

Bayes' Theorem Illustrated (My Way) - rms
http://lesswrong.com/lw/2b0/bayes_theorem_illustrated_my_way

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Luff
For me, the most intuitive way of illustrating Bayes' theorem is using Venn
diagrams: [http://blog.oscarbonilla.com/2009/05/visualizing-bayes-
theor...](http://blog.oscarbonilla.com/2009/05/visualizing-bayes-theorem/)

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chrismealy
That's really nice. Thanks for the link. Bayes' theorem is a lot less
complicated than its enthusiasts make it seem, especially Yudkowsky. If you
understand conditional probability and if you know how to check your work in
algebra then you already know Bayes' theorem.

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erikstarck
This post makes me wish I had access to the web when I went to school. I would
probably have launched a collaborative lets-explain-the-math-book-together
site or something. Or maybe I would just have played World of Warcraft all day
long.

What would you have done (or: what did you do if you're not an old f*rt such
as me) if you went to school today, with all the technology available?

EDIT: I'm 34, by the way. Not _that_ old. :)

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mazuhl
There is a demand for this kind of thing outside of just high-school. I'm not
in a position to go back to high-school or university, but I'd like (and would
pay) to be able to "study along" with other people on a course/textbook.

(This is partly a lazyweb request - if this exists, someone tell me where!)

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NEPatriot
As would I. Kind of like a crossfit.com or dailyburn for education. Social,
community based learning.

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Sukotto
I wish authors of these sorts of articles put the correct solution _first_
instead of the incorrect one. I'm more likely to remember the first proof I
read and this sort of thing screws me up.

Other than that, I found it a really interesting read.

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pjscott
I will confess: I never memorized Bayes theorem. I just imagine rectangles
getting chopped into overlapping pieces, and visually derive it every time I
need to use it. I've found that this actually worked better for me than trying
to apply a formula, since you're less likely to forget intuitions when you're
thinking through a problem.

Pictures are, by far, my favorite way to explain Bayes theorem.

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JoeAltmaier
Monty Hall problem explained wrong. There is no "probability" of Monty opening
any "goat door". Monty KNOWS which doors contain goats,and always opens one of
them. You have a better chance choosing the remaining door Monty "owns"
because he had a 2-out-of-three chance to begin with (you chose randomly and
uniformly). He still has that chance. No information was added when he opened
a door, because he can ALWAYS open a goat door.

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kd5bjo
It is explained correctly. There are two doors with goats, and he opens one of
them randomly if you didn't pick one of them. Note that he explains it twice;
the first time with the common logic error that he tends to make and the
second correctly.

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JoeAltmaier
Whether Monty opens a door or not doesn't change your probability - the door
you chose has 1/3 chance. Wave your hands all you want and show off bogus math
if you like.

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JoeAltmaier
Ok, smart guys. Imagine Monty didn't have any "probability" of opening a "goat
door": he just opens the 1st one (or only one if he only holds 1). It doesn't
change anything about the problem; but that fake math quits working.

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gwillen
I almost believed you, until I ran through this version of the problem, and
realized that, if I know Monty always opens the lower-numbered goat door, it
actually gives a completely different result.

In particular, if I pick door 2, and Monty picks door 3, this _guarantees_
that the car is behind door 1 under your version of the problem. Meanwhile, if
I pick door 2, and Monty picks door 1, it is now 50/50 whether I should switch
or not, instead of 2/3 to 1/3. Try the math yourself and see.

So the reason the "fake math" quits working is that you've changed the
problem; if you do the math using the method at the link, for your version of
the problem, you _rightly_ get different results, and I believe they are
correct.

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JoeAltmaier
Not quite. You may have picked the right door all along. It clearly doesn't
matter then which door Monty opens, since they both show goats.

