the war in Europe by at least two years. Turing’s work remained
classified and little known outside the intelligence community
for many decades.
■ ■ Jerome Cornfield, an employee of the National Institutes of
Health and a Bayesian autodidact, pioneered the use of case-control studies as part of his effort to link smoking with cancer.
Cornfield went on to become the most influential biostatistician
of his time. It is interesting that R. A. Fisher, who consulted for
the tobacco industry, vigorously disputed Cornfield’s analysis.
■ ■ Albert Madansky of the RAND Corporation used Bayesian
logic to estimate the probability of an accidental nuclear detonation—a probabilistic analysis of an unprecedented event.
In a similar manner, the actuary L. H. Longley-Cook estimated
the probability of two planes crashing in midair before such an
event had ever happened. Longley-Cook’s prescient Bayesian
analysis anticipated two such crashes in the subsequent years.
■ ■ The Princeton/Bell Labs statistician and Exploratory Data
Analysis pioneer John Tukey used Bayesian “shrinkage” to
forecast presidential elections for NBC. Tukey’s work was a
forerunner of Nate Silver’s hierarchical Bayes election forecasting at Five ThirtyEight.com.
Actuaries play a particularly notable role in McGrayne’s hidden history of 20th-century Bayes. Albert Wurts Whitney, one
of the earliest members of the CAS, led a committee focused
on providing a methodology for pricing workers’ compensation
insurance using the meager data available at the time. Though
versed in statistics and the Bayes-Laplace theory, Whitney was
also a pragmatist. He appreciated the need for a simple formula
that working actuaries and underwriters could use to combine
relevant pieces of information with subjective judgments, background knowledge, and collateral data sets. Whitney’s famous
credibility expression—Z=P/(P+K)—anticipated the shrinkage
estimator that Charles Stein discovered in the 1950s.
Also remarkable in the development of Bayesian statistics is
the role played by the midcentury actuary Arthur Bailey. Bailey, who merits an entire chapter of McGrayne’s book, studied
actuarial science at the University of Michigan and, as was typical, started his career as a frequentist in the Fisherian mold. At
first dismayed by the apparent lack of rigor behind Whitney’s
credibility theory, Bailey spent much of the 1940s studying the
issue. His library included a 1940 reprint of Bayes’ paper with
a preface by Bell Telephone’s Edward Molina. In 1950, Bailey,
by then a vice president at Kemper, presented the fruit of his
investigations—a paper entitled “Credibility Procedures: Laplace’s Generalization of Bayes’ Rule and the Combination of
Collateral Knowledge with Observed Data” at a CAS event.
Bailey’s paper anticipated the work of such core 20th-century
Bayesians as Jimmy Savage and Bruno de Finetti. One particular passage in Bailey’s paper vividly captures the actuarial
profession’s early embrace of the Bayesian philosophy:
At present, practically all methods of statistical estimation appearing in textbooks… are based on an equivalent
to the assumption that any and all collateral information
or a priori knowledge is worthless. There have been rare
instances of rebellion against this philosophy by practical statisticians who have insisted that they actually had
a considerable store of knowledge apart from the specific
observations being analyzed… However it appears to be
only in the actuarial field that there has been an organized
revolt against discarding all prior knowledge when an estimate is to be made using newly acquired data.
Bailey’s paper was positively reviewed by the Harvard stat-
istician Richard von Mises, who stated that he hoped it would
help “the unjustified and unreasonable attacks on the Bayes
theory, initiated by R.A. Fisher, fade out.”
The paper attracted the right audience. Jimmy Savage, then
a recent convert to the Bayesian paradigm, learned of Bailey’s
work from University of Michigan actuarial science professor
Allen Mayerson. He subsequently reported Bailey’s work to
Bruno de Finetti, himself a former actuary. The two attended
a conference together in Trieste, where they spread the word
about Bailey and the Bayesian roots of actuarial credibility the-
ory. Among the conference attendees were Dennis Lindley, one
of the leading Bayesians of the second half of the 20th century,
and Hans Bühlmann, who went on to develop Bailey’s work into
a full theory of Bayesian credibility.
As Bayesian methodology continues its march into the statistical mainstream, The Theory that Would Not Die serves as a
helpful—and highly entertaining—lesson in the extraordinary,
and often hidden, contributions that Bayesian methods historically have made in scholarship, government, military intelligence,
jurisprudence, medicine, actuarial science, and beyond.
JAMES GUSZCZA, a fellow of the Casualty Actuarial Society
and member of the Academy, is an assistant professor of
actuarial science at the University of Wisconsin: Madison
THOMAS N. HERZOG, a fellow of the American Statistical
Association, an associate of the Society of Actuaries, and a
member of the Academy, was most recently distinguished
scholar in insurance regulation at the National Association of
insurance Commissioners in Washington.
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