Bayes' Theorem Illustrated (My Way)

http://lesswrong.com/lw/2b0/bayes_theorem_illustrated_my_way

by rms • 16 years ago

94 18 16 years ago

erikstarck• 16 years ago

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. :)

th• 16 years ago

Probably the most helpful resource online for me academically has been Wikipedia. I have had TAs and professors who recommended reading specific Wikipedia articles to brush up on related topics, especially in math classes.

mazuhl• 16 years ago

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!)

NEPatriot• 16 years ago

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

bockris• 16 years ago

Not a direct answer to your question but I like this website for 'explain the math' type articles.

http://betterexplained.com/

(The author is HN user kalid.)

MikeCapone• 16 years ago

I wish I had access to Khan Academy (http://www.khanacademy.org/) back when I was in high-school.

Luff• 16 years ago

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

rms• 16 years ago

Agreed.

nerme• 16 years ago

I know, I know, really immature... but...

...isn't it kind of funny that he made the venn diagram on mammograms look like the same body part being tested for cancer?

chrismealy• 16 years ago

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.

Sukotto• 16 years ago

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.

JoeAltmaier4• 16 years ago

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.

kd5bjo• 16 years ago

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.

JoeAltmaier4• 16 years ago

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.

pjscott• 16 years ago

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.

Bayes' Theorem Illustrated (My Way)

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