wedrifid comments on Trouble with Bayes Theorem? (The actual math is confusing) - Less Wrong

8 Post author: TheatreAddict 25 September 2011 04:49AM

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Comment author: wedrifid 25 September 2011 05:21:42AM 5 points [-]

But when I try to do the same with percentages, it all gets sort of screwy. I take the 80 percent of women (.8) divided by that same 80 percent (.8) plus 9.5 percent of women without cancer who test postive for it (.095). So I get .8/.8+.095=89%.

Let's look at those numbers closely. In particular the numbers on the denominator (80% + 9.5%). What are those percentages of?

  • 80% of women with breast cancer
  • 9.5% of women without cancer

When we add 80% + 9.5% and get 89.5% what is that 89.5% of? Nothing that makes sense because those are two completely different units. It's like adding 80% of an apple with 10% of an orange. We end up with 90% of an appleorange which just looks silly.

I recommend taking a look at An Intuitive Explanation of Eliezer Yudkowsky’s Intuitive Explanation of Bayes’ Theorem.

Comment author: Xachariah 25 September 2011 01:24:52PM 1 point [-]

I came to reccomend that page and the Children's Book version of Bayes Theorem. Bayes Theorem didn't click until I read both of those.

It may seem silly, but I still visualize Bayesian updates as colored polygons.

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