Statistical Science

Richard Price, the First Bayesian

Stephen M. Stigler

Full-text: Open access


Roughly half of Bayes’s famous essay was written by Richard Price, including the Appendix with all of the numerical examples. A study of this Appendix reveals Price (1) unusually for the time, felt it necessary to allow in his analysis for a hypothesis having been suggested by the same data used in its analysis, (2) was motivated (covertly in 1763, overtly in 1767) to undertake the study to refute David Hume on miracles, and (3) displayed a remarkable sense of collegiality in scientific controversy that should stand as a model for the present day. Price’s analysis of the posterior in one particular example, including locating the posterior median and giving and interpreting credible regions, qualifies him as the first person to apply Bayes’s theory.

Article information

Statist. Sci., Volume 33, Number 1 (2018), 117-125.

First available in Project Euclid: 2 February 2018

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Thomas Bayes Richard Price David Hume history


Stigler, Stephen M. Richard Price, the First Bayesian. Statist. Sci. 33 (2018), no. 1, 117--125. doi:10.1214/17-STS635.

Export citation


  • For the life of Richard Price, see Thomas (1977), Frame (2015), and Pearson (1978). For philosophical discussions of Bayes, Price, Hume, induction, and miracles, see Hacking (1975), Daston (1988), Dawid and Gillies (1989), Gillies (1987), Earman (2002), Kruskal (1988), Harris (2015), and Zabell (2005). For Price’s work in actuarial science see Bellhouse (2017). For discussions of Bayes’s Essay in detail see by Dale (1999, 2003), Stigler (1982, 1986), Cléro (2017), and Hald (1998); for circumstances involving its origin, Stigler (1983, 1999, 2013).
  • Bayes, T. (1764). An essay towards solving a problem in the doctrine of chances. Philos. Trans. R. Soc. Lond. 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.” Reprinted by Molina and Deming (1940). Translated into French with extensive commentary by Cléro (2017).
  • Bellhouse, D. (2002). On some recently discovered manuscripts of Thomas Bayes. Historia Math. 29 383–394.
  • Bellhouse, D. (2004). The reverend Thomas Bayes, FRS: A biography to celebrate the tercentenary of his birth. Statist. Sci. 19 3–32.
  • Bellhouse, D. (2017). Leases for Lives: Life Contingent Contracts and the Emergence of Actuarial Science in Eighteenth-Century England. Cambridge Univ. Press, Cambridge.
  • Cléro, J.-P., trans. and ed. (2017). Essai en vue de résoudre un problème de la doctrine des chances, Méthode de calcul de la probabilité exacte de toutes conclusions fondées sur l’induction. Hermann, Paris.
  • Dale, A. I. (1986). A newly-discovered result of Thomas Bayes. Arch. Hist. Exact Sci. 35 101–113.
  • Dale, A. I. (1999). A History of Inverse Probability: From Thomas Bayes to Karl Pearson, 2nd ed. Springer, New York. 1st ed. 1991.
  • Dale, A. I. (2003). Most Honourable Remembrance: The Life and Work of Thomas Bayes. Springer, New York.
  • Daston, L. (1988). Classical Probability in the Enlightenment. Princeton Univ. Press, Princeton, NJ.
  • Dawid, P. and Gillies, D. (1989). A Bayesian analysis of Hume’s argument concerning miracles. Philos. Q. 39 57–65.
  • Earman, J. (2002). Bayes, Hume, Price, and miracles. In Bayes’s Theorem (R. Swinburne, ed.). Proc. Br. Acad. 113 91–109. British Acad., London.
  • Fienberg, S. E. (2006). When did Bayesian inference become “Bayesian”? Bayesian Anal. 1 1–40.
  • Frame, P. (2015). Liberty’s Apostle: Richard Price, His Life and Times. Univ. Wales Press, Cardiff.
  • Gillies, D. A. (1987). Was Bayes a Bayesian? Historia Math. 14 325–346.
  • Hacking, I. (1975). The Emergence of Probability. Cambridge Univ. Press, Cambridge.
  • Hald, A. (1998). A History of Mathematical Statistics from 1750 to 1930. Wiley, New York.
  • Harris, J. A. (2015). Hume: An Intellectual Biography. Cambridge Univ. Press, Cambridge.
  • Hartley, D. (1749). Observations on Man, His Frame, His Duty, and His Expectations. Richardson, London.
  • Hume, D. (1748). Of miracles. In Philosophical Essays Concerning Human Understanding. Millar, London.
  • Jevons, W. S. (1877). Principles of Science, 2nd ed. Macmillan, London. 1st ed. 1871, in 2 volumes.
  • Kruskal, W. H. (1988). Miracles and statistics: The casual assumption of independence. J. Amer. Statist. Assoc. 83 929–940.
  • Molina, E. C. and Deming, W. E. (1940). Facsimiles of Two Papers by Bayes. Hafner, New York.
  • Morgan, W. (1815). Memoirs of the Life of the Rev. Richard Price, D.D. F.R.S. R. Hunter and R. Rees, London.
  • Pearson, K. (1978). The History of Statistics in the 17th and 18th Centuries, Against the Changing Background of Intellectual, Scientific and Religious Thought (Lectures from 19211933) (E. S. Pearson, ed.). Charles W. Griffin, London.
  • Price, R. (1758). A Review of the Principal Questions and Difficulties in Morals. Millar, London. 2nd ed. 1769, 3rd ed. 1787.
  • Price, R. (1765). A demonstration of the second rule in the essay towards the solution of a problem in the doctrine of chances. Philos. Trans. R. Soc. Lond. 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”.
  • Price, R. (1767). Four Dissertations. Millar and Cadell, London. 2nd ed. 1768, 3rd ed. 1772, 4th ed. 1777.
  • Price, R. (1771). Observations on Reversionary Payments. T. Cadell, London. 2nd ed. 1772, 3rd ed. 1773, 4th ed. 1783.
  • Stephens, J. (1980). When did David Hume meet Richard Price? Price-Priestley Newsl. 4 30–39.
  • Stigler, S. M. (1982). Thomas Bayes’s Bayesian inference. J. Roy. Statist. Soc. Ser. A 145 250–258.
  • Stigler, S. M. (1983). Who discovered Bayes’s theorem? Amer. Statist. 37 290–296.
  • Stigler, S. M. (1986). The History of Statistics. Harvard Univ. Press, Cambridge, MA.
  • Stigler, S. M. (1999). Statistics on the Table. Harvard Univ. Press, Cambridge, MA.
  • Stigler, S. M. (2004). Comment on Bellhouse (2004) [Bayes’s date of birth]. Statist. Sci. 19 39–40.
  • Stigler, S. M. (2013). The true title of Bayes’s essay. Statist. Sci. 28 283–288.
  • Thomas, D. O. (1977). The Honest Mind: The Thought and Work of Richard Price. Oxford Univ. Press, Oxford.
  • Thomas, D. O. and Peach, B. (1983). The Correspondence of Richard Price. Volume I: July 1748–March 1778. Duke Univ. Press, Durham, NC.
  • Venn, J. (1888). The Logic of Chance, 3rd ed. Macmillan, London.
  • Zabell, S. L. (2005). Symmetry and Its Discontents: Essays on the History of Inductive Philosophy. Cambridge Univ. Press, Cambridge.