0.1 I. j. good: an appreciation

By this time I had begun to assemble a collection of reprints and other copies of Jack's papers. I recall writing to him and asking fora copy of one and receiving a remarkable note in return. the key paragraph went something like:

According to my files I sent you a reprint of the requested paper on December 17, 1970. I am enclosing a copy of my short publicationlist, and suggest you request a different paper.

Of course, by then Jack's short publication list was longer than virtually any of the papers, and I dutifully made a differentselection!

While working on my book with Yvonne Bishop and Paul Holland (1975), I had repeated occasionsto go back to Jack's papers. One that I studied in particular, not yet mentioned, was his 1953 paper on the frequency offrequencies (Good, 1954) which suggests a method for summarizing large contingency tables by tabulating the frequency of thefrequencies and then fitting distributions to it; this was also the “species” problem as in “How many words did Shakespeare know?”When it came time to choose a publisher for our book, an influential factor in our choice of MIT Press was the fact that it was thepublisher of Jack's 1965 book; that was company we were pleased to keep. Both his book and ours were mainstays in the MIT Presscatalogue for decades. As committed as Jack has been to the subjective Bayesian or personalprobability perspective, his research papers show a remarkably catholic perspective on approaches to inference, and he haswritten repeatedly and at length about the Bayes/non-Bayes-compromise, e.g., (Good and Crook, 1974), as a matter of methodological approachrather than simply one of practice. Fred Mosteller too shared this pluralistic perspective, although he was never a committedsubjectivist. This is part of the intellectual tradition to which I would like to be linked, being myself a true subjectivistphilosophically, but practically using lots of maximum likelihood tools and indeed anything else that I can justify heuristically if not philosophically. How many kinds of Bayesians are there? Accordingto Jack: 46,656 varieties (1971), and I suspect that several of these correspond to Jack wearing different hats, including hisalter ego, K. Caj Doog. See also (Good, 1983b).

The reprinting of a collection of Jack's papers in 1983 (Good, 1983a) gave me a bound version of some of his work tokeep close at hand and I have repeatedly referred to it, especially on matters on philosophy and on Bayesian and contingency table history.

Jack's interest in statistical fallacies and paradoxes is long-standing, including his 1968 encyclopediaarticle (Good, 1968) and his comment on Colin Blyth's article on Simpson's paradox (Good, 1972), so it was not a surprise when hewrote a lengthy piece on the topic, with new results and generalizations (Good and Mittal, 1985). It is a wonderful resourceand it has been used not only by me but also by students with whom I have worked.

A little over four years ago I set out to answer the question: When did Bayesian inference become “Bayesian,” i.e., when did the termsupplant “inverse probability”? I turned of course to several things that Jack had written, including the historical account in his1965 book on The Estimation of Probabilities and I shared an early draft of my findings with Jack.This prompted a couple of e-mail messages, a long letter, a mailing with reprints or Xerox copies of several papersdescribing his wartime work at Bletchley Park with Turing and later during the 1950s, several of which he had sent me before (I guess hehad stopped keeping track of the people to whom he had sent copies!), and a couple of telephone conversations. In the process I learnedmuch both about the evolution of Bayesian methods and ideas, and Jack's role in what I now refer to as the “neo-Bayesian revival”of the 1950s, a term he coined and a movement in which he played an important part. My paper (2006) would not have been thesame without him. And in case you are curious, he was not the first to write about “Bayesian inference,” even though he has many otherfirsts to his credit!

For me, virtually everything that Jack has written or opined about makes for “Good" reading and serious reflection—except perhaps forhis limericks. I'm very pleased to be able to contribute to the present collection.

References

Bishop, Y.M.M., S.E. Fienberg, and P.W. Holland (1975). Discrete Multivariate Analysis: Theory and Practice . MIT Press. Reprinted (2007) Springer-Verlag.

de Finetti, B. (1962). “Does It Make Sense To Speak Of `Good Probability Appraisers'?”

DeGroot, M.H. and S.E. Fienberg (1982). “Assessing Probability Assessors: Calibration andRefinement,” In S.S. Gupta and J.O. Berger, eds., Statistical Decision Theory and Related Topics III , Vol. 1, Academic Press, 291–314.

Fienberg, S.E. (2006). “When Did Baysian Inference Become “Bayesian”?” Bayesian Analysis , 1, 1–40.

Good, I.J. (1954). “The Population Frequencies of Species and the Estimation of Population Parameters,” Biometrika , 40, 237–264.

Good, I.J. (1956). “On the Estimation of Small Frequencies in Contingency Tables,” J. Roy. Statist. Soc., Series B , 18. 113–124.

Good, I.J., ed. (with the help of A.J. Mayne and John Maynard Smith) (1962). The Scientists Speculates: An Anthology of Partly-Baked Ideas, London, Heinmann, 1962 (Basic Books, New York, 1963; Paperback, Capricorn Books, New York, 1965.)

Good, I.J. (1963). “Maximum Entropy for Hypothesis Formulation, Especially for Multidimensional ContingencyTables,” Ann. Math. Statist. , 34, 911–934.

Good, I.J. (1965). The Estimation of Probabilities: An Essay on Modern Bayesian Methods. M.I.T. Press.

Good, I.J. (1968). “Fallacies, Statistical,” International Enc. Social Sciences , Macmillian and Free Press, 5, 292–301.

Good, I.J. (1969). “A Subjective Evaluation of Bode's Law and anObjective Test for Approximate Numerical Rationality (with discussion),” J. Amer. Statist. Assoc. , 64, 23–66.

Good, I.J. (1971) “46656 varieties of Bayesians.” Letter in American Statistician , 25: 62– 63. Reprinted in Good Thinking , (Good 1983a), pp. 20–21.

Good, I.J. (1972). “Comments on Colin Blyth's two papers: On Simpson's Paradox and the Sure-thing Principle and Some Probability Paradoxes in Choice From Among Random alternatives ,” J. Amer. Statist. Assoc. , 67, 374–375.

Good, I.J. and J.F. Crook (1974). “The Bayes/Non-Bayes Compromise and the Multinomial Distribution,” J. Amer. Statist. Assoc. , 69, 711–720.

Good, I.J. (1976). “On the Application of Symmetric Dirichlet distributions and their mixtures to contingencytables,” Ann. Statist. , 4, 1159–1189.

Good, I.J. (1983a). Good Thinking: The Foundations of Probability and its Applications. Univ. of Minnesota Press.

Good, I.J. (1983b). “Who is a Bayesian?” Letter in American Statistician 37 (Feb.), 95.

Good, I.J. and Y. Mittal (1985). “The Amalgamation and Geometry of Two-by-Two Contingency Tables,” Ann. Statist. , 15, 694–711.

Tukey, J.W., F. Mosteller, and S.E. Fienberg (1965). “Scoring Probability Forecasts." Department of Statistics,Harvard University, Memorandum NS-37.