UPDATE 11am response to commentator: is there an association between inability to understand Bayes’ theorem with ethnic prejudice?
UPDATE 3:30PM explaining risk of false positives to congressmen and commentators
Congressman Chairman: Muslims! Terrorists! Muslims! Terrorists!
Witness: Let A be the event of terrorism, and B be the event of Muslimism. Then P(A|B)≠P(B|A)
Congressman: What are you talking about?
Witness: You seem to be confusing the probability that a Muslim person will be a terrorist with the probability that a terrorist person will be a Muslim
Congressman: And you seem to be confusing everyone in this hearing, smartass.
Congressman: What did you just call me?
Witness: it’s simple, the probability that a Muslim will be a terrorist will be 13,000 times lower than the probability that a terrorist will be a Muslim. That is, the ratio of the probability of being a terrorist to the probability of being a Muslim is about 1 over 13,000 (P(A)/P(B)).
Congressman: so even the math department has been taken over by politically correct academic radicals who hate America?
Witness: even if you think that the Probability of a Terrorist being a Muslim is 95.3%, the probability of a Muslim being a Terrorist is only 0.0007%. That is less than the probability of a left-handed octogenarian Olympic discus-thrower being struck by lightning.
Congressman: or maybe even less than the probability that anyone is listening to you?
Witness: maybe this picture will help.
Congressman: I’m calling your state legislature right now to fire your radical butt.
POSTCRIPT: response to commentator:
Mr. McKinney, perhaps your prejudices led you to mis-read the piece. 13,000 was how much larger one conditional probability was than another, which is helpful for understanding Bayes’ Theorem but not for policy. The policy-relevant probability is that of a Muslim being a terrorist, which based on a Rand report was calculated here as 0.007 percent.
Regards, Bill Easterly
POSTCRIPT 2 3:30PM
To the Congressman and Mr. McKinney (again):
One other probability you may want to consider is that Al-Qaeda’s recruiting will become more successful by a δ >= 0.0007 percent after you have persecuted the 99.9993 percent of Muslims who are innocent.