What did Fisher mean by "inverse probability" in 1912--1922?
A. W. F. Edwards
Source: Statist. Sci. Volume 12, Number 3
(1997), 177-184.
Abstract
The method of maximum likelihood was introduced by R. A. Fisher in 1912, but not until 1922 under that name. This paper seeks to elucidate what Fisher understood by the phrase "inverse probability," which he used in various ways before defining "likelihood" in 1921 to clarify his meaning.
First Page:
Show
Hide
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ss/1030037907
Mathematical Reviews number (MathSciNet): MR1617520
Digital Object Identifier: doi:10.1214/ss/1030037907
Zentralblatt MATH identifier: 0955.62526
References
BAy ES, T. 1764. An essay towards solving a problem in the doctrine of chances. Philos. Trans. Roy. Soc. 53 370 418. Reprinted in Studies in the history of probability and statistics IX: Thomas Bay es' essay towards solving a probZ lem in the doctrine of chances with a biographical note by. Z. G. A. Barnard Biometrika 45 293 315 1958 and in PearZ. son and Kendall 1970. Z.
BERNOULLI, J. 1713. Ars Conjectandi. Thurnisius, Basilea.
BOOLE, G. 1854. An Investigation of the Laws of Thought.
BOX, J. F. 1978. R. A. Fisher: The Life of a Scientist. Wiley, New York. Z.
Mathematical Reviews (MathSciNet): MR500579
DALE, A. I. 1988. On Bay es' theorem and the inverse Bernoulli theorem. Historia Math. 15 348 360. Z.
Mathematical Reviews (MathSciNet): MR89j:01029
Zentralblatt MATH: 0672.01012
Digital Object Identifier: doi:10.1016/0315-0860(88)90026-2
DALE, A. I. 1991. A History of Inverse Probability. Springer, New York. Z.
Mathematical Reviews (MathSciNet): MR93d:60003
DE MOIVRE, A. 1738. The Doctrine of Chances, 2nd ed. Woodfall,
DE MORGAN, A. 1838. An Essay on Probabilities and Their Application to Life Contingencies and Insurance Offices. Longman, Orme, Brown, Green, & Longmans, London. Z.
EDWARDS, A. W. F. 1972. Likelihood. Cambridge Univ. Press.
Mathematical Reviews (MathSciNet): MR1191161
EDWARDS, A. W. F. 1974a. The history of likelihood. Interna tional Statistical Review 42 9 15. Reprinted in Edwards Z. 1992. Z.
Mathematical Reviews (MathSciNet): MR353514
Digital Object Identifier: doi:10.2307/1402681
JSTOR: links.jstor.org
EDWARDS, A. W. F. 1974b. A problem in the doctrine of chances. In Proceedings of the Conference on Foundational Questions Z in Statistical Inference O. Barndorff-Nielsen, P. Blæsild and. G. Schou, eds. 43 60. Aarhus Univ. Reprinted in Edwards Z. 1992. Z.
EDWARDS, A. W. F. 1978. Commentary on the arguments of Thomas Bay es. Scand. J. Statist. 5 116 118. Z. Z.
Mathematical Reviews (MathSciNet): MR518602
EDWARDS, A. W. F. 1986. Is the reference in Hartley 1745 to Bayesian inference? Amer. Statist. 40 109 110. Z. Z.
Mathematical Reviews (MathSciNet): MR841576
Digital Object Identifier: doi:10.2307/2684867
JSTOR: links.jstor.org
EDWARDS, A. W. F. 1992. Likelihood expanded edition. Johns Hopkins Univ. Press. Z.
Mathematical Reviews (MathSciNet): MR1191161
EDWARDS, A. W. F. 1996. The early history of the statistical estimation of linkage. Annals of Human Genetics 60 237 249. Z.
FISHER, R. A. 1912. On an absolute criterion for fitting frequency curves. Messenger of Mathematics 41 155 160. Z.
FISHER, R. A. 1915. Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika 9 507 521. Z.
FISHER, R. A. 1921. On the ``probable error'' of a coefficient of correlation deduced from a small sample. Metron 1 3 32. Z.
