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 | References | Similar Articles | Additional Information

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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Additional Information

**Bradley Efron**

Affiliation:
Department of Statistics, 390 Serra Mall, Stanford, California 94305-4065

Email:
brad@stat.stanford.edu

DOI:
http://dx.doi.org/10.1090/S0273-0979-2012-01374-5

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.