## Statistical Science

- Statist. Sci.
- Volume 13, Number 2 (1998), 95-122.

### R. A. Fisher in the 21st century (Invited paper presented at the 1996 R. A. Fisher Lecture)

**Full-text: Open access**

#### Abstract

Fisher is the single most important figure in 20th century statistics. This talk examines his influence on modern statistical thinking, trying to predict how Fisherian we can expect the 21st century to be. Fisher's philosophy is characterized as a series of shrewd compromises between the Bayesian and frequentist viewpoints, augmented by some unique characteristics that are particularly useful in applied problems. Several current research topics are examined with an eye toward Fisherian influence, or the lack of it, and what this portends for future statistical developments. Based on the 1996 Fisher lecture, the article closely follows the text of that talk.

#### Article information

**Source**

Statist. Sci. Volume 13, Number 2 (1998), 95-122.

**Dates**

First available in Project Euclid: 9 August 2002

**Permanent link to this document**

http://projecteuclid.org/euclid.ss/1028905930

**Digital Object Identifier**

doi:10.1214/ss/1028905930

**Mathematical Reviews number (MathSciNet)**

MR1647499

**Zentralblatt MATH identifier**

01571027

**Keywords**

Statistical inference Bayes frequentist fiducial empirical Bayes model selection bootstrap confidence intervals

#### Citation

Efron, Bradley. R. A. Fisher in the 21st century (Invited paper presented at the 1996 R. A. Fisher Lecture). Statist. Sci. 13 (1998), no. 2, 95--122. doi:10.1214/ss/1028905930. http://projecteuclid.org/euclid.ss/1028905930.

#### References

- SAVAGE, L. J. H. 1976. On rereading R. A. Fisher with discus. Z sion. Ann. Statist. 4 441 500. Savage say s that Fisher's work greatly influenced his seminal book on subjective Bayesianism. Fisher's great ideas are examined lovingly. here, but not uncritically.Z. Mathematical Reviews (MathSciNet): MR53:7698

Zentralblatt MATH: 0325.62008

Digital Object Identifier: doi: 10.1214/aos/1176343456

Project Euclid: euclid.aos/1176343456 - YATES, F. and MATHER K. 1971. Ronald Ay lmer Fisher. In Z. Collected Papers of R. A. Fisher K. Mather, ed. 1 23 52. Z Univ. Adelaide Press. Reprinted from a 1963 Roy al Statistical Society memoir. Gives a nontechnical assessment of. Fisher's ideas, personality and attitudes toward science. Z. Z
- BOX, J. F. 1978. The Life of a Scientist. Wiley, New York. This is both a personal and an intellectual biography by Fisher's daughter, a scientist in her own right and also an historian of science, containing some unforgettable vignettes of precocious mathematical genius mixed with a difficulty in ordinary human interaction. The sparrow quote in Section 4 is. put in context on page 130.Mathematical Reviews (MathSciNet): MR500579
- FISHER, R. A. 1925. Theory of statistical estimation. Proc. Z Cambridge Philos. Soc. 22 200 225. Reprinted in the Mather collection, and also in the 1950 Wiley Fisher collection Contributions to Mathematical Statistics. This is my choice for the most important single paper in statistical theory. A competitor might be Fisher's 1922 Philosophical Society paper, but as Fisher himself points out in the Wiley collection, the 1925 paper is more compact and businesslike. than was possible in 1922, and more sophisticated as well. Z. EFRON B. 1995. The statistical century. Roy al Statistical SociZ. Z ety News 22 5 1 2. This is mostly about the postwar boom in statistical methodology and uses a different statistical. triangle than Figure 8.
- FISHER, R. A. 1934. Two new properties of mathematical likeliZ hood. Proc. Roy. Soc. Ser. A 144 285 307. Concerns two situations when fully efficient estimation is possible in finite samples: one-parameter exponential families, where the MLE is a sufficient statistic, and location scale families, where there are exhaustive ancillary statistics. Reprinted in. the Mather and the Wiley collections. Section 4 Z.
- EFRON, B. 1978. Controversies in the foundations of statistics. Z Amer. Math. Monthly 85 231 246. The Bay es Frequentist Fisherian argument in terms of what kinds of averages should the statistician take. Includes Fisher's famous circle. example of ancillarity. Z. Mathematical Reviews (MathSciNet): MR58:7950

