than we do William of Occam. There is a

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, John Wilmot, Earl of Rochester had described it as ‘The Rendevouz of Fooles, Buffoones, and Praters/ Cuckolds, Whores, Citizens, their Wives and Daughters’. The Reverend Thomas Bayes was not a particularly popular preacher in the ‘Rendevous of Fooles’, but he did establish a reputation as a scholar and was even invited to

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Frenchman, Berlin resident and the president of the Berlin Academy, Pierre Louis Moreau de Maupertuis (1698–1759). Maupertuis was born in 1698, four years before Thomas Bayes, in Saint-Malo, a port on the Brittany coast of France. He studied mathematics in Paris and in 1723 was admitted to the Académie des

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(1960). Chapter 18: Opening Up the Razor 1. Russell, B., Our Knowledge of the External World (Jovian Press, 2017). 2. Bellhouse, D. R., ‘The Reverend Thomas Bayes, FRS: A Biography to Celebrate the Tercentenary of His Birth’, Statistical Science, 19, 3–43 (2004). 3. Wilmott, J., The Debt to Pleasure (Carcanet, 2012

Why Machines Learn: The Elegant Math Behind Modern AI

by Anil Ananthaswamy  · 15 Jul 2024  · 416pp  · 118,522 words

cornerstone of machine learning is calculus, co-invented by no less a polymath than Isaac Newton. The field also relies heavily on the work of Thomas Bayes, the eighteenth-century English statistician and minister who gave us the eponymous Bayes’s theorem, a key contribution to the field of probability and statistics

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of the cornerstones of probability theory and, indeed, of machine learning. TO BAYES OR NOT TO BAYES There’s delicious irony in the uncertainty over Thomas Bayes’s year of birth. It’s been said that he was “born in 1701 with probability 0.8.” The date of his death, however, is

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said he could explain why the machine learned”: “New Navy Device Learns by Doing,” p. 25. GO TO NOTE REFERENCE IN TEXT Thomas Bayes, the eighteenth-century English statistician and minister: “Thomas Bayes,” Quick Info, MacTutor, n.d., mathshistory.st-andrews.ac.uk/Biographies/Bayes/. GO TO NOTE REFERENCE IN TEXT German mathematician Carl

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Science 33, No. 1 (2018): 117–25. GO TO NOTE REFERENCE IN TEXT Royal Tunbridge Wells in England: “Thomas Bayes: English Theologian and Mathematician,” Science & Tech, Britannica, n.d., www.britannica.com/biography/Thomas-Bayes. GO TO NOTE REFERENCE IN TEXT Bayes and Price were kindred spirits: Stigler, “Richard Price, the First Bayesian,” p

Radical Uncertainty: Decision-Making for an Unknowable Future

by Mervyn King and John Kay  · 5 Mar 2020  · 807pp  · 154,435 words

development of the new theory of probability was the achievement of an unlikely hero – an obscure eighteenth-century country Presbyterian clergyman in England. The Reverend Thomas Bayes is by chance buried in what is now the centre of London’s financial district. Among his papers he left a theorem that is one

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I n the eighteenth century there were country clergymen of exceptional intelligence who had time on their hands. They benefited from a secure reference narrative. Thomas Bayes was one; Thomas Malthus another. In 1798, Malthus set out what might be regarded as the first growth model in economics. He hypothesised that population

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he held, the first as telegraph boy for Western Electric and the other as CEO of the corporation which is now General Electric. The Reverend Thomas Bayes died unknown. But such examples are few, and to find them we have to go some way back in history. The most common profile of

The Book of Why: The New Science of Cause and Effect

by Judea Pearl and Dana Mackenzie  · 1 Mar 2018

or rung-three query about your Bayesian network, you must draw it with scrupulous attention to causality. REVEREND BAYES AND THE PROBLEM OF INVERSE PROBABILITY Thomas Bayes, after whom I named the networks in 1985, never dreamed that a formula he derived in the 1750s would one day be used to identify

