Turing's anticipation of empirical bayes in connection with the cryptanalysis of the naval Enigma

Journal of Statistical Computation and Simulation

Volumn 66, Issue 2, 2000, Pages 101-111

  Good, I J ^a  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

Bletchley park; Coverage of a sample; Cryptology; Empirical bayes; Enigma; Language statistics; Probabilities of unobserved events; Species sampling; Turing; Word frequencies

Indexed keywords

EID: 0034349144     PISSN: 00949655     EISSN: None     Source Type: Journal    
DOI: 10.1080/00949650008812016     Document Type: Article

References (20)

1. Copeland, B. J. and Proudfoot, Diane "Alan Turing's forgotten ideas in computer science", Sc. Amer. (April, 1999). pp. 98-103.
2. Corbet, A. S., Fisher, R. A. and Williams, C. B. (1943) "The relation between the number of species and the number of individuals in a random sample of an animal population", J. Anim. Ecol., 12, 42-58. (The theory was due to Fisher.)
3. Erskine, R., Good, I. J. and Weiss, E. A. (1999) "Joan Murray: an obituary", Annals of the History of Computing, 21(4), scheduled for December.
4. Good, I. J. (1953) "The population frequencies of species and the estimation of population parameters", Biometrika, 40, 237-264. (Publication number 38.)
5. Good, I. J., "Statistics of language", In: Encyclopedia of Linguistics, Information and Control (Meetham, A. R. Ed., Pergamon Press, 1969), pp. 567-581. (Publication number 524.)
6. Good, I. J. (1968) Review of H. E. Robbins, "Estimating the total probability of the unobserved outcomes of an experiment", Annals Math. Statist., 39, 256-257; Math. Rev., 36 (1968), 929-930, Rev. No. 4747. (In this review, the word 'series' was a misprint for 'species'.) (Publication number 609.)
7. Good, I. J. (1968) Review of H. E. Robbins, "Estimating the total probability of the unobserved outcomes of an experiment", Annals Math. Statist., 39, 256-257; Math. Rev., 36 (1968), 929-930, Rev. No. 4747. (In this review, the word 'series' was a misprint for 'species'.) (Publication number 609.)
8. Good, I. J. (1976) "The Bayesian influence, or how to sweep subjectivism under the carpet", Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science (Proc. of a Conference in May, 1973 at the Univ. of W. Ontario Hooker, C. A. and Harper, W. Eds.), Vol. 2: Foundations and Philosophy of Statistical Inference, Dordrecht, Holland: Reidel (1976), pp. 125-174. (#838 was largely republished in #1364.) (Publication number 838.)
9. Good, I. J. (1976) "Goodness of fit for the distribution of species frequencies", M20, Communications in Statist., Simul. and Comput., B5(2,3), 143,144. (Publication number 1027.)
10. Good, I. J. (1979) "Turing's statistical work in World War II" (Studies in the history of probability and statistics. XXXVII.) Biometrika, 66, 393-396. (Publication number 1201.)
11. Good, I. J., Good Thinking: The Foundations of Probability and its Applications, University of Minnesota Press (Dec. 1, 1983). (Publication number 1364.)
12. Good, I. J. (1979) "Introductory remarks for the article in Biometrika, 66, 'A. M. Turing's statistical work in World War II", In: collected works of A. M. Turing. Pure Mathematics; with a special section on Turing's contributions to Statistics by I. J. Good (Britton, J. L. Ed., North Holland, 1992), pp. 211-223. (Publication number 1822.)
13. Good, I. J. (1991) Introduction to Herbert Robbins (1995), In: Breakthroughs in Statistics, Vol. 1 (Kotz, S. and Johnson, N. L. Eds., 1991, Springer), pp. 379-387. (Publication number 1851.)
14. Good, I. J., "Enigma and Fish", the version in the paperback edn. of Codebreakers: the inside story of Bletchley Park (Hinsley, F. H. and Alan Stripp, Eds., Oxford Univ. Press, 1994), Chap. 19, pp. 149-166, esp. pp. 155-156. The correction of the hardback edition on pp. 155-156 is due to Joan Clarke Murray (see Fig. 2). The publishers didn't mention that the paperback edition contained corrections to the hardback. Their reason was presumably that they didn't want to undermine the sales of the hardback which was a best seller. (Publication number 2117H.)
15. Good, I. J. and Toulmin, G. H. (1956) "The number of new species, and the increase of population coverage, when a sample is increased", Biometrika, 43, 45-63. (Publication number 86.)
16. Hodges, A. (1983) Alan Turing: the Enigma (Barnett Books, London).
17. Holdeman, L. V., Good, I. J. and Moore, W. E. C., "Human fecal flora: variation in bacterial composition within individuals and a possible effect of emotional stress", Applied and Environmental Microbiology, 31 (March, 1976), 359-375, esp. p. 373.
18. Kahn, David (1991) Seizing the Enigma: the Race to Break U-boat Codes (Houghton-Mifflin, Boston).
19. Robbins, Herbert, E. (1955) "An empirical Bayes approach to statistics", Proc. 3rd Berkeley Symp. Math. Statist. Prob., 1, 157-163. Reproduced in part in Breakthroughs in Statistics, 1 (Kotz, S. and Johnson, N. L. Eds.), 388-394.
20. Robbins, Herbert, E. (1955) "An empirical Bayes approach to statistics", Proc. 3rd Berkeley Symp. Math. Statist. Prob., 1, 157-163. Reproduced in part in Breakthroughs in Statistics, 1 (Kotz, S. and Johnson, N. L. Eds.), 388-394.