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At the end did you mean “(e.g. likelihood ratios [LRs])”? There are other relative measures including posterior odds (POs) which are LRs only under near-flat priors.
That was precisely what I meant. I own a copy of Richard Royall’s monograph Statistical Evidence: A Likelihood Paradigm and he had convinced me that a distinction between questions of belief revision, choosing a course of action, and summarizing information from experiments (broadly defined to include observational studies) is useful.
I wanted your opinion on data reporting, as I agree with Royall that questions of “what the data say” should not, in principle, depend on the prior of the experimenter. I’d prefer reports that permit me to substitute my own prior or \alpha.
I don’t want to burden you any further as you have been very generous in giving your time and expertise in this thread until I have some time to think more about what you have posted.
For context, I’ve been thinking about this comment by Herman Chernoff on Bradley Efron’s paper “Why Isn’t Everyone Bayesian” I posted in another thread:
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With the help of theory, I have developed insights and intuitions that prevent me from giving weight to data dredging and other forms of statistical heresy. This feeling of freedom and ease does not exist until I have a decision theoretic, Bayesian view of the problem … I am a Bayesian decision theorist in spite of my use of Fisherian tools.