Mammography problem from 'Intro to Bayes' in my own words/picture

by jwhendy1 min read9th Apr 201113 comments

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I've been reading through the sequences, and am currently working through the Intro to Bayes' Theorem (by the fact that I'm reading the Intro to Bayes (finally), you can tell that I'm pretty early in the process). It's been quite thought provoking. I'm finally getting questions right more reliably, and wanted to share one of the visualization tools that helped me, at least. There are many "applets" strewn about, written in Java, that help one to visualize what the various probability components are doing. In the mammography example, at least, an the idea of a sieve popped into my head as a neat way to think about what the test is doing.

I'm planning to take fairly extensive notes (more about that in a soon-to-come post), but thought I'd share a little "re-write" of that problem with a graphic in case it's of any use, and also in case I've blundered in my understanding. Re-writing things in my own words helps make them my own -- I realize that this is probably going to come across as really, really, incredibly, simplistic, but it's where I'm at!

In case it's not intuitive... it's supposed to show 100% of women broken into their measured partitions of 1% with cancer and 99% without. Those respective groups are then "sifted," and the known reliability of the sieve for each of those groups is used to determine p(cancer|test+).

I'm open to aesthetic critiques as well -- I enjoy making things like this and knowing how intuitive it is to look at is helpful. It didn't turn out how my mind visualized it, but I figured it was decent enough for a start.

This was made using emacs org-mode, LaTeX, and TikZ.

Update: per some comments, I tried to make things more clear in a redo. The original picture shown is HERE.

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