# Glowing Review

A glowing review of the book, “The Theory That Would Not Die”, by Christian Robert in current issue of Chance :

Afew days ago, prior to reading her book and writing this review, I had lunch with the author ofThe Theory That Would Not Die, Sharon McGrayne, in a Parisian café. We had a wonderful chat about why she wrote the book and about the people she met during its completion. Among others, she mentioned the considerable support provided by Dennis Lindley, Persi Diaconis, and Bernard Bru. This conversation also acted as an introduction to the interview on Page 24. (I had not fully read the book before because of delays in the delivery, presumably linked to Yale University Press not correctly forecasting the phenomenal success of the book and scaling the reprints accordingly.)My reaction to the book is one of enthusiasm. It tells the story and stories of Bayesian statistics and Bayesians in a most entertaining, if unmathematic, manner. There will be some who object to such a personification of science, which should be (much) more than the sum of the characters who contributed to it, or even to the need to mention those characters once the concepts they uncovered were incorporated within the theory.

Overall, I share the materialist belief that those concepts are existing per se and thus would have been found sooner or later by A or X. However, and somehow paradoxically, I also support the perspective that, since (Bayesian) statistical science is as much philosophy as it is mathematics and computer science, the components that led to its current state were contributed by individuals for whom the path to those components mattered. This is why I find the title particularly clever and, as Peter Müller pointed out, much more to the point than a sentence explicitly involving Bayes Theorem.

While the book inevitably starts with the (patchy) story of Thomas Bayes’s life—including his passage at Edinburgh University—and a nice nonmathematical description of his ball experiment, the next chapter is about “the man who did everything”: Pierre-Simon (de) Laplace, for whom the author and I share the same admiration. How Laplace attacked the issue of astronomical errors is brilliantly depicted, rooting the man within statistics and explaining why he would soon move to the “probability of causes” and rediscover plus generalize Bayes' theorem. That his (admittedly unpleasant) thirst for honors and official positions would later cast disrepute on his scientific worth is difficult to fathom in retrospect.

The next chapter is about the dark ages of [not yet] Bayesian statistics, and I particularly liked the links to the French army, in which I discovered that the great Henri Poincaré testified at Dreyfus’s trial using a Bayesian argument, that Bertillon had completely missed the probabilistic point, and that the military judges were then all aware of Bayes' theorem, thanks to Bertrand’s probability book being used at Ecole Polytechnique. (The last point actually was less of a surprise, given that I had collected some documents about the involvement of late 19th/early 20th century French artillery officers in the development of Bayesian techniques.)

The description of the fights between Fisher and Bayesians and non-Bayesians, alike, is both entertaining and sad. Sad also is the fact that Jeffreys' 1939 masterpiece got so little recognition at the time. (While I knew about Fisher’s unreasonable stand on smoking, going as far as defending the assumption that “lung cancer might cause smoking,” the Bayesian analysis of Jerome Cornfield was unknown to me. And quite fascinating.) The figure of Fisher actually permeates the whole book as a negative and bullying figure preventing further development of early Bayesian statistics, but also as an ambivalent anti-Bayesian who eventually tried to create his own brand of Bayesian statistics in the format of fiducial statistics (Seidenfeld, 1992).

“… and then there was the ghastly de Gaulle.” D. Lindley.”The following part of

The Theory That Would Not Dieis about Bayesian contributions to the (second World) war, at least from the Allied side. Again, I knew most of Alan Turing’s involvement in Bletchley Park’s Enigma, but the story is well told and, as in previous occasions, I cannot but be moved by the absurd waste of such a superb intellect by a blind administrative machine.The role of Albert Madansky in the assessment of the (lack of) nuclear weapons safety is also described well, stressing the inevitability of a Bayesian assessment of a one-time event that had (thankfully) not yet happened. The above quote from Dennis Lindley is the conclusion of his argument on why Bayesian statistics were not called Laplacean; I would suggest the French post-war attraction for abstract statistics in the wake of Bourbaki also did a lot against this recognition in addition to de Gaulle’s isolationism and ghastliness (or maybe they were one and the same).

The involvement of John Tukey into military research was also a novelty for me, but not so much as his use of Bayesian (small area) methods for NBC election night previsions. The conclusion of Chapter 14 on why Tukey felt the need to distance himself from Bayesianism is quite compelling. Maybe paradoxically, I ended up appreciating Chapter 15 even more for the part about the search for a missing H-bomb near Palomares, Spain, as it exposes the plusses a Bayesian analysis would have brought.

“There are many classes of problems where Bayesian analyses are reasonable, mainly classes with which I have little acquaintance.” J. TukeyWhen approaching near recent times and contemporaries, McGrayne gives detailed coverage of the coming-of-age of Bayesians like Jimmy Savage and Lindley, as well as the impact of Stein’s paradox (a personal epiphany), along with the important impact of Howard Raiffa and Robert Schlaifer, both on business schools and modeling prior beliefs (via conjugate priors). I did not know anything about their scientific careers, but

Applied Statistical Decision Theoryis a beautiful book that prefigured both DeGroot’s (1970) and Berger’s (1985). (As an aside, I was amused by Raiffa using Bayesian techniques for horse betting based on race bettors, as I had vaguely played with the idea during my spare, if compulsory, time in the French navy!)Similarly, while I had read detailed scientific accounts of Frederick Mosteller and David Wallace’s superb Federalist Papers study, they were only names to me. Chapter 12 mostly remedied this lack.

“We are just starting.” P. DiaconisThe final part—titled “Eureka!”—is about the computer revolution we witnessed in the 1980s, culminating with the (re)discovery of MCMC methods we covered in our own “history.” Because it contains stories that are closer to today’s time, it inevitably crumbles into shorter and shorter accounts. However,

The Theory That Would Not Dieconveys the essential message that Bayes rule had become operational, with its own computer language and objects such as graphical models and Bayesian networks that could tackle huge amounts of data and real-time constraints. And used by companies like Microsoft and Google. The final pages mention neurological experiments about how the brain operates in a Bayesian-like way (a direction much followed by neurosciences).In conclusion, I highly enjoyed reading through

The Theory That Would Not Die, and I am sure most of my Bayesian colleagues will as well. Being Bayesians, they will compare the contents with their subjective priors about Bayesian history, but will update those profitably in the end. (The most obvious missing part in my opinion is the absence of E. T. Jaynes and the MaxEnt community, which would deserve a chapter on its own.)As an insider, I have little idea about how the book would be perceived by the layman: It does not contain any formula apart from (the discrete) Bayes rule at some point, so everyone can read through it. The current success of_The Theory That Would Not Die_ shows that it reaches much further than academic circles. It may be that the general public does not necessarily grasp the ultimate difference between frequentists and Bayesians, or between Fisherians and Neyman-Pearsonians, as to why _p_-values should not be used (see also the next review). However, _The Theory That Would Not Die_ goes over all the elements that explain these differences. In particular, the parts about single events are quite illuminating on the specificities of the Bayesian approach. I will certainly (more than) recommend it to all of my graduate students.