Efron, Simon, and the Bootstrap


Peter Bruce

Date Published:
January 22, 2021

It was 1994, and University of Maryland Professor Julian Simon was frustrated that he was not properly recognized for his contribution to the bootstrap.  The statistics profession credited Bradley Efron with inventing the bootstrap in 1979, as did the back cover of Efron’s own 1985 book (with Tibshirani) An Introduction to the Bootstrap. Simon had published a number of resampling examples, including a bootstrap example, in his 1969 book Basic Research Methods in Social Science, and had been seeking recognition from noted statisticians after Efron’s methods gained popularity.  Finally, in 1994, Simon decided to take the bull by the horns and make his claim in paid advertising.

Simon did not hold commercial activity to be a lower form of human endeavor, the way many academics do.  Though his fame came in the arena of economics and demographics, where he was a libertarian and enthusiastic free-marketeer, his academic home was always in a business school.  Among his many books was How to Start and Operate a Mail Order Business.  Though this book was a best-seller, it did not  endear him to his academic colleagues, who tended to dismiss him as the “mail order author.”  Simon also enjoyed the idea of settling academic arguments by betting. His famous bet against the doom-sayer Paul Ehrlich garnered more attention than a dozen academic papers. Simon took the cornucopian view that “things will continue getting better,” and bet Ehrlich, author of The Population Bomb, that the price of any five commodities would be lower ten years later.  The price of all five metals dropped, with Simon winning both the bet and considerable publicity.


For more about why Simon felt confident in his prediction, check out his seminal book The Ultimate Resource (hint – human ingenuity is the ultimate resource.)

Side note:  I predict the idea of the “population bomb” will also be proved wrong, or have an entirely opposite meaning, in several decades, as we realize the implications of dramatically declining population growth rates.

Simon put his resampling ideas into practice with software he developed called Resampling Stats (which I helped commercialize, and we still sell).  In advertising, started in 1994, he began advancing the claim that he was the inventor of the bootstrap. This got Efron’s attention, who demanded that Simon drop the claim.  Efron stated that “Your 1967 (sic) book has many nice examples, including one that I found was quite bootstrap-like. However, an example does not make a theory.” Efron went on to say

“I will drop my objection if the offending sentence was changed to something like ‘following early examples by Julian Simon (the creator of Resampling Stats) and subsequent development by Bradley Efron, resampling has become…’”

Despite Efron’s tacit acknowledgment of his 1969 work, Simon saw the matter not as a negotiation but a contest.  He continued to correspond with well known statisticians, including Geoffrey Watson, Peter Hall, Leland Wilkinson, Allen Wallis, Peter Hall, and others, until his death in 1998.

In the end, Simon did receive “official” recognition for his work in the journal Statistical Science, in its “Silver Anniversary of the Bootstrap” issue (May, 2003).  Peter Hall’s article, “A Short Prehistory of the Bootstrap,” devotes a section to Simon and his writings.  Hall placed Simon’s statistical work in the context of his free-market ideology, saying he “misinterpreted change as explicit conflict.”  Hall also wrote “The clarity with which Simon… anticipated in the 1960’s the massive changes that computing would bring to statistics undoubtedly placed him apart from many of his peers.  However, his main contribution to statistics was surely as an advocate and popularizer of Monte Carlo experimentation and of resampling methods, not as a developer of specific techniques.”

One thing that both Simon and Efron faced was widespread skepticism that such a simple method as the bootstrap (taking samples with replacement from an original sample) was both powerful and statistically sound.  In that respect, Efron’s development of the theory was essential to the wider acceptance of the bootstrap in the statistical community, while Simon’s popular advocacy helped bring it to an audience beyond statisticians.

I worked with Julian Simon for 10 years, and carried on developing and distributing his Resampling Stats software after his death.  To him I owe much. I also believe the statistical community owes Julian Simon much, primarily for helping to shift the profession (however little) away from theory and towards a more useful empirical orientation.  Data exploration and data mining are manifestations of this trend. Simon’s specific contributions were to sow the seeds of computer-intensive experimentation (his 1969 examples with dice and coins or numbered cards, translated readily to the computer), and to keep a keen eye on the every-day practitioner.  Very few statisticians are honored with an obituary in the Wall Street Journal; here is Simon’s (though devoid of content about resampling, which probably went over the head of colleagues and opponents from his more famous contests.)

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