(I’m understanding your comment as providing an example of a situation where volatility goes to 0 with additional evidence.)
I think “volatility” (being able to predict yellow or red ball) is going higher?
But I feel like there is a real chance I’m talking past you and maybe wrong?
For example, you might be talking about forming beliefs about volatility. In my example, beliefs about volatility upon seeing the yellow ball are now more stable over time (even if volatility rises) as you know which bin you’re drawing from.
(Feel free to let me know if I misread. I’m also not sure what you mean by “like this.”)
I guess I’m just repeating my example, where searches or explorations are revealing something like “a new latent state”, so that previous information that was being used to form beliefs, are no longer relevant.
It’s true this statement doesn’t have much evidence behind it (but partially because I’m sort of confused now what exactly the example is talking about).
Ok, I didn’t understand the OP’s examples or what he was saying (so I missed sort of the point of his post). So I think he’s saying in the fourth example the range of reasonable beliefs could increase over time by collecting more information.
This seems unlikely and unnatural so I think you’re right. I retract my comment.
Ah sorry, I meant to use “volatility” to refer to something like “expected variance in one’s estimate of their future beliefs,” which is maybe what you refer to as “beliefs about volatility.”
(I’m understanding your comment as providing an example of a situation where volatility goes to 0 with additional evidence.)
I agree it’s clear that this happens in some situations—it’s less immediately obvious to me whether this happens in every possible situation.
(Feel free to let me know if I misread. I’m also not sure what you mean by “like this.”)
I think “volatility” (being able to predict yellow or red ball) is going higher?
But I feel like there is a real chance I’m talking past you and maybe wrong?
For example, you might be talking about forming beliefs about volatility. In my example, beliefs about volatility upon seeing the yellow ball are now more stable over time (even if volatility rises) as you know which bin you’re drawing from.
I guess I’m just repeating my example, where searches or explorations are revealing something like “a new latent state”, so that previous information that was being used to form beliefs, are no longer relevant.
It’s true this statement doesn’t have much evidence behind it (but partially because I’m sort of confused now what exactly the example is talking about).
Ok, I didn’t understand the OP’s examples or what he was saying (so I missed sort of the point of his post). So I think he’s saying in the fourth example the range of reasonable beliefs could increase over time by collecting more information.
This seems unlikely and unnatural so I think you’re right. I retract my comment.
Ah sorry, I meant to use “volatility” to refer to something like “expected variance in one’s estimate of their future beliefs,” which is maybe what you refer to as “beliefs about volatility.”