Seriously, the main point of an experiment is to gather evidence. Coupled with prior beliefs, you get a posterior belief, but the most important point is how much evidence the experiment provides.
Sure, a full fledged posterior belief is needed to make an actual decision, like, what should we test next. And if a subject is deemed important enough that we need to be certain, we can replicate until we get enough evidence to trump any reasonable prior belief. (Mind publication bias, though, some replications are going to fail, and that's relevant evidence too.)
In the mean time, it would be nice if the papers just told "the experiment provides 20dB of evidence that A is wrong, and B is right", instead of saying "B is right (at p<0.01)". No you're not certain B is right just yet. Your evidence is significant, perhaps even decisive, but it is not certain. A one in a hundred fluke is not unheard of. Also, sharing likelihood ratios (instead of posterior beliefs) makes the whole debate a bit less heated.
Getting a double one on dice you just threw for the first time doesn't mean they are loaded to make you lose. It only provides about 15 decibels of evidence in favour of such a con job.
Is either of these universally true? Or is it possible that a "belief" associated with a given math tool can be chosen as appropriate to the problem being solved du jour?
When I learned Bayes' theorem in college stats class, there was no mention of beliefs. It was just a straightforward theorem related to conditional probability.
No. They believe you can measure an infinite number of trials (say # of heads vs tails) and whatever ratio you get is the probability of heads.
However it's problematic because you can measure a million coin flips and get heads every time. It's not possible to actually measure an infinite number of trials - you need to imagine it.
They still non-trivially define/demarcate what the population actually is. That is kind of a belief because it is a choice not given by nature, and there are infinitely many choices one could choose.
Nature does not give you choice, it gives you the frequency (say, in the form of the intensity of a spectral line of an atom), and it is the base of the scientific method to listen to what nature is trying to tell you. There is nothing subjective in this process. Arguing otherwise is like saying that atheists “believe” in the non-existence of god.
Nature is telling you an infinite number of things, the process of selecting what to measure and what to exclude in the measurement is a choice.
In terms of frequentism, how you define what the population distribution you are sampling from is exactly, is a choice.
You are limiting the discussion to what happens after you've chosen how and what the population distribution consists of.. that part is itself a nontrivial and subjective process.
Seriously, the main point of an experiment is to gather evidence. Coupled with prior beliefs, you get a posterior belief, but the most important point is how much evidence the experiment provides.
Sure, a full fledged posterior belief is needed to make an actual decision, like, what should we test next. And if a subject is deemed important enough that we need to be certain, we can replicate until we get enough evidence to trump any reasonable prior belief. (Mind publication bias, though, some replications are going to fail, and that's relevant evidence too.)
In the mean time, it would be nice if the papers just told "the experiment provides 20dB of evidence that A is wrong, and B is right", instead of saying "B is right (at p<0.01)". No you're not certain B is right just yet. Your evidence is significant, perhaps even decisive, but it is not certain. A one in a hundred fluke is not unheard of. Also, sharing likelihood ratios (instead of posterior beliefs) makes the whole debate a bit less heated.
Getting a double one on dice you just threw for the first time doesn't mean they are loaded to make you lose. It only provides about 15 decibels of evidence in favour of such a con job.