> You are talking about a completely unrelated process of updating priors about bias of independent events.
I hear you. I understand the point you are making.
But, the two issues are not entirely unrelated…
You are assuming - a priori - that the tosses are independent. That assumption can be tested. Right?
How would you test it?
Wouldn’t your belief in the independence of throws be affected by a long run of heads?
What if there was some mechanism whereby a previous head slightly increase the chance of it being heads again?
Even if we couldn’t conceive of what the mechanism was, certainly we could test for it, right? How would we do that?
I hear you. I understand the point you are making.
But, the two issues are not entirely unrelated…
You are assuming - a priori - that the tosses are independent. That assumption can be tested. Right? How would you test it? Wouldn’t your belief in the independence of throws be affected by a long run of heads? What if there was some mechanism whereby a previous head slightly increase the chance of it being heads again? Even if we couldn’t conceive of what the mechanism was, certainly we could test for it, right? How would we do that?