Standard presentations of proofs of the Likelihood Principle include a warning to the effect that the proof assumes that the statistical model of the experiment in question is adequate in some sense. Many commenters have pointed out that statisticians typically if not always know that their models are literally false. Thus, the fact that proofs of the Likelihood Principle assume that the model is adequate casts doubt on the significance of those proofs.
Advocates of the Likelihood Principle have responded to this concern in several ways. The most popular response seems to be the tu quoque response that every school of statistics uses models. Thus, the fact that advocates of the Likelihood Principle need to make the literally false assumption that their model is adequate puts them in no worse position than anyone else in statistics.
A significant problem for this response is the problem that all tu quoque responses share: they do not make the problem the objection raises go away. The fact that no one else is in any better position than the advocate of the Likelihood Principle does not mean that he or she is in a good position.
I am entertaining the alternative response that proofs of the Likelihood Principle do not need to assume model adequacy after all. [Read more…]