Comment author:Houshalter
03 June 2010 11:38:18PM
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0 points
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Updating your belief based on different pieces of evidence is useful, but (and its a big but) just believing strange things based on imcomplete evidence is bad. Also, this neglects the fact of time. If you had an infinite amount of time to analyze every possible scenario, you could get away with this, but otherwise you have to just make quick assumptions. Then, instead of testing wether these assumptions are correct, you just go with them wherever it takes you. If only you could "learn how to learn" and use the Bayesian method on different methods of learning; eg, test out different heuristics and see which ones give the best results. In the end, you find humans already do this to some extent and "traditional rationalism" and science is based off of the end result of this method. Is this making any sense? Sure, its useful in some abstract sense and on various math problems, but you can't program a computer this way, nor can you live your life trying to compute statistics like this in your head.

Other than that, I can see different places where this would be useful.

Comment author:thomblake
04 June 2010 04:08:42PM
7 points
[-]

nor can you live your life trying to compute statistics like this in your head

And so it is written, "Even if you cannot do the math, knowing that the math exists tells you that the dance step is precise and has no room in it for your whims."

Comment author:JoshuaZ
04 June 2010 01:55:47AM
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2 points
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I may not be the best person to reply to this given that I a) am much closer to being a traditional rationalist than a Bayesian and b) believe that the distinction between Bayesian rationalism and traditional rationalism is often exaggerated. I'll try to do my best.

Updating your belief based on different pieces of evidence is useful, but (and its a big but) just believing strange things based on incomplete evidence is bad.

So how do you tell if a belief is strange? Presumably if the evidence points in one direction, one shouldn't regard that belief as strange. Can you give an example of a belief that should considered not a good belief to have due to strangeness that one could plausibly have a Bayesian accept like this?

Also, this neglects the fact of time. If you had an infinite amount of time to analyze every possible scenario, you could get away with this, but otherwise you have to just make quick assumptions.

Well yes, and no. The Bayesian starts with some set of prior probability estimates, general heuristics about how the world seems to operate (reductionism and locality would probably be high up on the list). Everyone has to deal with the limits on time and other resources. That's why for example, if someone claims that hopping on one foot cures colon cancer we don't generally bother testing it. That's true for both the Bayesian and the traditionalist.

Sure, its useful in some abstract sense and on various math problems, but you can't program a computer this way, nor can you live your life trying to compute statistics like this in your head

I'm curious as to why you claim that you can't program a computer this way. For example, automatic Bayesian curve fitting has been around for almost 20 years and is a useful machine learning mechanism. Sure, it is much more narrow than applying Bayesianism to understanding reality as a whole, but until we crack the general AI problem, it isn't clear to me how you can be sure that that's a fault of the Bayesian end and not the AI end. If we can understand how to make general intelligences I see no immediate reason why one couldn't make them be good Bayesians.

I agree that in general, trying to generally compute statistics in one's head is difficult. But I don't see why that rules out doing it for the important things. No one is claiming to be a perfect Bayesian. I don't think for example that any Bayesian when walking into a building tries to estimate the probability that the building will immediately collapse. Maybe they do if the building is very rickety looking, but otherwise they just think of it as so tiny as to not bother examining. But Bayesian updating is a useful way of thinking about many classes of scientific issues, as well as general life issues (estimates for how long it will take to get somewhere, estimates of how many people will attend a party based on the number invited and the number who RSVPed for example both can be thought of in somewhat Bayesian manners). Moreover, forcing oneself to do a Bayesian calculation can help bring into the light many estimates and premises that were otherwise hiding behind vagueness or implicit structures.

Comment author:Sniffnoy
04 June 2010 09:32:13AM
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1 point
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Well for example, if you have a situation where the evidence leads you to believe that something is true, and there is an easy, simple, reliable test to prove its not true, why would the bayesian method waste its time? Immagine you witness something which could be possible, but its extremely odd. Like gravity not working or something. It could be a hallucinations, or a glitch if your talking about a computer, and there might be an easy way to prove it is or isn't. Under either scenerio, whether its a hallucination or reality is just weird, it makes an assumption and then has no reason to prove whether this is correct. Actually, that might have been a bad example, but pretty much every scenario you can think of, where making an assumption can be a bad thing and you can test the assumptions, would work.

Firstly, priors are important; if something has a low prior probability, it's not generally going to get to a high probability quickly. Secondly, not all evidence has the same strength. Remember in particular that the strength of evidence is measured by the likelihood ratio. If you see something that could likely be caused by hallucinations, that isn't necessarily very strong evidence for it; but hallucinations are not totally arbitrary, IINM. Still, if you witness objects spontaneously floating off the ground, even if you know this is an unlikely hallucination, the prior for some sort of gravity failure will be so low that the posterior will probably still be very low. Not that those are the only two alternatives, of course.

