I basically agree that the part of the original comment that you quote doesn’t make any sense at all, and am not attempting to come to the defence of confidence intervals over probabilities, but it does feel like there should be some way of giving statements of probability and indicating how sure one is about the statement at the same time. I think, in some sense, I want to be able to say how likely I think it is that I will get new information that will cause me to update away from my current estimate, or give a second-derivative of my uncertainty, if you will.
Let’s say we have two bags, one contains 1 million normal coins, one contains 500,000 2-headed coins and 500,000 2-tailed coins. Now, I draw a coin from the first bag and toss it—I have a 50% chance of getting a head. I draw a coin from the second bag and toss it—I also have a 50% chance of getting a head, but it does feel like there’s some meaningful difference between the two situations. I will admit, though, that I have basically no idea how to formalise this—I assume somebody, somewhere, does.
I basically agree that the part of the original comment that you quote doesn’t make any sense at all, and am not attempting to come to the defence of confidence intervals over probabilities, but it does feel like there should be some way of giving statements of probability and indicating how sure one is about the statement at the same time. I think, in some sense, I want to be able to say how likely I think it is that I will get new information that will cause me to update away from my current estimate, or give a second-derivative of my uncertainty, if you will.
Let’s say we have two bags, one contains 1 million normal coins, one contains 500,000 2-headed coins and 500,000 2-tailed coins. Now, I draw a coin from the first bag and toss it—I have a 50% chance of getting a head. I draw a coin from the second bag and toss it—I also have a 50% chance of getting a head, but it does feel like there’s some meaningful difference between the two situations. I will admit, though, that I have basically no idea how to formalise this—I assume somebody, somewhere, does.