Stupid Questions Open Thread Round 3

OpenThreadGuy

From Costanza's original thread (entire text):

"This is for anyone in the LessWrong community who has made at least some effort to read the sequences and follow along, but is still confused on some point, and is perhaps feeling a bit embarrassed. Here, newbies and not-so-newbies are free to ask very basic but still relevant questions with the understanding that the answers are probably somewhere in the sequences. Similarly, LessWrong tends to presume a rather high threshold for understanding science and technology. Relevant questions in those areas are welcome as well. Anyone who chooses to respond should respectfully guide the questioner to a helpful resource, and questioners should be appropriately grateful. Good faith should be presumed on both sides, unless and until it is shown to be absent. If a questioner is not sure whether a question is relevant, ask it, and also ask if it's relevant."

Meta:

How often should these be made? I think one every three months is the correct frequency.

Costanza made the original thread, but I am OpenThreadGuy. I am therefore not only entitled but required to post this in his stead. But I got his permission anyway.

Meta:

I still haven't figured out a satisfactory answer to the previous meta question, how often these should be made. It was requested that I make a new one, so I did.
I promise I won't quote the entire previous threads from now on. Blockquoting in articles only goes one level deep, anyway.

From the last thread:

From Costanza's original thread (entire text):

"This is for anyone in the LessWrong community who has made at least some effort to read the sequences and follow along, but is still confused on some point, and is perhaps feeling a bit embarrassed. Here, newbies and not-so-newbies are free to ask very basic but still relevant questions with the understanding that the answers are probably somewhere in the sequences. Similarly, LessWrong tends to presume a rather high threshold for understanding science and technology. Relevant questions in those areas are welcome as well. Anyone who chooses to respond should respectfully guide the questioner to a helpful resource, and questioners should be appropriately grateful. Good faith should be presumed on both sides, unless and until it is shown to be absent. If a questioner is not sure whether a question is relevant, ask it, and also ask if it's relevant."

Meta:

How often should these be made? I think one every three months is the correct frequency.

Costanza made the original thread, but I am OpenThreadGuy. I am therefore not only entitled but required to post this in his stead. But I got his permission anyway.

Meta:

I still haven't figured out a satisfactory answer to the previous meta question, how often these should be made. It was requested that I make a new one, so I did.
I promise I won't quote the entire previous threads from now on. Blockquoting in articles only goes one level deep, anyway.

If zero and one aren't probabilities, how does Bayesian conditioning work? My understanding is that a Bayesian has to be certain of the truth of whatever proposition that she conditions on when updating.

If you observe X then the thing you update on is "I observed X" and not just "X". Just because you observed something doesn't mean it was necessarily the case (you could be hallucinating etc.). So while you don't assign probability 1 to "X" you do assign probability 1 to "I observed X", which is fine.

17Richard_Kennaway14y

Zero and one are probabilities. The apparent opposite claim is a hyperbole intended to communicate something else, but people on LessWrong persistently make the mistake of taking it literally. For examples of 0 and 1 appearing unavoidably in the theory of probability, P(A|A) =1 and P(A|-A)=0. If someone disputes either of these formulae, the onus is on them to rebuild probability theory in a way that avoids them. As far as I know, no-one has even attempted this. But P(A|B) = P(A&B)/P(B) for any positive value of P(B). You can condition on evidence all day without ever needing to assert a certainty about anything. Your conclusions will all be hypothetical, of the form "if this is the prior over A and this B is the evidence, this is the posterior over A". If the evidence is uncertain, this can be incorporated into the calculation, giving conclusions of the form "given this prior over A and this probability distribution over possible evidence B, this is the posterior over A." If you are uncertain even of the probability distribution over B, then a hard-core Bayesian will say that that uncertainty is modelled by a distribution over distributions of B, which can be folded down into a distribution over B. Soft-core Bayesians will scoff at this, and turn to magic, a.k.a. model checking, human understanding, etc. Hard-core Bayesians will say that these only work to the extent that they approximate to Bayesian inference. Soft-core Bayesians aren't listening at this point, but if they were they might challenge the hard-core Bayesians to produce an actual method that works better.

9Desrtopa14y

This isn't necessary. In many circumstances, you can approximate the probability of an observation you're updating on to 1, such as an observation that a coin came up heads. An observation never literally has a probability of 1 (you could be hallucinating, or be a brain in a jar, etc.) Sometimes observations are uncertain enough that you can't approximate them to 1, but you can still do the math to update on them ("Did I really see a mouse? I might have imagined it. Update on .7 probability observation of mouse.")

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Stupid Questions Open Thread Round 3

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Stupid Questions Open Thread Round 3

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