Statistical Science

R.A. Fisher and the making of maximum likelihood 1912-1922

John Aldrich

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In 1922 R. A. Fisher introduced the method of maximum likelihood. He first presented the numerical procedure in 1912. This paper considers Fisher's changing justifications for the method, the concepts he developed around it (including likelihood, sufficiency, efficiency and information) and the approaches he discarded (including inverse probability).

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Statist. Sci., Volume 12, Number 3 (1997), 162-176.

First available in Project Euclid: 22 August 2002

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Fisher Pearson Student Bayes's postulate inverse probability maximum likelihood sufficiency efficiency information


Aldrich, John. R.A. Fisher and the making of maximum likelihood 1912-1922. Statist. Sci. 12 (1997), no. 3, 162--176. doi:10.1214/ss/1030037906.

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  • BENNETT, J. H., ed. 1971. Collected Papers of R. A. Fisher 1-5. Adelaide Univ. Press. Z.
  • BENNETT, J. H., ed. 1983. Natural Selection, Heredity, and Eugenics. Oxford Univ. Press. Z.
  • BENNETT, J. H., ed. 1990. Statistical Inference and Analy sis: Selected Correspondence of R. A. Fisher. Oxford Univ. Press. Z.
  • BENNETT, T. L. 1908. Errors of observation. Technical Lecture 4, Cairo, Ministry of Finance, Survey Department Egy pt. Z.
  • BOX, J. F. 1978. R. A. Fisher: The Life of a Scientist. Wiley, New York. Z.
  • BRUNT, D. 1917. The Combination of Observations. Cambridge Univ. Press. Z.
  • CHAUVENET, W. 1891. A Manual of Spherical and Practical
  • CONNIFFE, D. 1992. Key nes on probability and statistical inference and the links to Fisher. Cambridge Journal of Economics 16 475 489. Z.
  • EDDINGTON, A. S. 1914. Stellar Movements and the Structure of the Universe. Macmillan, New York. Z.
  • EDGEWORTH, F. Y. 1908. On the probable errors of frequency constants. J. Roy. Statist. Soc. 71 381 397, 499 512, 651 678; 72 81 90. Z.
  • EDWARDS, A. W. F. 1972. Likelihood. Cambridge Univ. Press. Z.
  • EDWARDS, A. W. F. 1974. The history of likelihood. Internat. Statist. Rev. 42 9 15. Z.
  • EDWARDS, A. W. F. 1994. What did Fisher mean by `inverse probability' in 1912 22? In Three contributions to the history of statistics, Preprint 3, Inst. Mathematical Statistics, Univ. Copenhagen. Z.
  • EFRON, B. 1982. Maximum likelihood and decision theory. Ann. Statist. 10 340 356. Z.
  • FIENBERG, S. E. and HINKLEY, D. V., eds. 1980. R. A. Fisher: An Appreciation. Springer, New York. Z.
  • FISHER, R. A. 1911. Mendelism and biometry. Unpublished
  • FISHER, R. A. 1912. On an absolute criterion for fitting fre quency curves. Messenger of Mathematics 41 155 160. CP1 Z. in Bennet 1971, vol. 1. Z.
  • FISHER, R. A. 1915. Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large
  • FISHER, R. A. 1918. The correlation between relatives on the supposition of Mendelian inheritance. Transactions of the Roy al Society of Edinburgh 52 399 433. CP9 in Bennett Z. 1971, vol. 1. Z.
  • FISHER, R. A. 1919. The genesis of twins. Genetics 4 489 499.
  • FISHER, R. A. 1920. A mathematical examination of the methods of determining the accuracy of an observation by the mean error, and by the mean square error. Monthly Notices of the Roy al Astronomical Society 80 758 770. CP12 in Z. Bennett 1971, vol. 1. Z.
  • FISHER, R. A. 1921. On the ``probable error'' of a coefficient of correlation deduced from a small sample. Metron 1 3 32.
  • FISHER, R. A. 1922a. On the mathematical foundations of theoretical statistics. Philos. Trans. Roy. Soc. London Ser. A
  • FISHER, R. A. 1922b. The goodness of fit of regression formulae, and the distribution of regression coefficients. J. Roy.
  • FISHER, R. A. 1923. Note on Dr. Burnside's recent paper on errors of observation. Proc. Cambridge Philos. Soc. 21
  • FISHER, R. A. 1925a. Theory of statistical estimation. Proc.
  • FISHER, R. A. 1925b. Statistical Methods for Research Workers. Oliver & Boy d, Edinburgh. Z.
  • FISHER, R. A. 1930. Inverse probability. Proc. Cambridge Ph
  • FISHER, R. A. 1934a. Two new properties of mathematical likelihood. Proc. Roy. Soc. Ser. A 144 285 307. CP108 in Z. Bennett 1971, vol. 3. Z.
  • FISHER, R. A. 1934b. Discussion on ``On the two different aspects of the representative method,'' by J. Ney man. J. Roy. Statist. Soc. 97 614 619. Z.
