The Bayes theorem applied to the Scandal

The Bayes theorem applied to the Scandal

A friend sends along the following analysis:

Early indicators are that 5% of Catholic clergy in the US since 1950 have been implicated in sex abuse of a minor.

These indicators also show that roughly 90% of these incidents of abuse are homosexual in form, with about 80% involving male post-pubescent youth, and the remainder pre-pubescent boys.

Let’s assume that Richard’s Sipe’s estimate of homosexually active priests is correct, at 15% of all clergy. (Although some have estimated the numbers as high as 40 percent, I think that’s too high. Fifteen percent is conservative.)

Then, according to the Bayes Theorem*, the probability of abuse being perpetrated upon a child by a gay priest is 30%, a pretty high proportion, but still under 50%! (This doesn’t analyze the probability of whether a priest will be faithful to celibacy promise at all, including with adults.)

Also, the probability of abuse being perpetrated by a ‘straight’ priest is 0.6%, a value somewhat less than that of the gays.

.....let’s see, that’s an Odds Ratio of 51 to 1, or, the gay is a mere 51 times more likely to hit on a minor than the straight.

Who was it… oh yes, it was Father Stephen Rossetti of the St. Luke’s Institute, who said that gays are no more likely to abuse a minor than straights.

I wonder if the insurance actuaries base their calculations on the views of the Rev. Rossetti or formula of the Rev. Bayes?

(note: Rev. Thomas Bayes (d. 1761) was a Presbyterian minister.)

Update For clarification and simplifaction, let me re-phrase the conclusion. The likelihood that an abuser will come from among the population of homosexual priests is 51 times higher than it is he will come from among heterosexual priests, because a smaller population (as a percentage) is reponsible for the vast majority (90 percent) of abuse cases. So, it’s not just 9 times greater, but 51 times greater.