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Discussion of “On the Birnbaum argument for the strong likelihood principle”. (English) Zbl 1332.62018

Summary: D. Mayo [ibid. 29, No. 2, 227–239 (2014; Zbl 1332.62025)] claims to have refuted A. Birnbaum’s argument in [J. Am. Stat. Assoc. 57, 269–306, 307–326 (1962; Zbl 0107.36505)] that the Likelihood Principle is a logical consequence of the Sufficiency and Conditionality Principles. However, this claim fails because her interpretation of the Conditionality Principle is different from Birnbaum’s. Birnbaum’s proof cannot be so readily dismissed.

MSC:

62A01 Foundations and philosophical topics in statistics
62D05 Sampling theory, sample surveys
62B05 Sufficient statistics and fields
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References:

[1] Birnbaum, A. (1962). On the foundations of statistical inference. J. Amer. Statist. Assoc. 57 269-326. · Zbl 0107.36505
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[10] Mayo, D. (2014). On the Birnbaum argument for the strong likelihood principle. Statist. Sci. 29 227-239. · Zbl 1332.62025
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