On the definition and some justification of the Likelihood Principle

Abstract

Two points have been raised about the Likelihood Principle (LP). The first relates to the definition of LP: it has been shown that one of the two available definitions is hardly acceptable outside a strictly Bayesian context. The cue for the second issue is taken from Birnbaum's proof (and other similar proofs) that the LP - in its strong version - is implied by other more fundamental principles, which most statisticians tend to accept; some of these principles or axioms, after subjection to severe critical discussion, have been recognized as inadequate for general agreement. Moreover, it is shown that Birnbaum's proof - as well as others with the same demonstration structure - is logically false.