You're missing the point about conditional probability.

P(has a F-91W | is a terrorist) != P(is a terrorist | F-91W)

Via Bayes theorem you can fix this with a ratio P(is a terrorist)/P(has a F-91W)

So if the global population of people with F-91W is large relative to the population of terrorists, you are going to have a lot of false positives.

e.g. say that 100% of terrorists have a F-91W, that there are 10,000 terrorists, and that 100M people have F-91W then you still only have a .01% chance that a given F-91W wearer is a terrorist.

Obviously there is more information to go on than just a watch, but that's the point you were replying to.

You're missing the fact that they talked about ALREADY suspect "detainees" in the parent comment -- not the general public.

And you are missing the point about other reasons to suspect F91W users, which have nothing to do with counting watches worn by known terrorists.

Also, you probably don't know whether this watch actually was common in Afganistan in early 2000s.

No, I am not.

That was the purpose of: "Obviously there is more information to go on than just a watch, but that's the point you were replying to."

Your reply did not, in any way, address the conditional probability issue. Which is important, although clearly oversimplified in my example.

This has nothing particular to do with terrorist detection, but to do with detection of any sort where the true positive rate is low (e.g. cancer screening, drug detection,etc.). This is often a very real problem in practical application, and saying "but they actually really found X" does not address it at all. It is exactly that sort of muddy thinking that causes problems with detection in application.

Obviously this is manageable by including enough different information that the marginals get much tighter - if you can find the right ones - but that wasn't the point being made. A cogent reply would have pointed out how exactly additional information was used to reduce this risk.

There is a possibility that you reading too much into the comment which started this thread. It appears to have quite literally meant "the CIA caught terrorists with X so they figured everyone with X is a terrorist". Without convincing evidence that:

a) this was the reasoning used

b) this reasoning was invalid

> Your reply did not, in any way, address the conditional probability issue.

I think I did it here:

Also, you probably don't know whether this watch actually was common in Afganistan in early 2000s.

I was responding to this:

  "Actually, they say they found time bomb detonators based on this watch."

Which, as a response to raising the false positive rate issue, is entirely missing the point.

For what it's worth: Also, you probably don't know whether this watch actually was common in Afganistan in early 2000s.

Also doesn't actually address the issue with false positive rates and conditional probability, but it is a fair point that the (clearly stated) oversimplification is, in fact, oversimplified.