Comment author:JoshuaZ
04 June 2010 03:16:46AM
0 points
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Well for example, if you have a situation where the evidence leads you to believe that something is true, and there is an easy, simple, reliable test to prove its not true, why would the bayesian method waste its time? Immagine you witness something which could be possible, but its extremely odd. Like gravity not working or something. It could be a hallucinations, or a glitch if your talking about a computer, and there might be an easy way to prove it is or isn't. Under either scenerio, whether its a hallucination or reality is just weird, it makes an assumption and then has no reason to prove whether this is correct. Actually, that might have been a bad example, but pretty much every scenario you can think of, where making an assumption can be a bad thing and you can test the assumptions, would work.

If there is an "easy, simple, reliable test" to determine the claim's truth within a high confidence, why do you think a Bayesian wouldn't make that test?

Well if you can't program a viable AI out of it, then its not a universal truth to rationality.

Can you expand your logic for this? In particular, it seems like you are using a definition of "universal truth to rationality" which needs to be expanded out.

Comment author:Houshalter
04 June 2010 01:06:11PM
0 points
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If there is an "easy, simple, reliable test" to determine the claim's truth within a high confidence, why do you think a Bayesian wouldn't make that test?

Because its not a decision making theory, but a one that judges probability. The bayesian method will examine what it has, and decide the probability of different situations. Other then that, it doesn't actually do anything. It takes an entirely different system to actually act on the information given. If it is a simple system and just assumes to be correct whichever one has the highest probability, then it isn't going to bother testing it.

Comment author:JoshuaZ
04 June 2010 01:36:50PM
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1 point
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The bayesian method will examine what it has, and decide the probability of different situations. Other then that, it doesn't actually do anything. It takes an entirely different system to actually act on the information given. If it is a simple system and just assumes to be correct whichever one has the highest probability, then it isn't going to bother testing it.

But a Bayesian won't assume which one has the highest probability is correct. That's the one of the whole points of a Bayesian approach, every claim is probabilistic. If one claim is more likely than another, the Bayesian isn't going to lie to itself and say that the most probable claim now has a probability of 1. That's not Bayesianism. You seem to be engaging in what may be a form of the mind projection fallacy, in that humans often take what seems to be a high probability claim and then treat it like it has a much, much higher probability (this is due to a variety of cognitive biases such as confirmation bias and belief overkill). A good Bayesian doesn't do that. I don't know where you are getting this notion of a "simple system" that did that. If it did, it wouldn't be a Bayesian.

Comment author:Houshalter
04 June 2010 02:31:19PM
0 points
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But a Bayesian wont' assume which one has the highest probability is correct. That's the one of the whole points of a Bayesian approach, every claim is probabilistic. If one claim is more likely than another, the Bayesian isn't going to lie to itself and say that the most probable claim now has a probability of 1. That's not Bayesianism. You seem to be engaging in what may be a form of the mind projection fallacy, in that humans often take what seems to be a high probability claim and then treat it like it has a much, much higher probability (this is due to a variety of cognitive biases such as confirmation bias and belief overkill). A good Bayesian doesn't do that. I don't know where you are getting this notion of a "simple system" that did that. If it did, it wouldn't be a Bayesian.

I'm not exactly sure what you mean by all of this. How does a bayesian system make decisions if not by just going on its most probable hypothesis?

Comment author:jimrandomh
04 June 2010 03:04:35PM
6 points
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To make decisions, you combine probability estimates of outcomes with a utility function, and maximize expected utility. A possibility with very low probability may nevertheless change a decision, if that possibility has a large enough effect on utility.

Comment author:Houshalter
04 June 2010 03:41:46PM
-1 points
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See the reply I made to AlephNeil. Also, this still doesn't change my scenario. If theres a way to test a hypothesis, I see no reason the bayesian method ever would, even if it seems like common sense to look before you leap.

Anyone know why I can only post comments every 8 minutes? Is the bandwidth really that bad?

Comment author:jimrandomh
04 June 2010 03:56:05PM
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3 points
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Bayesianism is only a predictor; it gets you from prior probabilities plus evidence to posterior probabilities. You can use it to evaluate the likelihood of statements about the outcomes of actions, but it will only ever give you probabilities, not normative statements about what you should or shouldn't do, or what you should or shouldn't test. To answer those questions, you need to add a decision theory, which lets you reason from a utility function plus a predictor to a strategy, and a utility function, which takes a description of an outcome and assigns a score indicating how much you like it.

The rate-limit on posting isn't because of bandwidth, it's to defend against spammers who might otherwise try to use scripts to post on every thread at once. I believe it goes away with karma, but I don't know what the threshold is.

