8/16/01

 

STA6934:  R. A. Fisher in the 21st Century

 

MWF, Period 5, GF230

 

George Casella

 

·        This class will be organized as a discussion seminar. 

 

·        Each week a discussion leader will choose a topic for discussion, identify a paper or portion of a paper by Fisher relevant to the topic along with a more current paper. 

 

·        Casella will lead the discussion for the first few periods. 

 

·        After that, class participants will be responsible for reading the paper before the class (expect a quiz!) and leading a discussion once or twice during the semester. 

 

·        The discussion leader will

§         One week prior to the discussion, provide the class with

§         A two or three sentence description of the topic of interest,

§         The Fisher and more current reference (or urls),

§         A couple of points to consider for discussion.

§         Start the discussion with a short (15 minute) presentation to focus ideas and then lead a class discussion

 

·        To start off

 

o       Weds 8/22: Organizational meeting

o       Mon 8/27:  No Class (Casella out of town)

o       Weds 9/5:  Barnard (1990), Efron (1998)

o       Mon 9/10 - Wed 9/12:  Fisher (1922) and Savage (1976).

o       Mon 9/17 - Wed 9/19:  Fisher (1922), Fisher (1925) and Savage (1976) continued.

o       Mon 9/24: Class participant discussions begin.

 

 

Possible Topic

Fisher’s paper(s)

Later paper(s)

sufficiency

1925

Stigler 1973

ancillarity

 

Barndorff-Nielsen 1983

Basu Chapter I

Buehler JASA 1982

Information

1925

Basu Chapter I

Efron/Hinkley 1978

likelihood

1925,1934

Barndorff-Nielsen 1983

Efron 1982

Reid 1995

estimation

1922,1925

Rao 1947, Hodges/Lehmann 1951

design

1926

 

randomization

Design of Experiments

Basu Chapters XV, XVI

p-values

 

 

conditioning

 

 

confidence

 

 

testing

 

Lehmann/Scheffe 1951

Inference (fiducial and otherwise)

 

Basu Chapter III

Lindley 1958, Seidenfeld 1992, Zabell 1992

Generalized linear Models

1935 Appendix to Bliss' paper

Wedderburn 1974, Firth 1987, McCullagh, 1983, Lindsay, 1982 Lindsay/Li 1997

Fisher's exact test

 

Berger/Boos 1994

Mehta/Patel 1983

 

Suggested Discussion Questions for Fisher’s papers:

 

1.      What motivated Fisher to address this topic?

2.      What was new or novel at the time?

3.      What statistical principles are presented?  Give an example of one.

4.      What statistical results are presented? Give an example of one.

5.      What was Fisher’s view of the usefulness?

6.      Are the principles and procedures relevant today?

 

 

Suggested Discussion Questions for more recent papers:

 

  1. What principles/procedures are addressed?
  2. How does the content relate to Fisher’s work? Give an example.
  3. What statistical results are presented? How do they relate/extend to Fisher’s work?  Give an example of one

4.      Why didn't Fisher develop the ideas himself?           

 

References -Fisher's Papers

 

1.      Theory of Statistical Estimation.  Proc.  Cambridge Philos.  Soc 22 200-225.  Efron's choice for the most important single paper in statistical theory.

2.      The arrangement of field experiments.  J Ministry Agric.  Great Brit. 33 503-513.

3.      Inverse Probability. Proc. of the Cambridge Philosophical Society 26, 528-535.

4.      Two new properties of mathematical likelihood.  Proc.  Roy.  Soc.  Ser.  A 144 285-307.

5.      The Fiducial Argument in Statistical Inference.  Annals of Eugenics 6, 391-398. (Also in R. A. Fisher, Contributions to Mathematical Statistics, New York:  Wiley, 1950.)

