"There are strong arguments in the statistics community that these frequentist methods are actually philosophically or mathematically incoherent!" Interesting. OTOH, they seem to work, give specific models to work with, at least in a more confining way can compare models, and supports a more rigid view of science. What I think I get about Bayesian methods is that they work too, gives more relaxed tools to work with, and has a smaller axiom set (1 -2 axioms, depending on what source I look at) to describe pretty much the same (or more) as the frequentist probability (3 axioms). I guess if we did a Bayesian analysis of the two approaches, the Bayesian approach would have some weight but we would keep the frequentist approach around?! That said, I look forward to see if the Bayesian view will be accepted or not.