  • FISHER, R. A. 1971. Statistical Methods and Scientific InferZ ence, 3rd ed. Hafner, New York. First edition published in. 1956. Z.
  • FISHER, R. A., THORNTON, H. G. and MACKENZIE, W. A. 1922. The accuracy of the plating method of estimating the density of bacterial populations. Annals of Applied Biology 9
  • GALTON, F. 1889. Natural Inheritance. Macmillan, London. Z.
  • GAUSS, C. F. 1809. Theoria Motus Corporum Coelestium. ExZ. tract in Trotter 1957, pp. 127 147. Z.
  • GAUSS, C. F. 1816. Bestimmung der Genauigkeit der Beobac
  • GAUSS, C. F. 1821. Theoria combinationis observationum e
  • GEISSER, S. 1980. Basic theory of the 1922 mathematical statisZ tics paper. In R. A. Fisher: An Appreciation S. E. Fienberg. and D. V. Hinkley, eds. 59 66. Springer, New York. Z.
  • KEy NES, J. M. 1911. The principal averages and the laws of error which lead to them. J. Roy. Statist. Soc. 74 322 331. Z.
  • MACKENZIE, D. A. 1981. Statistics in Britain 1865 1930. Edinburgh Univ. Press. Z.
  • MERRIMAN, M. 1884. A Textbook on the Method of Least Squares. Z. Wiley, New York. Eighth edition, 1911. Z.
  • NEy MAN, J. 1934. On the two different aspects of the represenZ. tative method with discussion. J. Roy. Statist. Soc. 97 587 651. 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. Z.
  • PEARSON, E. S. 1990. ``Student,'' A Statistical Biography of Z William Sealy Gosset edited and augmented by R. L.. Plackett with the assistance of G. A. Barnard. Oxford Univ. Press. Z.
  • PEARSON, K. 1892. The Grammar of Science. White, London. Z.
  • PEARSON, K. 1894. Contribution to the mathematical theory of evolution. Philos. Trans. Roy. Soc. London Ser. A 185 71 110. Z.
  • PEARSON, K. 1894 1896. Lectures on the Theory of Statistics Z 1 5. Five volumes of notes taken by Yule. Item 84 2 in. Pearson collection, University College, London. Z.
  • PEARSON, K. 1896. Mathematical contributions to the theory of evolution, III. Regression, heredity and panmixia. Philos. Trans. Roy. Soc. London Ser. A 187 253 318. Z.
  • PEARSON, K. 1902. On the sy stematic fitting of curves to observations and measurements, parts I and II. Biometrika 1 265 303; 2 1 23. Z.
  • PEARSON, K. 1907. On the influence of past experience on future expectation. Philosophical Magazine 13 365 378. Z.
  • PEARSON, K. 1915. On the distribution of the standard deviations of small samples: appendix I to papers by ``Student'' and R. A. Fisher. Biometrika 10 522 529.
  • PEARSON, K. 1920. Notes on the history of correlation. Biometrika 13 25 45. Z.
  • PEARSON, K. 1936. Method of moments and method of maximum likelihood. Biometrika 28 34 59. Z.
  • PEARSON, K. and FILON, L. N. G. 1898. Mathematical contributions to the theory of evolution IV. On the probable errors of frequency constants and on the influence of random selection on variation and correlation. Philos. Trans. Roy. Soc. Ser. A 191 229 311. Z.
  • PLACKETT, R. L. 1972. The discovery of the method of least squares. Biometrika 67 239 251. Z.
  • PLACKETT, R. L. 1989. Discussion of ``R. A. Fisher on the history of inverse probability'' by S. Zabell. Statist. Sci. 4 256 258. Z.
  • PRATT, J. W. 1976. F. Y. Edgeworth and R. A. Fisher on the efficiency of maximum likelihood estimation. Ann. Statist. 4 501 514.Z. Z.
  • SAVAGE, L. J. 1976. On rereading R. A. Fisher with discussion. Ann. Statist. 4 441 500. Z.
  • SMITH, K. 1916. On the ``Best'' values of the constants in frequency distributions. Biometrika 11 262 276. Z.
  • SOPER, H. E. 1913. On the probable error of the correlation coeffcient to a second approximation. Biometrika 9 91 115.
  • 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. 1973. Laplace, Fisher and the discovery of the concept of sufficiency. Biometrika 60 439 445. Z.
  • STIGLER, S. M. 1986. A History of Statistics. Belnap, Cambridge. Z. STUDENT 1908a. The probable error of a mean. Biometrika 6 1 25.Z. STUDENT 1908b. Probable error of a correlation coefficient. Biometrika 6 302 310. Z. Z.
  • TROTTER, H. F. 1957. Gauss's work 1803 1826 on the theory of least squares. Technical Report 5, Statistical Techniques Research Group, Princeton Univ. Z.
  • WELCH, B. L. 1958. ``Student'' and small sample theory. J. Amer. Statist. Assoc. 53 777 788. Z.
  • YULE, G. U. 1897. On the theory of correlation. J. Roy. Statist. Soc. 60 812 854. Z.
  • ZABELL, S. 1989. R. A. Fisher on the history of inverse probabilZ. ity with discussion. Statist. Sci. 4 247 263.