

The Mathematics of Changing Your Mind - jonburs
http://www.nytimes.com/2011/08/07/books/review/the-theory-that-would-not-die-by-sharon-bertsch-mcgrayne-book-review.html?pagewanted=all

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IvoDankolov
I had to do a double take when I saw Bayes's theorem on that illustration -
"wait a second, did I read that domain name correctly"?

Even more surprising is that they would use the terminology of prior and
posterior probabilities and the like, applied correctly. It gives one the
impression that the author knows what he is talking about.

I don't know how motivating this article would be to someone without training
in probability theory, though. I mean, it's all well and good to be factually
correct, but showering people outside of the field with technical terms and
"weird" claims can, I think, be very counterproductive.

Concerning the theorem itself, no effort was actually made to at least
rephrase it in a more friendly way. It's not enough to just poke fun at
yourself with "(trumpets sound here)". Many people, even with formal
mathematical training do not intuitively understand why it is true, and
without that, applying it for probability calculations would feel like hollow
and mindless mechanical work.

To that effect, I also recommend Eliezer's explanation, found at [0]. I must
admit that I kind of glossed over it, because I had the correct intuition
regardless of not formally knowing the theorem (no idea how to reproduce that,
unfortunately, because it would be a pretty good tool), but even so, I found
it both funny and informative. And as a bonus, it doesn't assume that you have
any rigorous training in mathematics (a common misconception among
mathematical explanations).

[0] : <http://yudkowsky.net/rational/bayes>

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wnoise
> Even more surprising is that they would use the terminology of prior and
> posterior probabilities and the like, applied correctly. It gives one the
> impression that the author knows what he is talking about.

Well, the author of the review is John Allen Paulos, a mathematics professor.

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kqr2
An intuitive expanation of Bayes' theorem:

<http://yudkowsky.net/rational/bayes>

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gosub
An Intuitive Explanation of Eliezer Yudkowsky’s Intuitive Explanation of
Bayes’ Theorem:

<http://commonsenseatheism.com/?p=13156>

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tmoertel
While I can understand why probability textbooks present Bayes' Theorem as

P(A|B) = [ P(B|A) * P(A) ] / P(B),

I've always thought the following rewrite makes more sense when the
probabilities represent degrees of belief:

P(A|B) = P(A) * [ P(B|A) / P(B) ]

In other words:

(posterior belief) = (prior belief) * (evidence adjustment)

Also, while Bayes' Theorem follows from probability axioms, Bayes' Rule for
updating beliefs in light of new evidence (which has the same formulation) is
justified by Cox's Theorem:

<http://en.wikipedia.org/wiki/Coxs_theorem>

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kilian
Is there any way for us paywalled people to read this?

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_delirium
Apart from the obvious (buy a subscription), you can open the link in an
incognito/private-browsing session, since the NYT monthly page limit seems to
be based on cookies.

