Fair enough. Can I take your point to be “when things get super complicated, sometimes you can make conceptual progress only by not worrying about keeping track of everything?” The only trouble is that once you stop keeping track of probability/significance, it becomes difficult to pick it up again in the future—you’d need to gather additional evidence in a better-understood way to check what’s going on. Actually, that’s a good analogy for hypothesis generation, with the “difficult to keep track of” stuff becoming the problem of uncertain priors.
My point is more like: If scientific interest only rests on some limited aspect of the problem, you can’t avoid priors by, e.g., simpy reporting likelihood ratios. Likelihood ratios summarize information about the entire problem, including the auxiliary, scientifically uninteresting aspects. The Bayesian way of making statements free of the auxiliary aspects (marginalization) requires, at the very least, a prior over those aspects.
I’m not sure if I agree or disagree with the third sentence on down because I don’t understand what you’ve written.
Fair enough. Can I take your point to be “when things get super complicated, sometimes you can make conceptual progress only by not worrying about keeping track of everything?” The only trouble is that once you stop keeping track of probability/significance, it becomes difficult to pick it up again in the future—you’d need to gather additional evidence in a better-understood way to check what’s going on. Actually, that’s a good analogy for hypothesis generation, with the “difficult to keep track of” stuff becoming the problem of uncertain priors.
My point is more like: If scientific interest only rests on some limited aspect of the problem, you can’t avoid priors by, e.g., simpy reporting likelihood ratios. Likelihood ratios summarize information about the entire problem, including the auxiliary, scientifically uninteresting aspects. The Bayesian way of making statements free of the auxiliary aspects (marginalization) requires, at the very least, a prior over those aspects.
I’m not sure if I agree or disagree with the third sentence on down because I don’t understand what you’ve written.