First, nowhere in here have I made a probability estimate. I’ve made a prediction about what will happen on the next roll of this die. You are inferring that i made that prediction on the basis of a probability estimate, and you admittedly have good reasons to infer that.
Yes. I have explained (in some amount of detail) what I mean by confidence, such that it is distinct from probability, as relates to prediction.
And yes, as a human you are in fact constrained (in practice) to making predictions based on internal probability estimates (based on my understanding of neuroscience).
Confidence, like probability, is not binary.
You can have fairly high confidence in the implied probability of P1 given K1 and K2, and likewise little confidence in a probability estimate of P1 in the case of a die of unknown dimension—this should be straightforward.
Second… are you now saying that I can be confident in P1? Because when I asked you that in the first place you answered no. I suspect I’ve misunderstood you somewhere.
Yes, and the mistake is on my part: wow that first comment was a partial brainfart. I was agreeing with you, and meant to say yes but … I’ll edit in a comment to that effect.
Yes. I have explained (in some amount of detail) what I mean by confidence, such that it is distinct from probability, as relates to prediction.
And yes, as a human you are in fact constrained (in practice) to making predictions based on internal probability estimates (based on my understanding of neuroscience).
Confidence, like probability, is not binary.
You can have fairly high confidence in the implied probability of P1 given K1 and K2, and likewise little confidence in a probability estimate of P1 in the case of a die of unknown dimension—this should be straightforward.
Yes, and the mistake is on my part: wow that first comment was a partial brainfart. I was agreeing with you, and meant to say yes but … I’ll edit in a comment to that effect.
Ah!
I feel much better now.
I should go through this discussion again and re-evaluate what I think you’re saying based on that clarification before I try to reply .