Thursday, October 20, 2011

The very best Bayes Explanation?

Is by the very interesting Eliezer S. Yudkowsky. Spend some time on his site. It's good to think.

Why is Bayes important?
Here's a story problem about a situation that doctors often encounter:

1% of women at age forty who participate in routine screening have breast cancer.  80% of women with breast cancer will get positive mammographies.  9.6% of women without breast cancer will also get positive mammographies.  A woman in this age group had a positive mammography in a routine screening.  What is the probability that she actually has breast cancer?

Next, suppose I told you that most doctors get the same wrong answer on this problem - usually, only around 15% of doctors get it right. Most doctors estimate the probability to be between 70% and 80%, which is wildly incorrect.

What do you think the answer is?
(see below for the answer. See Yudkowsky for why.)

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