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April 18[edit]

Bayes' Theorem[edit]

The wiki article about it has an illustration with a decision tree that I couldn't understand. Is the following an ok way to think of it and explain it?

Think of a big square with area 1 representing a probability space. Draw two filled circles A and B (maybe unequal sizes) inside the square for the events A and B, so they partly overlap like a Venn diagram. Their areas are the probabilities Pr[A] and Pr[B]. Let C be the intersection of A and B.
Pr[A|B] just means you've picked a point in B and now you want to know the likelihood that it's also in A. That is, it's in the intersection C. So this likelihood is Pr[C]/Pr[B]. Similarly Pr[B|A] is Pr[C]/Pr[A]. Rearranging terms you get Pr[A|B]=Pr[B|A]*Pr[A]/Pr[B] which is Bayes' Theorem.

If yes, is this somehow a wonderful or amazing fact? Why is it usually written as that equation, instead of thinking of intersecting events like the circles above? Thanks! 50.0.136.56 (talk) 03:52, 18 April 2017 (UTC)[reply]

Let's add a link to the article: Bayes' theorem. StuRat (talk) 04:32, 18 April 2017 (UTC)[reply]

Thanks. There's also a separate article Bayes' rule whose purpose I couldn't discern. 50.0.136.56 (talk) 04:37, 18 April 2017 (UTC)[reply]

That's just a redirect to the same article. --76.71.6.254 (talk) 10:53, 18 April 2017 (UTC)[reply]

That was not a redirect until today's edit by Trovatore (special:diff/775983852). --CiaPan (talk) 12:44, 18 April 2017 (UTC)[reply]

It's possible I jumped the gun a little on that one, but I figured it was easy to undo if someone didn't like it. Looking on the talk page, apparently there's some concern that the rule might be useful even in situations where the hypotheses of the theorem are not strictly met. It seems to me that that clarification could be made within a single article, but it may be that it's content that ought to be merged. --Trovatore (talk) 18:12, 18 April 2017 (UTC)[reply]

Oh. You might've mentioned it here, since it was being discussed. Oh well, not important. --76.71.6.254 (talk) —Preceding undated comment added 18:44, 18 April 2017 (UTC)[reply]