According to secret documents issued to interrogators at Guantánamo Bay, obtained and released by The Guardian, "the Casio F-91W digital watch was declared to be 'the sign of al-Qaeda' and a contributing factor to continued detention of prisoners by the analysts stationed at Guantánamo Bay. Briefing documents used to train staff in assessing the threat level of new detainees advise that possession of the F91W – available online for as little as £4 – suggests the wearer has been trained in bomb making by al-Qaeda in Afghanistan." United States Military intelligence officials have identified the F91W as a watch that terrorists use when constructing time bombs.

One learns something new every day. Good that I went with the W59 instead :)

United States Military intelligence officials have identified the F91W as a watch that terrorists use when constructing time bombs.

https://en.wikipedia.org/wiki/File:Al_Qaida_watch_timer_on_p...

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.

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

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.

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.

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

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.

The point was that sensitivity and specificity are always a trade off. Failing to understand this correctly has been a huge problem in practice.

Examining everyone who breathes, after all, has very high sensitivity.

Only that "wearing F91Ws" increases the chances of them being a terrorist, which is already pretty high, given that we're talking about "detainees", not random people.