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2013 What does the proof of Birnbaum’s theorem prove?
Michael Evans
Electron. J. Statist. 7: 2645-2655 (2013). DOI: 10.1214/13-EJS857


Birnbaum’s theorem, that the sufficiency and conditionality principles entail the likelihood principle, has engendered a great deal of controversy and discussion since the publication of the result in 1962. In particular, many have raised doubts as to the validity of this result. Typically these doubts are concerned with the validity of the principles of sufficiency and conditionality as expressed by Birnbaum. Technically it would seem, however, that the proof itself is sound. In this paper we use set theory to formalize the context in which the result is proved and show that in fact Birnbaum’s theorem is incorrectly stated as a key hypothesis is left out of the statement. When this hypothesis is added, we see that sufficiency is irrelevant, and that the result is dependent on a well-known flaw in conditionality that renders the result almost vacuous.


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Michael Evans. "What does the proof of Birnbaum’s theorem prove?." Electron. J. Statist. 7 2645 - 2655, 2013.


Published: 2013
First available in Project Euclid: 25 October 2013

zbMATH: 1294.62002
MathSciNet: MR3121626
Digital Object Identifier: 10.1214/13-EJS857

Primary: 62A01
Secondary: 62F99

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society


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