“Perhaps the notion of “update speed” might make sense in a more continuous setting, but in a discrete setting like this it is clear it does not.”
However, the concept of “speed” works equally well in discrete and continuous systems—as the GOL illustrates. “Discreteness” is an irrelevance.
You really seem to be missing the point here. I’m sorry but from your posts I can’t help but get the idea that you don’t really understand how this sort of prediction scheme works. Sure, “update speed” in the sense you described it elsewhere in the thread makes sense, but who cares? Update speed in these you described it elsewhere in the thread is a consequence of the prior (or current state, rather), it isn’t some sort of parameter, and it’s not clear it’s something at all stable or meaningful. You’ve established the existence of something trivial and probably irrelevant. In the parametric sense you seemed to be originally using it, it doesn’t exist. Can we agree on this?
Probably nobody cares—apart from you, it seems. Apparently, one can’t get away with using the phrase “update speed” in connection with an intelligent agent without getting bounced.
When you said:
“I don’t understand how this notion of “update speed” translates into the Bayesian setting.”
...and I said...
“Say you think p(heads) is 0.5. If you see ten heads in a row, do you update p(heads) a lot, or a little? It depends on how confident you are of your estimate. If you had previously seen a thousand coin flips from the same coin, you might be confident of p(heads) being 0.5 - and therefore update little. If you were told that it was a biased coin from a magician, then your estimate of p(heads) being 0.5 might be due to not knowing which way it was biased. Then you might update your estimate of p(heads) rapidly—on seing several heads in a row. Like that.”
...IMO, the conversation could and should have stopped—right there.
You really seem to be missing the point here. I’m sorry but from your posts I can’t help but get the idea that you don’t really understand how this sort of prediction scheme works. Sure, “update speed” in the sense you described it elsewhere in the thread makes sense, but who cares? Update speed in these you described it elsewhere in the thread is a consequence of the prior (or current state, rather), it isn’t some sort of parameter, and it’s not clear it’s something at all stable or meaningful. You’ve established the existence of something trivial and probably irrelevant. In the parametric sense you seemed to be originally using it, it doesn’t exist. Can we agree on this?
Probably nobody cares—apart from you, it seems. Apparently, one can’t get away with using the phrase “update speed” in connection with an intelligent agent without getting bounced.
When you said:
“I don’t understand how this notion of “update speed” translates into the Bayesian setting.”
...and I said...
“Say you think p(heads) is 0.5. If you see ten heads in a row, do you update p(heads) a lot, or a little? It depends on how confident you are of your estimate. If you had previously seen a thousand coin flips from the same coin, you might be confident of p(heads) being 0.5 - and therefore update little. If you were told that it was a biased coin from a magician, then your estimate of p(heads) being 0.5 might be due to not knowing which way it was biased. Then you might update your estimate of p(heads) rapidly—on seing several heads in a row. Like that.”
...IMO, the conversation could and should have stopped—right there.