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JoshuaZ comments on Bayes' Theorem Illustrated (My Way) - Less Wrong

126 Post author: komponisto 03 June 2010 04:40AM

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Comment author: JoshuaZ 03 June 2010 10:17:19PM *  4 points [-]

It might help to read the sequences, or just read Jaynes. In particular, one of the central ideas of the LW approach to rationality is that when one encounters new evidence one should update one's belief structure based on this new evidence and your estimates using Bayes' theorem. Roughly speaking, this is in contrast to what is sometimes described as "traditional rationalism" which doesn't emphasize updating on each piece of evidence but rather on updating after one has a lot of clearly relevant evidence.

Edit: Recommendation of Map-Territory sequence seems incorrect. Which sequence is the one to recommend here?

Comment author: Vive-ut-Vivas 03 June 2010 10:34:16PM *  2 points [-]
Comment author: Houshalter 03 June 2010 11:38:18PM *  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.

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 *  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.

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 09:24:37AM 1 point [-]

(reductionism and non-locality would probably be high up on the list).

Guessing here you mean locality instead of nonlocality?

Comment author: JoshuaZ 04 June 2010 12:45:21PM 0 points [-]

Yes, fixed thank you.