h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

That Bayes Theorem was actually:

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

Am I wrong?

How were you planning on getting P(B|A) there?
From the formula
P(B|A) = P(A|B)*P(A)/P(B)?

Well, something like that, anyway. But it's definately *not* what's given in the entry - IIRC that's just the definition of conditional probabilities...

A wee search for Bayes' Theorem on the net, and now I know you are absolutely right. P(A|B) = P(B|A)*P(A)/P(B) is the correct formula.
Silly me thought it wouldn't be usefull, but of course it is _if_ your data gives you P(B|A), P(A) and P(B).
No wonder I almost failed stats.

Stop me if I'm wrong, but doesn't P(A,B) = P(A|B)*P(B) make sense?

Tut Tut. Don't you people know nuffink? I would have thought the answer was obvious! Start a movement- Eat more prunes
Pete

Well, it's true, though I don't know about it making *sense*... what kind of sense?

The answer is simple.

P(A|B) := P(A,B) / P(B)

(This is a *definition*, not a theorem.)

With this you can easily transform the two representations of Bayes' theorem into each other. (Given that P(B) > 0, which is mosty -- also in the entry -- taken for granted.)

Bayes' Theorem is usually defined for a sequence of probabilities, but that's too complicated for the entry. I did say it was the simplest statement . If we're picky, all theorems are simply consequences of definitions. Bayes' Theorem can also be seen as:

P(B)P(A|B) = P(A)P(B|A)

or even:

P(A|B) prop to P(A,B)

In most mathematical areas the very fundamental theorems look blindingly obvious.