# Eh, what?July 21, 2004 4:25 PM   Subscribe

An Intuitive Explanation of Bayesian Reasoning. [Page contains Java]
posted by Gyan (9 comments total)

I got the answer to the breast cancer question at the very beginning correct without the laborious explanation (or I got it roughly right, I would have said 7.69%, not 7.8%). Same easy (and correct) answer for the Pearl/Egg/Blue question...

I got less than 3 hours of sleep last night and worked a 12+ hour day (damn you bored Korean crackers/open proxy maintainers).

What are the chances I can stay awake to read the rest of this very detailed article?

Go!

[Thanks Gyan!]
posted by togdon at 5:06 PM on July 21, 2004

Ok, so this is the crux for me:

"Even if you happen to be one of the fortunate people who can easily grasp and apply abstract theorems, the mental-juggling problem is still something to bear in mind if you ever need to explain Bayesian reasoning to someone else.

If you do find yourself losing track, my advice is to forget Bayes' Theorem as an equation and think about the graph. p(A) and p(~A) are at the top. p(X|A) and p(X|~A) are the projection factors. p(X&A) and p(X&~A) are at the bottom. And p(A|X) equals the proportion of p(X&A) within p(X&A)+p(X&~A). The graph isn't shown here - but can you see it in your mind?

And if thinking about the graph doesn't work, I suggest forgetting about Bayes' Theorem entirely - just try to work out the specific problem in gizmos, hoses, and sparks, or whatever it is."

I guess I get the theorem, and I sort of understand how it gets applied, but there's no way I'd think of these problems in terms of the theorem... Gizmos, hoses, and sparks I get. This I do not:

p(X|A)*p(A)
p(A|X) =   ---------------------------
p(X|A)*p(A) + p(X|~A)*p(~A)

posted by togdon at 5:36 PM on July 21, 2004

With the breast-cancer thing, I saw how to arrive at the answer because I realized the question was about false postives, false negatives etc. in testing for presence or absence of something, and I just needed to find out how many in each of the four groups to calculate the answer.

Is that what the equation togdon is showing above really saying?
posted by alumshubby at 5:45 PM on July 21, 2004

alumshubby, Here's the Rosetta stone of his example:

"To find the chance that a woman with positive mammography has breast cancer, we computed:

p(positive|cancer)*p(cancer)
-------------------------------------------------------------
p(positive|cancer)*p(cancer) + p(positive|~cancer)*p(~cancer)

which is
p(positive&cancer) / [p(positive&cancer) + p(positive&~cancer)]
which is
p(positive&cancer) / p(positive)
which is
p(cancer|positive)

Like I said, I get gizmos, hoses, and sparks. It's cool that there's a forumla to plug things into to get the answer, but I doubt I'll ever see a problem and think "Oh boy! It's Bayesian!"
posted by togdon at 5:58 PM on July 21, 2004

That is one of the least intuitive intuitive things I've ever seen, but I guess intuitive is in the eye of the intuiter.
posted by signal at 7:11 PM on July 21, 2004

Apparently I still suck at math.

Well, I'd better get a pen and pencil and see if I can drill this into me. God knows if Baynesian reasoning comes up in my industrious career of living heavy objects and moving them onto trucks, I'd better be damn well prepared.
posted by Veritron at 7:23 PM on July 21, 2004

Fantastic link, Gyan. I salute you.
posted by trharlan at 8:48 PM on July 21, 2004

wtf? I hate to think of what the unintuitive explanation is like.
posted by Pericles at 4:18 AM on July 22, 2004

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