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army1987 comments on Rationality Quotes April 2012 - Less Wrong
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Huh, sure, if the likelihood is a reversed Heaviside step. If the likelihood is itself a Gaussian, then the posterior is a Gaussian whose mean is the weighed average of that of the prior and that of the likelihood, weighed by the inverse squared standard deviations. So even if the st.dev. of the likelihood was half that of the prior for each race, the difference in posterior means would shrink by five times.
Right- there's lots of information out there that will narrow your IQ estimate of someone else more than their race will, like that they're a professional physicist or member of MENSA, but evidence only becomes worthless when it's independent of the quantity you're interested in given the other things you know.
Can you give an example of evidence becoming worthless? (I can't think of any.)
You have a theory that a certain kind of building is highly prone to fire. You see a news report that mentions that a building of that kind has burnt down on Main Street. The news report supports your theory - unless you were a witness to the fire the previous night.
In this case, if the news report is consistent with my recollections, it seems that is evidence of the reliability of the news, and of the reliability of my memory, and additional evidence that the event actually occurred that way.
No?
Yeah, true. But having been there the previous night, and making good observations the previous night, certainly makes the news report go from pretty strong evidence to almost nothing.
EDIT: Really the important thing I think, is that if your observations are good enough than the evidence from the news report is "worthless", in the sense that you shouldn't pay to find out whether there was a news report that backs up your observations. It's not worth the time it takes to hear it..
Hm.
Maybe I'm missing your point altogether, but it seems this is only true if the only thing I care about is the truth of that one theory of mine. If I also care about, for example, whether news reports are typically reliable, then suddenly the news report is worth a lot more.
But, sure, given that premise, I agree.
If you were promoting the theory before that point, the police may still have some pointed questions to ask you.
I'm talking about how valuable the evidence is to you, the theory-promoter. If you were there, then the news report tells you nothing you didn't already know.
I understood your point. I was simply making a joke.
Suppose A gives me information about B, and B gives me information about C; they're dependent. (Remember, probabilistic dependence is always mutual.) A gives me information about C (through B) only if I don't know B. If I know B, then A is conditionally independent of C, and so learning A tells me nothing about C.
So essentially... a new fact is useless only if it's a subset of knowledge you already have?
That seems like a fine way to put it.