Trouble is, we already have data. Lots of it. So is there some algebraic trick which lets us add that new layer to the hypothesis without going back to evidential square one?
Bayesian updating is timeless. It doesn’t care whether you observed the data before or after you wrote the hypothesis.
So, it sounds like you are suggesting that we can back out all that data, change our hypothesis and prior, and then read the data back in. In theory, yes. But sometimes we don’t even remember the data that brought us to where we are now. Hence the desirability of a trick. Is there an updating-with-new-hypothesis rule to match Bayes’s updating-with-new-evidence rule?
Bayesian updating is timeless. It doesn’t care whether you observed the data before or after you wrote the hypothesis.
So, it sounds like you are suggesting that we can back out all that data, change our hypothesis and prior, and then read the data back in. In theory, yes. But sometimes we don’t even remember the data that brought us to where we are now. Hence the desirability of a trick. Is there an updating-with-new-hypothesis rule to match Bayes’s updating-with-new-evidence rule?