There are a lot of great comments on my last post, “Better Living Through Statistics: Muslim Terrorists Edition.” A few observations:

That Muslims are far more likely to be terrorists than others is barely relevant to our day-to-day lives given that we live in a world where almost no one is a terrorist. p(Terrorist|Muslim) might be much, much higher than p(Terrorist|non-Muslim), but in a world where both are maybe a few one-hundredths or one-thousandths of one percent, that information probably isn’t very informative or a sufficient justification for looking skeptically at someone wearing traditional Muslim garb in a grocery store or on a plane. The fundamental problem is that people dramatically over-estimate the likelihood of terrorism.

If p(Muslim|Terrorist) is 95.3%–the number from Easterly’s post; I haven’t verified it, but for the sake of the argument, let’s assume it’s accurate–and there has been a terrorist attack, then yes, the terrorist was probably a Muslim. Some commenters are absolutely right to point this out, but this doesn’t mean we should be suspicious of Muslims in immigration policy, security policy, or day-to-day life.

Consider sex crimes like child molestation or rape. I don’t have estimates in front of me but my impression is that p(male|child molester) and p(male|rapist) are both pretty high. Therefore, it’s probable that the perpetrator was a male given that a child has been molested or given that someone has been raped. Given that there are so many men and so few child molesters and rapists among them, you’re looking for a needle in a very large haystack. Similarly, Muslim terrorists are needles in very large haystacks given that there are so many Muslim non-terrorists.

Unfortunately, I agree with Tyler Cowen’s claim even though I hope he’s wrong: “There is a good chance these events doom immigration reform, by the way.” Given that there are so few terrorists to begin with, there’s no reason it should.