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Discussion: Foundations of statistical inference, revisited. (English) Zbl 1332.62024
Summary: This is an invited contribution to the discussion on Professor D. Mayo’s paper [ibid. 29, No. 2, 227–239 (2014; Zbl 1332.62025)]. Mayo clearly demonstrates that statistical methods violating the likelihood principle need not violate either the sufficiency or conditionality principle, thus refuting A. Birnbaum’s claim [J. Am. Stat. Assoc. 57, 269–306, 307–326 (1962; Zbl 0107.36505)]. With the constraints of Birnbaum’s theorem lifted, we revisit the foundations of statistical inference, focusing on some new foundational principles, the inferential model framework, and connections with sufficiency and conditioning.

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