Hmm. Considering that I was trying to come up with an example to illustrate how explicit the assumptions are, the assumptions aren’t that explicit in my example are they?
Prior knowledge about the world --> mathematical constraints --> prior probability distribution
The assumptions I used to get the constraints are that the best estimate of your next measurement is the average of your previous ones, and that the best estimate of its squared deviation from that average is some number s^2, maybe the variance of your previous observations. But those aren’t states of the world, those are assumptions about your inference behavior.
Then I added later that the real assumptions are that you’re making unbiased measurements of some unchanging quantity mu, and that the mechanism of your instrument is unchanging. These are facts about the world. But these are not the assumptions that I used to derive the constraints, and I don’t show how they lead to the former assumptions. In fact, I don’t think they do.
Well. Let me assure you that the assumptions that lead to the constraints are supposed to be facts about the world. But I don’t see how that’s supposed to work.
Hmm. Considering that I was trying to come up with an example to illustrate how explicit the assumptions are, the assumptions aren’t that explicit in my example are they?
Prior knowledge about the world --> mathematical constraints --> prior probability distribution
The assumptions I used to get the constraints are that the best estimate of your next measurement is the average of your previous ones, and that the best estimate of its squared deviation from that average is some number s^2, maybe the variance of your previous observations. But those aren’t states of the world, those are assumptions about your inference behavior.
Then I added later that the real assumptions are that you’re making unbiased measurements of some unchanging quantity mu, and that the mechanism of your instrument is unchanging. These are facts about the world. But these are not the assumptions that I used to derive the constraints, and I don’t show how they lead to the former assumptions. In fact, I don’t think they do.
Well. Let me assure you that the assumptions that lead to the constraints are supposed to be facts about the world. But I don’t see how that’s supposed to work.