Discussion of "On the Birnbaum Argument for the Strong Likelihood Principle"

TL;DR

This paper critically examines Deborah Mayo's refutation of Birnbaum's argument for the Likelihood Principle, emphasizing the importance of correct interpretation of the Conditionality Principle in the debate.

Contribution

The paper clarifies the differences in interpreting the Conditionality Principle and defends Birnbaum's original proof against Mayo's refutation.

Findings

Mayo's interpretation of the Conditionality Principle differs from Birnbaum's.

Birnbaum's proof remains valid under the correct interpretation.

The debate hinges on the interpretation of foundational principles in statistical inference.

Abstract

Deborah Mayo claims to have refuted Birnbaum's argument 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. [arXiv:1302.7021]