Digital Object Identifier: doi: 10.2307/2321163

JSTOR: links.jstor.org - EFRON, B. 1982. Maximum likelihood and decision theory. Ann. Z Statist. 10 240 356. Examines five questions concerning maximum likelihood estimation: What kind of theory is it? How is it used in practice? How does it look from a frequentistic decision-theory point of view? What are its principal virtues and defects? What improvements have been sug. gested by decision theory? Z. Mathematical Reviews (MathSciNet): MR83j:62006

Zentralblatt MATH: 0494.62004

Digital Object Identifier: doi: 10.1214/aos/1176345778

Project Euclid: euclid.aos/1176345778 - CIFARELLI, D. and REGAZZINI, E. 1996. De Finetti's contribution to probability and statistics. Statist. Sci. 11 253 282. The second half of the quote in my Section 4, their Section 3.2.2, goes on to criticize the Ney man Pearson school. De Finetti is less kind to Fisher in the discussion following Savage's Z. 1976 article.Mathematical Reviews (MathSciNet): MR98b:01033

Digital Object Identifier: doi: 10.1214/ss/1032280303

Project Euclid: euclid.ss/1032280303 - DICICCIO, T. and EFRON, B. 1996. Bootstrap confidence interZ. Z vals with discussion. Statist. Sci. 11 189 228. Presents and discusses the cd4 data of Figure 2. The bootstrap confi-. dence limits in Table 1 were obtained by the BC method. aMathematical Reviews (MathSciNet): MR1436647

Digital Object Identifier: doi: 10.1214/ss/1032280214

Project Euclid: euclid.ss/1032280214 - REID, N. 1995. The roles of conditioning in inference. Statist. Sci. 10 138 157. This is a survey of the p formula, what I called the magic formula following Ghosh's terminology, and many other topics in conditional inference; see also the Z. discussion following the companion article on pages 173 199, in particular McCullagh's commentary. Gives an extensive bibliography.Z. Zentralblatt MATH: 0955.62524

Mathematical Reviews (MathSciNet): MR1368097

Digital Object Identifier: doi: 10.1214/ss/1177010027

Project Euclid: euclid.ss/1177010027 - EFRON, B. and HINKLEY, D. 1978. Assessing the accuracy of the maximum likelihood estimator: observed versus expected Z Fisher information. Biometrika 65 457 487. Concerns ancillarity, approximate ancillarity and the assessment of ac. curacy for a MLE.Mathematical Reviews (MathSciNet): MR80g:62021

Zentralblatt MATH: 0401.62002

Digital Object Identifier: doi: 10.1093/biomet/65.3.457

JSTOR: links.jstor.org - EFRON, B. 1993. Bay es and likelihood calculations from conZ fidence intervals. Biometrika 80 3 26. Shows how approximate confidence intervals can be used to get good approximate confidence densities, even in complicated prob. lems with a great many nuisance parameters.Mathematical Reviews (MathSciNet): MR1225211

Zentralblatt MATH: 0773.62021

Digital Object Identifier: doi: 10.1093/biomet/80.1.3

JSTOR: links.jstor.org - EFRON, B. and GONG, G. 1983. A leisurely look at the bootstrap, the jackknife, and cross-validation. Amer. Statist. 37 36 48. ZThe chronic hepatitis example is discussed in Section 10 of. this bootstrap jackknife survey article. Z. O'HAGAN, A. 1995. Fractional Bay es factors for model compariZ. son with discussion. J. Roy. Statist. Soc. Ser. B 57 99 138. ZThis paper and the ensuing discussion, occasionally rather heated, give a nice sense of Bayesian model selection in the. Jeffrey s tradition. Z. Mathematical Reviews (MathSciNet): MR694281

Digital Object Identifier: doi: 10.2307/2685844

JSTOR: links.jstor.org - KASS, R. and RAFTERY, A. 1995. Bay es factors. J. Amer. Statist. Z Soc. 90 773 795. This review of Bayesian model selection features five specific applications and an enormous bibliog. raphy.
- EFRON, B. 1996. Empirical Bay es methods for combining likelihoods. J. Amer. Statist. Assoc. 91 538 565.Mathematical Reviews (MathSciNet): MR97c:62018

