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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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A 250-year argument: Belief, behavior, and the bootstrap
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by Bradley Efron PDF
Bull. Amer. Math. Soc. 50 (2013), 129-146 Request permission


The year 2013 marks the 250th anniversary of Bayes rule, one of the two fundamental inferential principles of mathematical statistics. The rule has been influential over the entire period—and controversial over most of it. Its reliance on prior beliefs has been challenged by frequentism, which focuses instead on the behavior of specific estimates and tests under repeated use. Twentieth-century statistics was overwhelmingly behavioristic, especially in applications, but the twenty-first century has seen a resurgence of Bayesianism. Some simple examples are used to show what’s at stake in the argument. The bootstrap, a computer-intensive inference machine, helps connect Bayesian and frequentist practice, leading finally to an empirical Bayes example of collaboration between the two philosophies.
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Additional Information
  • Bradley Efron
  • Affiliation: Department of Statistics, 390 Serra Mall, Stanford, California 94305-4065
  • Email:
  • Received by editor(s): February 8, 2012
  • Received by editor(s) in revised form: February 10, 2012
  • Published electronically: April 25, 2012
  • Additional Notes: The author’s work in supported in part by NIH grant 8R37 EB002784.
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Bull. Amer. Math. Soc. 50 (2013), 129-146
  • MSC (2010): Primary 97K70
  • DOI:
  • MathSciNet review: 2994997