 

Fisher’s papers are available to download from the University of Adelaide, http://www.library.adelaide.edu.au/digitised/fisher/

 

 

References -Other Papers

 

 

  1. Barndorff-Nielsen, O.  (1983).  On a formula for the distribution of the maximum likelihood estimator. Biometrika 70 343-365.
  2. Barnard, G.  (1990).  Fisher:  A Retrospective.  Chance 3 22-32.
  3. Basu, D.  (1964).  Recovery of ancillary information.  Contributions to Statistics, Pergammon Press, Oxford 7-20.  Republished in Sankhya 26 (1964) 3-16.  (All of the Basu references have been collected in Statistical Information and Likelihood:  A Collection of Critical Essays  edited by J. K. Ghosh,  Springer Lecture Notes in Statistics No. 45, 1988.  This is Chapter I.
  4. Basu, D.  (1975).  Statistical information and likelihood (with discussion). Sankhya A 37  1-71.  Reprinted as Chapters II-V of Statistical Information and Likelihood
  5. Basu, D.  (1980).  Randomization analysis of experimental data:  The Fisher randomization test (with discussion). J. Amer. Statist. Assoc. 75 575-595. Reprinted as Chapters XV and XVI of Statistical Information and Likelihood
  6. Basu, D.  (1981).  On ancillary statistics, pivotal quantities and confidence statements. Topics in Applied Statistics (Y. P. Chaubey and T. D. Dwivedi, eds.)  Concordia University, Montreal.  Reprinted as Chapter IX of Statistical Information and Likelihood
  7. Berger, Roger L. and Boos, Dennis D. (1994).  P values maximized over a confidence set for the nuisance parameter.  J Amer.  Statist.  Assoc. 89: 1012-1016
  8. Bliss, C. (1935).  The calculation of the dose-mortality curve.  Annals of Applied Biology 22: 134-167.
  9. Buehler, R. J.  (1982).  Some ancillary statistics and their properties. J. Amer. Statist. Assoc. 77 581-589
  10. Efron, B. (1982). Maximum likelihood and decision theory. Annals of Statistics 10 340-356.
  11. Efron, B.  (1998).  R. A. Fisher in the 21st Century (with discussion).  Statistical Science 13 95-122.
  12. Efron, B.  and  Hinkley, D.  (1978).  Assessing the accuracy of the maximum likelihood estimator: observed vs. expected Fisher information.  Biometrika 65 457-487.
  13. Firth, D.  On the efficiency of quasi-likelihood estimation.  Biometrika 74, 233-245.
  14. Hodges, J. L., Jr , and Lehmann, E. L.  (1951).  Some applications of the Cramér-Rao inequality,   Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 13-22.
  15. Lehmann, E. L. and Scheffe, H.  (1951).  Completeness, Similar Regions, and Unbiased Estimation – Part I.  Sankhya 10, 305-340.
  16. Lindley, D. V. (1958).  Fiducial distributions and Bayes' theorem.  J Roy.  Statist. Soc.  Ser.  B 20: 102-107
  17. Lindsay, Bruce. (1982).  Conditional score functions: some optimality results. Biometrika 69: 503-512
  18. Lindsay, Bruce G.; Li, Bing. (1997).  On second-order optimality of the observed Fisher information.  Ann.  Statist. 25: 2172-2199

19.  McCullagh, Peter. (1983).  Quasilikelihood functions.  Ann.  Statist. 11: 59-67.

20.  Mehta, Cyrus R. and Patel, Nitin R. (I 983).  A network algorithm for performing Fisher's exact test in r x c contingency tables.  J Amer.  Statist.  Assoc. 78: 427-434.

21.  Rao, C. R.  (1947?)  Information and the accuracy attainable in the estimation of statistical parameters.  ??

22.  Rao, C. R.  (1947?)  Sufficient statistics and minimum variance estimates.  ??

23.  Reid, N. (I 995).  The roles of conditioning in inference (with discussion).  Statistical Science 10 138-157.

24.  Savage, L. J. (1976).  On Rereading R. A. Fisher (with discussion).  Annals of Statistics 4 441-500

25.  Seidenfeld, T.  (1992).  R. A. Fisher’s Fiducial Argument and Bayes Theorem.  Statistical Science 7, 358-368.

26.  Stigler, S. M. (1973).  Studies in the history of probability and statistics XXXII. Biometrika 60 39-445.

27.  Wedderburn, R. W. M. (1974).  Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method.  Biometrika 61: 439-447.

28.  Zabell, S.  (1992).  R. A. Fisher and the Fiducial Argument.  Statistical Science 7, 339-387.