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The true title of Bayes’s essay. (English) Zbl 1331.60006
Summary: New evidence is presented that Richard Price gave Thomas Bayes’s famous essay [Philos. Trans. R. Soc. Lond. 53, 370–418 (1763; Zbl 1250.60007)] a very different title from the commonly reported one. It is argued that this implies Price almost surely and Bayes not improbably embarked upon this work seeking a defensive tool to combat David Hume on an issue in theology.
Reviewer: Reviewer (Berlin)

60-03 History of probability theory
01A50 History of mathematics in the 18th century
62C10 Bayesian problems; characterization of Bayes procedures
01A70 Biographies, obituaries, personalia, bibliographies
Biographic References:
Bayes, Thomas
Full Text: DOI Euclid
[1] Bayes, T. (1764). An Essay toward solving a Problem in the Doctrine of Chances. In Philosophical Transactions of the Royal Society of London 53 370-418. Offprint unchanged, but with title page giving the title as “A Method of Calculating the Exact Probability of All Conclusions founded on Induction.” The 1763 volume of the Phil. Trans. was reprinted (with completely reset type) in 1774 in Wittenberg, by C. C. Dürr, Printer for the University. The reprint covers 185-211 there and is in the original English, but a conspectus in Latin is added at the front of the volume: THOM. BAYES Tentamen soluendi problema, ad doctrinam probabilium pertinens; in qua nonnulla emendat, ipsumque computum probabilium nouis augmentis locupletat, quae tamen in pauca conferri vix possunt. · Zbl 1250.60007
[2] Bellhouse, D. R. (2004). The Reverend Thomas Bayes, FRS: A biography to celebrate the tercentenary of his birth. Statist. Sci. 19 3-43. · Zbl 1079.01020 · doi:10.1214/088342304000000189
[3] Bellhouse, D. R. (2011). Abraham De Moivre : Setting the Stage for Classical Probability and Its Applications . CRC Press, Boca Raton, FL. · Zbl 1235.01020
[4] Dale, A. I. (1986). A newly-discovered result of Thomas Bayes. Arch. Hist. Exact Sci. 35 101-113. · Zbl 0596.01016 · doi:10.1007/BF00357623
[5] Dale, A. I. (1999). A History of Inverse Probability . 2nd ed. Studies in the History of Mathematics and Physical Sciences 16 . Springer, New York. · Zbl 0922.01006
[6] Dale, A. I. (2003). Most Honourable Remembrance : The Life and Work of Thomas Bayes . Springer, New York. · Zbl 1030.01031
[7] Daston, L. (1988). Classical Probability in the Enlightenment . Princeton Univ. Press, Princeton, NJ.
[8] Dawid, P. and Gillies, D. (1989). A Bayesian analysis of Hume’s argument concerning miracles. The Philosophical Quarterly 39 57-65.
[9] Earman, J. (2002). Bayes, Hume, Price, and miracles. In Bayes’s Theorem , Proc. Br. Acad. 113 91-109. British Acad., London.
[10] Edwards, A. W. F. (1992). Likelihood , Expanded ed. Johns Hopkins Univ. Press, Baltimore, MD. · Zbl 0833.62004
[11] Gillies, D. A. (1987). Was Bayes a Bayesian? Historia Math. 14 325-346. · Zbl 0634.01009 · doi:10.1016/0315-0860(87)90065-6
[12] Hacking, I. (1965). Logic of Statistical Inference . Cambridge Univ. Press, London. · Zbl 0133.41604
[13] Hacking, I. (1975). The Emergence of Probability : A Philosophical Study of Early Ideas About Probability , Induction and Statistical Inference . Cambridge Univ. Press, London. · Zbl 0311.01004
[14] Hald, A. (1998). A History of Mathematical Statistics from 1750 to 1930. Wiley, New York. · Zbl 0979.01012
[15] Hartley, D. (1749). Observations on Man , his Frame , his Duty , and his Expectations . Richardson, London.
[16] Hume, D. (1748). Of Miracles. Essay 10 in Philosophical Essays concerning Human Understanding . Millar, London.
[17] Hutton, C. (1815). A Philosophical and Mathematical Dictionary . New ed. London.
[18] Hutton, C., Shaw, G. and Peterson, R. (1809). The Philosophical Transactions of the Royal Society of London , from their Commencement , in 1665, to the Year 1800; Abridged . C. and R. Baldwin, London.
[19] Kruskal, W. (1988). Miracles and statistics: The casual assumption of independence. J. Amer. Statist. Assoc. 83 929-940. · doi:10.1080/01621459.1988.10478682
[20] Pearson, K. (1978). The History of Statistics in the 17 th and 18 th Centuries Against the Changing Background of Intellectual , Scientific and Religious Thought ( Lectures from 1921 - 1933) (E. S. Pearson, ed.). Macmillan Co., New York. · Zbl 0439.01006
[21] Poisson, S.-D. (1837). Recherches sur les Probabilités des Jugements . Bachelier, Paris.
[22] Price, R. (1765). A Demonstration of the Second Rule in the Essay toward the Solution of a Problem in the Doctrine of Chances. Philosophical Transactions of the Royal Society of London 54 296-325. Offprint unchanged, but with title page giving the title as “A Supplement to the Essay on a Method of Calculating the Exact Probability of All Conclusions founded on Induction”.
[23] Price, R. (1767). Four Dissertations . Millar and Cadell, London.
[24] Priestley, J. (1791). Discourse on Occasion of the Death of Dr. Price . J. Johnson, London.
[25] Rees, A., ed. (1807). The Cyclopaedia ; or Universal Dictionary of Arts , Sciences , and Literature . Longman et al., London. This was issued first in parts, with Volume 7 issued in February 1807. The full set was then published in 39 volumes, with 6 volumes of plates, in 1819. The article “Chance” occupies pp. 3I:4-3M:3, Rees Project notation.
[26] Stigler, S. M. (1983). Who discovered Bayes’s theorem? Amer. Statist. 37 290-296. Reprinted as Chapter 15 in Stigler (1999). · Zbl 0537.62004
[27] Stigler, S. M. (1986). The History of Statistics : The Measurement of Uncertainty Before 1900. The Belknap Press of Harvard Univ. Press, Cambridge, MA. · Zbl 0656.62005
[28] Stigler, S. M. (1999). Statistics on the Table : The History of Statistical Concepts and Methods . Harvard Univ. Press, Cambridge, MA. · Zbl 0997.62506
[29] Thomas, D. O., Stephens, J. and Jones, P. A. L. (1993). A Bibliography of the Works of Richard Price . Scolar Press, Aldershot, UK.
[30] Watson, W. P. (2013). Catalogue 19: Science , Medicine , Natural History . W. P. Watson Rare Books, London.
[31] Zabell, S. L. (2005). Symmetry and Its Discontents : Essays on the History Of Inductive Probability . Cambridge Univ. Press, New York. · Zbl 1100.01001
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