FISHER, R. A. 1922. On the mathematical foundations of theoretical statistics. Philos. Trans. Roy. Soc. London Ser. A 222 309 368. Z.
FISHER, R. A. 1930. Inverse probability. Proc. Cambridge Philos. Soc. 26 528 535. Z.
FISHER, R. A. 1932. Inverse probability and the use of likelihood. Proc. Cambridge Philos. Soc. 28 257 261. Z.
Zentralblatt MATH: 0005.17404
FISHER, R. A. 1936. Uncertain inference. Proceedings of the American Academy of Arts and Science 71 245 258. Z. Z.
Zentralblatt MATH: 0015.36301
GEISSER, S. 1992. Introduction to Fisher 1922 On the mathematical foundations of theoretical statistics. In BreakZ throughs in Statistics 1. Foundations and Basic Theory S.. Kotz and N. L. Johnson, eds. 1 10. Springer, New York. Z.
Mathematical Reviews (MathSciNet): MR1194401
Zentralblatt MATH: 0825.62414
HARTLEY, D. 1745. Observations on Man, His Frame, His Duty,
HUME, D. 1739. A Treatise of Human Nature L. A. Selby. Bigge, ed., 1888 and later printings. Clarendon, Oxford. Z.
JEFFREy S, H. 1938. Maximum likelihood, inverse probability, and the method of moments. Annals of Eugenics 8 146 151. Z.
LAPLACE, P. S. DE 1774. Memoire sur la probabilite des causes ´ ´
MOLINA, E. C. 1931. Bay es' theorem: an expository presentation. Ann. Math. Statist. 2 23 37. Z.
PEARSON, E. S. 1968. Some early correspondence between W. S. Gosset, R. A. Fisher and Karl Pearson, with notes and comments. Biometrika 55 445 457. Reprinted in Pearson Z. and Kendall 1970. Z.
Mathematical Reviews (MathSciNet): MR235641
JSTOR: links.jstor.org
PEARSON, E. S. 1990. `Student': A Statistical Biography of Z William Sealy Gosset R. L. Plackett, ed., with the assis. tance of G. A. Barnard. Clarendon, Oxford. Z.
Mathematical Reviews (MathSciNet): MR94k:62001
Zentralblatt MATH: 0711.01030
PEARSON, E. S. and KENDALL, M. G. 1970. Studies in the History of Statistics and Probability. Griffin, London.
Mathematical Reviews (MathSciNet): MR51:1889
PEARSON, K. 1902. On the sy stematic fitting of curves to observations and measurements. Biometrika 1 265 303. Z.
SMITH, C. A. B. 1986. The development of human linkage analysis. Annals of Human Genetics 50 293 311.
Mathematical Reviews (MathSciNet): MR874222
Digital Object Identifier: doi:10.1111/j.1469-1809.1986.tb01035.x
SOPER, H. E., YOUNG, A. W., CAVE, B. M., LEE, A. and PEARSON, Z. K. 1917. On the distribution of the correlation coefficient in small samples. Appendix II to the papers of `Student' and R. A. Fisher. A cooperative study. Biometrika 11 328 413. Z.
STIGLER, S. M. 1983. Who discovered Bay es's Theorem? Amer. Statist. 37 290 296. Z.
STIGLER, S. M. 1986. Laplace's 1774 memoir on inverse probability. Statist. Sci. 1 359 378. Z.
Mathematical Reviews (MathSciNet): MR858515
Digital Object Identifier: doi:10.1214/ss/1177013620
Project Euclid: euclid.ss/1177013620
TODHUNTER, I. 1865. A History of the Mathematical Theory of Probability. Macmillan, Cambridge and London. Reprinted Z. 1965 by Chelsea, New York. Z.
VENN, J. 1866. The Logic of Chance. Macmillan, Cambridge and London. Z.
ZABELL, S. 1989. R. A. Fisher on the history of inverse probability. Statist. Sci. 4 247 263.
Zentralblatt MATH: 0955.01501
Mathematical Reviews (MathSciNet): MR1015275
Digital Object Identifier: doi:10.1214/ss/1177012488
Project Euclid: euclid.ss/1177012488