Bayes’ theorem and transgender lesbians

Some time ago I read a cool post on Tumblr, but I can’t find it anymore. It was about calculating P(trans|WLW), the fraction of women who love women that is transgender, from P(trans), the fraction of the general population that is transgender, P(WLW), the fraction of the population that is a woman-loving woman, and P(WLW|trans), the fraction of gynephillic trans women among trans people. Bayes’ theorem says

P(trans|WLW) = P(WLW|trans)P(trans)/P(WLW).

I remember that the resulting number was significant. As I could not find it again, here is a quick and dirty reconstruction. For every statistic, I picked the first one I found that did not seem completely unrealistic.

So Bayes’ theorem gives us P(trans|WLW) = 0.15.

Bonus: suicide attempts

While preparing this post, I stumbled upon this report. Page 8 lists:

  • P(attempted suicide) = 0.016.
  • P(attempted suicice|trans) = 0.41.

Bayes now says P(trans|attempted suicide) = 0.26. Big if true.*

Section of Doubt

Applying Bayes’ theorem like this seems to give unreasonably good mileage. That suggests that social scientists aren’t allowed to use numbers from different studies and get conclusions from them, or asymmetric misreporting makes these calculations error-prone.

The last number above is big. Makes one wonder why so little effort is spent explicitly targetting at-risk trans people.

* Added July 16th: I just met a subject expert, she said this figure sounded about right.

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