Appreciate your reply. I think the source of my confusion is there being uncertainty in the degree of plausibility that weassign given our knowledge or there being uncertainty in our degree of belief given our knowledge. This feels a bit unnatural to me because this quantity is not an external/physical and unknown quantity but one that we assign given our knowledge. If we were to think of probabilities as physical properties that are unknown, then it makes sense to me that there can uncertainty in its value. How would you reconcile this?
Uncertainty is a statement about my brain not the real world, if you replicate the initial conditions then it will always land either Head or Tails, so even if the coin is “fair” p(H∣θ)=0.5, then maybe p(H∣θ,very good at physics)=0.95. the uncertainty comes form be being stupid and thus being unable to predict the next coin toss.
Also there are two things we are uncertain about, we are uncertain about θ (the coins frequency) and we are uncertain about p(H∣θ), the next coin toss
So you are saying that “we” are uncertain about the degree of belief/plausibility that what our brain is going to assign? Then who are “we” exactly? Apologies for being glib but I really don’t understand
Also, it is a crime to have different priors given the same information according to us objective Bayesians so that can’t be the issue
Appreciate your reply. I think the source of my confusion is there being uncertainty in the degree of plausibility that we assign given our knowledge or there being uncertainty in our degree of belief given our knowledge. This feels a bit unnatural to me because this quantity is not an external/physical and unknown quantity but one that we assign given our knowledge. If we were to think of probabilities as physical properties that are unknown, then it makes sense to me that there can uncertainty in its value. How would you reconcile this?
The probability is an external/physical thing because your brain is physical, but I take your point.
I think the we/our distinction arises because we have different priors
That’s a very misleading way of looking at it.
These subjective Bayesians… :) I feel the same way about that statement. Could you please elaborate?
Uncertainty is a statement about my brain not the real world, if you replicate the initial conditions then it will always land either Head or Tails, so even if the coin is “fair” p(H∣θ)=0.5, then maybe p(H∣θ,very good at physics)=0.95. the uncertainty comes form be being stupid and thus being unable to predict the next coin toss.
Also there are two things we are uncertain about, we are uncertain about θ (the coins frequency) and we are uncertain about p(H∣θ), the next coin toss
So you are saying that “we” are uncertain about the degree of belief/plausibility that what our brain is going to assign? Then who are “we” exactly? Apologies for being glib but I really don’t understand
Also, it is a crime to have different priors given the same information according to us objective Bayesians so that can’t be the issue