Zentralblatt MATH: 0868.62018

Digital Object Identifier: doi: 10.2307/2291646

JSTOR: links.jstor.org - KASS, R. and WASSERMAN, L. 1996. The selection of prior distributions by formal rules. J. Amer. Statist. Assoc. 91 Z 1343 1370. Begins ``Subjectivism has become the dominant philosophical tradition for Bayesian inference. Yet in practice, most Bayesian analyses are performed with so-called. noninformative priors.... ''Mathematical Reviews (MathSciNet): MR1478684

Digital Object Identifier: doi: 10.1214/lnms/1215453065 - LINDLEY, D. V. 1974. The future of statistics a Bayesian 21st century. In Proceedings of the Conference on Directions for Mathematical Statistics. Univ. College, London. Z.
- SMITH, A. 1995. A conversation with Dennis Lindley. Statist. Z Sci. 10 305 319. This is a nice view of Bayesians and. Bayesianism. The 2020 prediction is attributed to de Finetti.Zentralblatt MATH: 0955.01546

Mathematical Reviews (MathSciNet): MR1390520

Digital Object Identifier: doi: 10.1214/ss/1177009940

Project Euclid: euclid.ss/1177009940 - , A so that density and likelihood have the form Z. Z. f, A and L ;, A ; the amplified formulas would then appear as
- , for example. The confidence density approach gives sensible results in such situations. My 1993 Biometrika paper argues, a la Kass, that this is a way of using frequentist methods to aid Bayesian calculations. Z. 4 Professor Hinkley notes the continued vitality of Tukey-sty le data analysis. In its purest form this line of work is statistics without probability theory Zsee, e.g., Mosteller and Tukey's 1977 book ``Data. Analy sis and Regression'' and as such I could not place it any where in the statistical triangle of Section 11. This is my picture's fault of course, not Tukey's. Problem-driven areas like neural networks often begin with a healthy burst of pure data analysis before settling down to an accommodation with statistical theory. Z. 5 I am grateful to Professor Fraser for presenting a more intelligible version of the magic formula. This was the spot in the talk where ``avoiding technicalities'' almost avoided coherency. ``Trick'' is a positive word in my vocabulary, reflecting a Caltech education, and I only wish I could think of some more Fisher-level tricks. Fisherian statistics was
- BENNETT, J. H. 1972. Collected Papers of R. A. Fisher. Univ. Adelaide Press. Z.
- BENNETT, J. H., ed. 1990. Statistical Inference and Analy sis. Selected Correspondence of R. A. Fisher. Oxford Univ. Press. Z.
- COX, D. R. 1982. A remark on randomization in clinical trials. Z. Utilitas Math. 21A 245 252. Birthday volume for F. Yates. Z.
- DEMPSTER, A. P. 1971. Model searching and estimation in the logic of inference. In Foundations of Statistical Inference Z. V. P. Godambe and D. A. Sprott, eds. 56 78. Holt, Rinehart and Winston, Toronto. Z. Mathematical Reviews (MathSciNet): MR53:6810
- EFRON, B. 1971. Forcing a sequential experiment to be balanced. Biometrika 58 403 417. Z. Z Mathematical Reviews (MathSciNet): MR47:1216

Zentralblatt MATH: 0226.62086

Digital Object Identifier: doi: 10.1093/biomet/58.3.403

JSTOR: links.jstor.org - EFRON, B. 1987. Better bootstrap confidence intervals with. discussion. J. Amer. Statist. Assoc. 82 171 200. Z. Mathematical Reviews (MathSciNet): MR88m:62053