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. In fact, causal aspirations were the driving force behind his analysis of “inverse probability.” A Presbyterian minister who lived from 1702 to 1761, the Reverend Thomas Bayes appears to have been a mathematics geek. As a dissenter from the Church of England, he could not study at Oxford or Cambridge and was

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cannot overrule a proposition with the force of natural law, such as “Dead people stay dead.” FIGURE 3.1. Title page of the journal where Thomas Bayes’s posthumous article on inverse probability was published and the first page of Richard Price’s introduction. For Bayes, this assertion provoked a natural, one

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within a foot of the end would be 1/12. On an eight-foot billiard table, the probability would be 1/8. FIGURE 3.2. Thomas Bayes’s pool table example. In the first version, a forward-probability question, we know the length of the table and want to calculate the probability

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“given that I know” is epistemological and should be governed by the logic of knowledge, not that of frequencies and proportions. From the philosophical perspective, Thomas Bayes’s accomplishment lies in his proposing the first formal definition of conditional probability as the ratio P(S | T) = P(S AND T)/P(T

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find a philosopher who placed counterfactuals at the heart of causality, we have to move ahead to David Hume, the Scottish philosopher and contemporary of Thomas Bayes. Hume rejected Aristotle’s classification scheme and insisted on a single definition of causation. But he found this definition quite elusive and was in fact

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Human Compatible: Artificial Intelligence and the Problem of Control

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Superforecasting: The Art and Science of Prediction

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Information: A Very Short Introduction

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The Human Cosmos: A Secret History of the Stars

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The Stuff of Thought: Language as a Window Into Human Nature

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Mapmatics: How We Navigate the World Through Numbers

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Human Frontiers: The Future of Big Ideas in an Age of Small Thinking

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Data Science for Business: What You Need to Know About Data Mining and Data-Analytic Thinking

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Mastering Pandas

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The Art of Statistics: Learning From Data

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Into the Wild

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The Art of Statistics: How to Learn From Data

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The Organized Mind: Thinking Straight in the Age of Information Overload

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The Great Mental Models: General Thinking Concepts

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In Pursuit of the Perfect Portfolio: The Stories, Voices, and Key Insights of the Pioneers Who Shaped the Way We Invest

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Immortality, Inc.

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The Ascent of Money: A Financial History of the World

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Little Brother

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Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures

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The Singularity Is Near: When Humans Transcend Biology

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We Are Data: Algorithms and the Making of Our Digital Selves

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Red-Blooded Risk: The Secret History of Wall Street

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From Bacteria to Bach and Back: The Evolution of Minds

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The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

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The Most Human Human: What Talking With Computers Teaches Us About What It Means to Be Alive

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Science Fictions: How Fraud, Bias, Negligence, and Hype Undermine the Search for Truth

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Antifragile: Things That Gain From Disorder

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The Undoing Project: A Friendship That Changed Our Minds

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Pirate Cinema

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Fluke: Chance, Chaos, and Why Everything We Do Matters

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Programming Computer Vision with Python

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Our Final Invention: Artificial Intelligence and the End of the Human Era

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How Medicine Works and When It Doesn't: Learning Who to Trust to Get and Stay Healthy

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The Skeptical Economist: Revealing the Ethics Inside Economics

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Programming Collective Intelligence

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Statistics hacks

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Entangled Life: How Fungi Make Our Worlds, Change Our Minds & Shape Our Futures

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Demystifying Smart Cities

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How to Read Numbers: A Guide to Statistics in the News (And Knowing When to Trust Them)

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Content: Selected Essays on Technology, Creativity, Copyright, and the Future of the Future

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The Price of Tomorrow: Why Deflation Is the Key to an Abundant Future

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Everydata: The Misinformation Hidden in the Little Data You Consume Every Day

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The Invisible Hands: Top Hedge Fund Traders on Bubbles, Crashes, and Real Money

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Beyond Weird

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The Devil's Derivatives: The Untold Story of the Slick Traders and Hapless Regulators Who Almost Blew Up Wall Street . . . And Are Ready to Do It Again

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Architects of Intelligence

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Market Risk Analysis, Quantitative Methods in Finance

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On Intelligence

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