That can help in some instances, but it won't work for everything. In particular, if the problem contains lots of parameters, some of which are of substantive interest and the rest of which are necessary for accurate modelling but are otherwise nuisances, then useful likelihood ratios don't exist.
In what cases can "95% statistical significance" be useful while appropriately selected and specified likelihood ratios can not be similarly useful? (Essentially I do not believe you.)
Let me clarify that I'm not defending the notion of statistical significance in data analysis -- I'm merely saying that the advice to publish likelihood ratios is not a complete answer for avoiding debate over priors.
I analyzed some data using two versions of a model that had ~6000 interest parameters and ~6000 nuisance parameters. One of my goals was to determine which version was more appropriate for the problem. The strict Bayesian answer is to compare different possible models using the Bayes factor, which marginalizes over every parameter in each vers...
I still can't see the relevance of Bayesian Statistics over Frequentist Statistics, and I take Less Wrong as evidence that this is a cause for clarification.
I'm looking for a historical narrative of the development of mathematics that tells me what mistake lead to frequentism over Bayesianism, which is supposedly the correct view. Alternatively, you can just say "Read PT:TLOS!" if it's that silly of a question.