I do not know where the idea that “speeds” are “parameters” and not “statistics” comes from. An entity being a statistic doesn’t imply that it is not a speed.
The same goes for discrete systems. They have the concept of speed too:
This is utterly irrelevant. The problem with what you say is not that there’s no notion of speed, it’s that there is precisely one way of doing updates, and it has no “speed” parameter.
In the game of life, the update speed is always once per generation. However, that doesn’t mean it has no concept of speed. In fact the system exhibits gliders with many different speeds.
It’s much the same with an intelligent agent’s update speed in response to evidence—some will update faster than others—depending on what they already know.
You claimed that:
“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.
“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.
In the game of life, the update speed is always once per generation. However, that doesn’t mean it has no concept of speed. In fact the system exhibits gliders with many different speeds.
This is not analogous. We are speaking of a complete system here.
It’s much the same with an intelligent agent’s update speed in response to evidence—some will update faster than others—depending on what they already know.
I have already addressed this. What you have called “update speed” is determined by current distribution.
I assure you that I could exhibit a GOL field that consisted entirely of gliders moving at c/2 - and then exhibit another GOL field that consisted entirely of gliders moving at c/4. These systems would have different characteristic speeds. Hopefully, you see the analogy now.
Just so. I never said otherwise. You already asked for clarification about whether I thought that the system’s “update speed” was to do with its prior Prob. Dist. - and I said that “yes”, it was.
Hm; there may not be a disagreement here. You seemed to be using it in a way that implied it was not determined by (or even was independent of) the prior. Was I mistaken there?
The idea was that some agents update faster than others (or indeed not at all).
If you like you can think of the agents that update relatively slowly as being confident that they are uncertain about the things they are unsure about. That confidence in their own uncertainty could indeed be represented by other priors.
If you want to think about it that way, please don’t say “other priors”. That’s very confusing, because “prior” in this context refers to the whole prior, not to pieces of it (which I’m not sure how you’re detangling from each other, anyway). If we’re talking about something of the universal-prior sort, it has one prior, over its total sensory experience; I’m not clear how you’re decomposing that or what alternative model you are suggesting.
The two types of prior probability I discussed were “belifs about the world” and “beliefs about the certainty of those beliefs”.
An agent that updates its beliefs about the world rapidly (in response to evidence) would have a low degree of certainty about those beliefs—while an agent that updates its beliefs about the world slowly would have a high degree of certainty that those beliefs were already correct—and were backed up with lots of existing evidence.
I gave an example of this already when I discussed the magician’s coin.
Except these aren’t separate things. That isn’t how this sort of system works! Its beliefs about the certainty of those beliefs are determined by its beliefs about the world.
Well, everything is about the world, if materialism is true.
You don’t seem to be even trying to perform a sympathetic reading. Leave aside quibbling about what is to do with the world—can you at least see that in the first case, updates happen quickly, and in the second case they happen slowly? “Speed” just refers to distance divided by time. Here distance is the probabiliy delta, and time is simply time. So, updates can happen fast and slow. Some systems update quickly, others update slowly—and others don’t update at all. This all seems fairly simple to me—what is the problem?
Right. I really don’t think that what I am saying is controversial. The way I remember it, I talked about systems with different update speeds—and you jumped on that.
Alternatively, I could say, I went with the assumption that you were attempting to carve the relevant concepts at the joints and getting it wrong, rather than that you were making a true statement which doesn’t even try to accomplish that.
M, sorry then. But you didn’t explain the term anywhere, so I assumed it meant what it sounded like—the original context makes it sound like you mean something separate from the prior, rather than something determined by it. If instead of talking about building an agent that were “confident in their priors” and “updated them slowly” you had just spoken of “priors that result in slow updating” I don’t think there would have been a problem. (I must admit I probably also wasn’t inclined to look for a sympathetic reading as your other comments about the universal prior seem to be just wrong. )
“Update speed” seems fine to me—when comparing:
.5, .500001, .500002, .500003, .500004...
....with...
.5, 0.7, 0.9, 0.94, 0.96
...but use whatever term you like.
That’s a statistic, not a parameter—and it’s a statistic ultimately determined by the prior.
