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Manfred comments on Help me teach Bayes' - Less Wrong Discussion
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Comments (19)
Probability is a mathematical object called a measure, which means it obeys exactly the same rules as area or volume. This is why the "visualizing Bayes' theorem" link is exactly true. Probabilities are like circles (or other shapes) with area equal to their probability, and these circles overlap when two things happen together. So I think the Venn diagram explanation might help students remember it.
I was under the impression that ET Jaynes did not like the circle diagram because it implied an infinitude of outcomes:
http://www-biba.inrialpes.fr/Jaynes/cc02m.pdf
Hm, good point. For example, for his statements "It will rain today" and "the roof will leak," the points in the Venn diagram you'd draw to show how these probabilities overlap don't correspond to anything real. On the other hand, it's really useful to picture this stuff, and you can imagine "chunking up" your space into regions corresponding to the different discrete outcomes (like a bar graph), and the exact same rules are followed, except now it seems a bit more meaningful.