As a counterargument to my previous post, if anyone wants an exposition of the likelihood principle, here is reasonably neutral presentation by Birnbaum 1962. For coherence and Bayesianism see Lindley 1990.
Edited to add: As Lindley points out (section 2.6), the consideration of the adequacy of a small model can be tested in a Bayesian way through consideration of a larger model, which includes the smaller. Fair enough. But is the process of starting with a small model, thinking, and then considering, possibly, a succession of larger models, some of which reject the smaller one and some of which do not, actually a process that is true to the likelihood principle? I don’t think so.
As a counterargument to my previous post, if anyone wants an exposition of the likelihood principle, here is reasonably neutral presentation by Birnbaum 1962. For coherence and Bayesianism see Lindley 1990.
Edited to add: As Lindley points out (section 2.6), the consideration of the adequacy of a small model can be tested in a Bayesian way through consideration of a larger model, which includes the smaller. Fair enough. But is the process of starting with a small model, thinking, and then considering, possibly, a succession of larger models, some of which reject the smaller one and some of which do not, actually a process that is true to the likelihood principle? I don’t think so.