Electronic Journal of Statistics

What does the proof of Birnbaum’s theorem prove?

Michael Evans

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Statist., Volume 7 (2013), 2645-2655.

Dates
First available in Project Euclid: 25 October 2013

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1382706342

Digital Object Identifier
doi:10.1214/13-EJS857

Mathematical Reviews number (MathSciNet)
MR3121626

Zentralblatt MATH identifier
1294.62002

Subjects
Primary: 62A01: Foundations and philosophical topics
Secondary: 62F99: None of the above, but in this section

Keywords
Sufficiency conditionality likelihood relations equivalence relations

Citation

Evans, Michael. What does the proof of Birnbaum’s theorem prove?. Electron. J. Statist. 7 (2013), 2645--2655. doi:10.1214/13-EJS857. https://projecteuclid.org/euclid.ejs/1382706342


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