Zentralblatt MATH: 0622.62039

Digital Object Identifier: doi: 10.2307/2289144

JSTOR: links.jstor.org - FISHER, R. A. 1928. Correlation coefficients in meteorology. Nature 121 712. Z.
- FISHER, R. A. 1929. Statistics and biological research. Nature 124 266 267. Z.
- FISHER, R. A. 1935. Design of Experiments. Oliver and Boy d, Edinburgh.Z.
- FISHER, R. A. 1956. Statistical Methods and Scientific InferZ ence. Oliver and Boy d, Edinburgh. Slightly revised versions. appeared in 1958 and 1960. Z.
- FISHER, R. A. 1958. The nature of probability. Centennial Review 2 261 274. Z.
- GELMAN, A., MENG, X.-L. and STERN, H. 1996. Posterior predicZ. tive assessments of model fitness with discussion. Statist. Sinica 6 773 807. Z.
- HALD, A. 1981. T. N. Thiele's contributions to statistics. Internat. Statist. Rev. 49 1 20. Z. Zentralblatt MATH: 0467.62003

Mathematical Reviews (MathSciNet): MR623007

Digital Object Identifier: doi: 10.2307/1403034

JSTOR: links.jstor.org - LANE, D. A. 1980. Fisher, Jeffrey s and the nature of probability. R. A. Fisher: An Appreciation Lecture Notes in Statist. 1. Springer, New York. Z. Mathematical Reviews (MathSciNet): MR82m:01061
- MAHALANOBIS, P. C. 1938. Professor Ronald Ay lmer Fisher. Sankhy a 4 265 272. Z.
- NEy MAN, J. 1977. Frequentist probability and frequentist statistics. Sy nthese 36 97 131. Z. Mathematical Reviews (MathSciNet): MR58:31490

Zentralblatt MATH: 0372.60002

Digital Object Identifier: doi: 10.1007/BF00485695 - RIPLEY, B. D. 1996. Pattern Recognition and Neural Networks. Cambridge Univ. Press. Z. Mathematical Reviews (MathSciNet): MR98a:68161
- SAVAGE, L. J. 1976. On rereading R. A. Fisher. Ann. Statist. 4 441 483. Z. Mathematical Reviews (MathSciNet): MR53:7698

Zentralblatt MATH: 0325.62008

Digital Object Identifier: doi: 10.1214/aos/1176343456

Project Euclid: euclid.aos/1176343456 - YATES, F. 1970. Experimental Design. Selected Papers of Frank Yates, C.B.E., F.R.S. Griffin, London.

#### See also

- Includes: D. R. Cox. Comment by D. R. Cox.
- Includes: Rob Kass. Comment by Rob Kass.
- Includes: Ole E. Barndorff-Nielsen. Comment by Ole E. Barndorff-Nielsen.
- Includes: D. V. Hinkley. Comment by D. V. Hinkley.
- Includes: D. A. S. Fraser. Comment by D. A. S. Fraser.
- Includes: A. P. Dempster. Comment by A. P. Dempster.
- Includes: Bradley Efron. Rejoinder by Bradley Efron.

### More like this

- R. A. Fisher: The Founder of Modern Statistics

Rao, C. Radhakrishna, Statistical Science, 1992 - The Interface Between Statistics and Philosophy of Science

Good, I. J., Statistical Science, 1988 - The Future of Indirect Evidence

Efron, Bradley, Statistical Science, 2010

- R. A. Fisher: The Founder of Modern Statistics

Rao, C. Radhakrishna, Statistical Science, 1992 - The Interface Between Statistics and Philosophy of Science

Good, I. J., Statistical Science, 1988 - The Future of Indirect Evidence

Efron, Bradley, Statistical Science, 2010 - R. A. Fisher on the History of Inverse Probability

Zabell, Sandy, Statistical Science, 1989 - 19th Century Logic between Philosophy and Mathematics

Peckhaus, Volker, Bulletin of Symbolic Logic, 1999 - The 1988 Wald Memorial Lectures: The Present Position in Bayesian Statistics

Lindley, Dennis V., Statistical Science, 1990 - On formalism freeness: Implementing Gödel's 1946 Princeton bicentennial lecture

Kennedy, Juliette, Bulletin of Symbolic Logic, 2013 - Introduction to R.A. Fisher on inverse probability and likelihood

Fienberg, Stephen E., Statistical Science, 1997 - Fisher in 1921

Stigler, Stephen, Statistical Science, 2005 - Applied probability before 1964, and after 2014

Kingman, J. F. C., Journal of Applied Probability, 2014