LETTER TO THE BOOKSHELF

# A letter regarding Tommaso Toffoli's review of *Probability Theory: The Logic of Science*

I was astonished to read, in Tommaso Toffoli's review of *Probability Theory: The Logic of Science*, by E. T. Jaynes, a gratuitous *ad hominem* attack on the late R. A. Fisher. How does it advance the debate on the relative merits of frequentist and Bayesian foundations of probability theory to directly slander Fisher as a "pooh-bah" (defined in my Concise Oxford Dictionary as a "pompous, self-important person"), and to write out his full name and titles, his (hard-earned) Cambridge education and honors in a way clearly meant to be mocking? Fisher died 42 years ago, and I did not know him personally; also I am not qualified to argue for or against his philosophy of statistical inference. But as a former agricultural researcher I can say that his contributions to statistics and experimental design for field and laboratory trials are worthy of respect. And as a member of Sigma Xi I can say that this kind of polemic has no place in a book review.

D. G. Rossiter

Department of Earth Systems Analysis

International Institute for Geo-Information Science and Earth Observation (ITC)

PO Box 6, 7500 AA Enschede, The Netherlands

*Reviewer Tommaso Toffoli replies:*

Dear Dr. Rossiter:

I'm sorry to hear that my review of E.T. Jaynes's book so aggrieved you.

Far from my mind was any intention to attack or ridicule Fisher. With the words that disturbed you I was attempting to succinctly convey the rationale for and the feelings that inspired some of Jaynes's passages. And even Jaynes's darts were directly mostly *ad peccatum* rather than *ad hominem;* he respected Fisher's scientific contributions but resented the way Fisher wielded his power sometimes to the detriment of the discipline.

You can verify this by reading, specifically, chapter 16 of *Probability Theory*. On page 493 Jaynes states that "Sir Ronald Aylmer Fisher was by far the dominant personality in this field in the period 1925–1960. . . . On the technical side, Fisher had a deep intuitive understanding and produced a steady stream of important research in genetics." On page 494 he continues: "Fisher's later dominance of the field derives less from his technical work than from his flamboyant personal style and the wordly power that went with his official position, in charge of the work and destiny of many students and subordinates. For 14 years (1919–1933) he was at the Rothamsted agricultural research facility with an increasing number of assistants and visiting students, then holder of the Chair of Eugenics at Cambridge, where he also became President of Caius College. He was elected Fellow of the Royal Society in 1929 and was knighted in 1952." And then on page 496, Jaynes says: "In sharp contrast [to Jeffreys], Fisher, possessed of a colossal, overbearing ego, thrashed about in the field, attacking the work of everyone else [a footnote provides details on this] with equal ferocity. Somehow, early in life, Fisher's mind became captured by the dogma that by 'probability' one is allowed to mean ONLY [emphasis mine] limiting frequency in a random experiment."

Concerning your last remark—that you find both frequentist and Bayesian methods useful—I'm quite sympathetic with you. Frequentist and Bayesian approaches are not antithetical; rather, the former is wholly encompassed by the latter. Jaynes has no problem with identifying probability with frequency when the latter is the ONLY information we have about a phenomenon. (And, in Fisher's empirical disciplines such as genetics and population statistics, this is often the case; see page 496.) Fisher's blindness was to refuse to accept (until rather late in his life; cf. page 495) that information may come in forms OTHER than frequency, and in that case the frequentist approach may fail while the Bayesian approach retains its power. But Fisher's CULPABLE sin (in Jaynes's eyes) was to use his authority to bully other researchers out of trying to break out of the "my frequentism right or wrong" discipline. Jaynes points out (on page 492) that "researchers in some fields such as medical testing found it impossible to get their work published if they failed to follow Fisher's recipes to the letter."

In conclusion, says Jaynes (on page 497), "we recognize Fisher's high competence in the problems which concerned him. . . . Had Fisher tried more complex problems, we think he would have perceived the superior power of Jeffreys' [Bayesian] methods rather quickly." In Dennis V. Lindley's words, "Inside every Non-Bayesian there is a Bayesian struggling to get out."

I think that if, after a first pass over Jaynes's book, you read Chapter 16 in its entirety, you'll be convinced that I did not aim to abuse Fisher or misrepresent Jaynes.

Sincerely,

Tom Toffoli

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