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Bulletin of the American Mathematical Society

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A 250-year argument: Belief, behavior, and the bootstrap

Author: Bradley Efron
Journal: Bull. Amer. Math. Soc. 50 (2013), 129-146
MSC (2010): Primary 97K70
Published electronically: April 25, 2012
MathSciNet review: 2994997
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Abstract: 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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Bradley Efron
Affiliation: Department of Statistics, 390 Serra Mall, Stanford, California 94305-4065

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.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.