I do not know where the idea that “speeds” are “parameters” and not “statistics” comes from. An entity being a statistic doesn’t imply that it is not a speed.
The same goes for discrete systems. They have the concept of speed too:
http://en.wikipedia.org/wiki/Glider_%28Conway%27s_Life%29
This is utterly irrelevant. The problem with what you say is not that there’s no notion of speed, it’s that there is precisely one way of doing updates, and it has no “speed” parameter.
In the game of life, the update speed is always once per generation. However, that doesn’t mean it has no concept of speed. In fact the system exhibits gliders with many different speeds.
It’s much the same with an intelligent agent’s update speed in response to evidence—some will update faster than others—depending on what they already know.
You claimed that:
“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.
This is not analogous. We are speaking of a complete system here.
I have already addressed this. What you have called “update speed” is determined by current distribution.
Re: “We are speaking of a complete system here”
I assure you that I could exhibit a GOL field that consisted entirely of gliders moving at c/2 - and then exhibit another GOL field that consisted entirely of gliders moving at c/4. These systems would have different characteristic speeds. Hopefully, you see the analogy now.
OK, sure. But then to continue the analogy, in the resulting speed is a function of the initial configuration. :)
Just so. I never said otherwise. You already asked for clarification about whether I thought that the system’s “update speed” was to do with its prior Prob. Dist. - and I said that “yes”, it was.
Hm; there may not be a disagreement here. You seemed to be using it in a way that implied it was not determined by (or even was independent of) the prior. Was I mistaken there?
The idea was that some agents update faster than others (or indeed not at all).
If you like you can think of the agents that update relatively slowly as being confident that they are uncertain about the things they are unsure about. That confidence in their own uncertainty could indeed be represented by other priors.
That’s not “other priors”, there’s just one prior. All the probabilities in Bayes’ Rule come from the updated-to-current version of the prior.
Other prior probabilities. There is one prior set of probabilities, which is composed of many prior probabilities and probability distributions.
If you want to think about it that way, please don’t say “other priors”. That’s very confusing, because “prior” in this context refers to the whole prior, not to pieces of it (which I’m not sure how you’re detangling from each other, anyway). If we’re talking about something of the universal-prior sort, it has one prior, over its total sensory experience; I’m not clear how you’re decomposing that or what alternative model you are suggesting.
The two types of prior probability I discussed were “belifs about the world” and “beliefs about the certainty of those beliefs”.
An agent that updates its beliefs about the world rapidly (in response to evidence) would have a low degree of certainty about those beliefs—while an agent that updates its beliefs about the world slowly would have a high degree of certainty that those beliefs were already correct—and were backed up with lots of existing evidence.
I gave an example of this already when I discussed the magician’s coin.
Except these aren’t separate things. That isn’t how this sort of system works! Its beliefs about the certainty of those beliefs are determined by its beliefs about the world.
Well, everything is about the world, if materialism is true.
You don’t seem to be even trying to perform a sympathetic reading. Leave aside quibbling about what is to do with the world—can you at least see that in the first case, updates happen quickly, and in the second case they happen slowly? “Speed” just refers to distance divided by time. Here distance is the probabiliy delta, and time is simply time. So, updates can happen fast and slow. Some systems update quickly, others update slowly—and others don’t update at all. This all seems fairly simple to me—what is the problem?
Well, sure. But that statement is trivial.
Right. I really don’t think that what I am saying is controversial. The way I remember it, I talked about systems with different update speeds—and you jumped on that.
Alternatively, I could say, I went with the assumption that you were attempting to carve the relevant concepts at the joints and getting it wrong, rather than that you were making a true statement which doesn’t even try to accomplish that.
M, sorry then. But you didn’t explain the term anywhere, so I assumed it meant what it sounded like—the original context makes it sound like you mean something separate from the prior, rather than something determined by it. If instead of talking about building an agent that were “confident in their priors” and “updated them slowly” you had just spoken of “priors that result in slow updating” I don’t think there would have been a problem. (I must admit I probably also wasn’t inclined to look for a sympathetic reading as your other comments about the universal prior seem to be just wrong. )