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woozle comments on What is Bayesianism? - Less Wrong

81 Post author: Kaj_Sotala 26 February 2010 07:43AM

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Comment author: woozle 28 February 2010 11:17:37PM 2 points [-]

Okay -- but in practicality, what if I don't have time (or mental focus, or whatever resources it takes) to explicitly identify, enumerate, and evaluate each piece of evidence that I may be considering? It took me over an hour just to get this far with a Bayesian analysis of one hypothesis, which I'm probably not even doing right.

Or do we step outside the realm of Bayesian Rationality when we look at practical considerations like "finite computing resources"?

Comment author: Eliezer_Yudkowsky 01 March 2010 12:24:15AM 3 points [-]

I'd actually say, start with the prior and with the strongest piece of evidence you think you have. This of itself should reveal something interesting and disputable.

Comment author: FAWS 01 March 2010 12:21:43AM *  0 points [-]

As someone who recently failed at an attempt at Bayesian analysis let my try to offer a few pointers: You correctly conclude that "What is the likelihood that evidence E would occur even if H were false?" is more immediately relevant than "What is the likelihood that evidence E would not occur if H were true?", which you only asked because you got the syntax wrong, "the likelihood that evidence E would occur even if H were false" would be P(E|~H). P(H) is your prior, the probability before considering any evidence E, not the probability in absence of any evidence. The considerations you list under evidence against are of the sort you would make when determining the priors, asking "What is the likelihood that Bush is a twit if H were true?" and so on would be very difficult to set probabilities for, you CAN threat it that way but it's far from straightforward.

Actually I have never seen a non-trivial example of this sort of analysis for this sort of real word problem done right on this site.

H = this sort of analysis is practical

E = user FAWS has not seen any example of this sort of analysis done right.

P(H)=0.9 smart people like Eliezer seem to praise Bayesian thinking, and people ask for priors and so on.

P(E|H)= 0.3 I haven't read every comment, probably not even 10%, but if this is used anywhere it would be here, and if it's practical it should be used at least somewhat regularly.

P(E|~H) =0.9 Might still be done even if impractical when it's a point of pride and / or group identification, which could be argued to be the case.

Calculating the posterior probability P(H|E):

P(H|E) = P(H&E)/P(E)= P(H)*P(E|H)/P(E)= P(H)*P(E|H)/(P(E|H)*P(H)+P(E|~H)\P(~H))= 0.9 * 0.3 /(0.3 * 0.9 + 0.9 * 0.1)= 0.75