The likelihood principle and its proof – a never-ending story…

An ongoing controversy in philosophy of statistics is the so-called “likelihood principle” essentially stating that all evidence which is obtained from an experiment about an unknown quantity θ is contained in the likelihood function of θ. Common classical statistical methodology, such as the use of significance tests, and confidence intervals, depends on the experimental procedure and unrealized events and thus violates the likelihood principle. The likelihood principle was identified by that name and proved in a famous paper by Allan Birnbaum in 1962. However, ever since both the principle itself as well as the proof has been highly debated. This presentation will illustrate the debate of both the principle and its proof, from 1962 and up to today. An often-used experiment to illustrate the controversy between classical interpretation and evidential confirmation based on the likelihood principle will also be presented and discussed