Comment author:SilasBarta
04 June 2010 04:11:31PM
2 points
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Anyone know why I can only post comments every 8 minutes? Is the bandwidth really that bad?

You face limits on your rate of posting if you're at or below 0 karma, which seems to be the case for you. How you got modded down so much, I'm not so sure of.

Comment author:JoshuaZ
04 June 2010 04:41:57PM
0 points
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By the same reason you were incorrect in your reply to AlephNeil, performing experiments can increase utility if what course of action is optimal is dependent on which hypothesis is most likely.

Comment author:AlephNeil
04 June 2010 03:05:17PM
5 points
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You try to maximize your expected utility. Perhaps having done your calculations, you think that action X has a 5/6 chance of earning you £1 and a 1/6 chance of killing you (perhaps someone's promised you £1 if you play Russian Roulette).

Presumably you don't base your decision entirely on the most likely outcome.

Comment author:Houshalter
04 June 2010 03:19:41PM
-1 points
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So in this scenario you have to decide how much your life is worth in money. You can go home and not take any chance of dying or risk a 1/6 chance to earn X amount of money. Its an extension on the risk/reward problem basically, and you have to decide how much risk is worth in money before you can complete it. Thats a problem, because as far as I know, bayesianism doesn't cover that.

Comment author:AlephNeil
04 June 2010 03:39:48PM
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7 points
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It's not the job of 'Bayesianism' to tell you what your utility function is.

This [by which I mean, "the question of where the agent's utility function comes from"] doesn't have anything to do with the question of whether Bayesian decision-making takes account of more than just the most probable hypothesis.

## Comments (191)

Best*0 points [-]Updating your belief based on different pieces of evidence is useful, but (and its a big but) just believing strange things based on imcomplete evidence is bad. Also, this neglects the fact of time. If you had an infinite amount of time to analyze every possible scenario, you could get away with this, but otherwise you have to just make quick assumptions. Then, instead of testing wether these assumptions are correct, you just go with them wherever it takes you. If only you could "learn how to learn" and use the Bayesian method on different methods of learning; eg, test out different heuristics and see which ones give the best results. In the end, you find humans already do this to some extent and "traditional rationalism" and science is based off of the end result of this method. Is this making any sense? Sure, its useful in some abstract sense and on various math problems, but you can't program a computer this way, nor can you live your life trying to compute statistics like this in your head.

Other than that, I can see different places where this would be useful.

And so it is written, "Even if you cannot do the math, knowing that the math exists tells you that the dance step is precise and has no room in it for your whims."

*2 points [-]I may not be the best person to reply to this given that I a) am much closer to being a traditional rationalist than a Bayesian and b) believe that the distinction between Bayesian rationalism and traditional rationalism is often exaggerated. I'll try to do my best.

So how do you tell if a belief is strange? Presumably if the evidence points in one direction, one shouldn't regard that belief as strange. Can you give an example of a belief that should considered not a good belief to have due to strangeness that one could plausibly have a Bayesian accept like this?

Well yes, and no. The Bayesian starts with some set of prior probability estimates, general heuristics about how the world seems to operate (reductionism and locality would probably be high up on the list). Everyone has to deal with the limits on time and other resources. That's why for example, if someone claims that hopping on one foot cures colon cancer we don't generally bother testing it. That's true for both the Bayesian and the traditionalist.

I'm curious as to why you claim that you can't program a computer this way. For example, automatic Bayesian curve fitting has been around for almost 20 years and is a useful machine learning mechanism. Sure, it is much more narrow than applying Bayesianism to understanding reality as a whole, but until we crack the general AI problem, it isn't clear to me how you can be sure that that's a fault of the Bayesian end and not the AI end. If we can understand how to make general intelligences I see no immediate reason why one couldn't make them be good Bayesians.

I agree that in general, trying to generally compute statistics in one's head is difficult. But I don't see why that rules out doing it for the important things. No one is claiming to be a perfect Bayesian. I don't think for example that any Bayesian when walking into a building tries to estimate the probability that the building will immediately collapse. Maybe they do if the building is very rickety looking, but otherwise they just think of it as so tiny as to not bother examining. But Bayesian updating is a useful way of thinking about many classes of scientific issues, as well as general life issues (estimates for how long it will take to get somewhere, estimates of how many people will attend a party based on the number invited and the number who RSVPed for example both can be thought of in somewhat Bayesian manners). Moreover, forcing oneself to do a Bayesian calculation can help bring into the light many estimates and premises that were otherwise hiding behind vagueness or implicit structures.

Guessing here you mean locality instead of nonlocality?

Yes, fixed thank you.

Comment deleted04 June 2010 03:05:45AM [+] (38 children)