Saturday, 2 January 2016
A NEW PROOF OF THE LIKELIHOOD PRINCIPLE BY GREG GANDENBERGER
ARTICLE BY GREG GANDENBERGER
Both Deborah Mayo and Michael Evans have recently refuted Birnbaum's celebrated 1962 proof that the Likelihood Principle is implied by the Sufficiency and Conditionality Principles, However in this article. Greg Gandenberger, a postdoctoral researcher at the University of Bristol. proves that the Likelihood Principle is implied by a combination of the Conditionality Principle and a Weak Ancillary Realisability Principle. The latter essentially says that one may replace the binary mathematical ancillary in a minimal experiment with an experimental ancillary without changing the evidential meanings of the outcomes.
The Likelihood Principle is an important cornerstone of the model-based Bayesian inferential paradigm. It is as yet unclear to me whether the assumptions involved in the new Realisability Principle are weak enough when compared with the Likelihood Principle itself to be of really useful purpose. However, Gandenberger's proof gives lots of credibility to the conceptual ideas invoked by Birnbaum in 1962.
DEBORAH MAYO: BAYESIAN DETRACTOR EXTRA-ORDINAIRE
ON RE-EVALUATING BAYESIAN AXIOMATIZATIONS OF SUBJECTIVE PROBABILITY AND UTILITY