It's a highly useful analysis as applied to, for instance, profiling for random stop-and-frisk street searches where you're just trying to find as many "evildoers" in a crowd as possible - most city cops would do well to realize that even if "profiling works", they're probably doing it far too aggressively, and actually ending up with fewer arrests per search than they would if they didn't profile at all. The paper's conclusion is not so useful when there may or may not be evildoers coming through your screening station and your task is to make sure that as few get through as possible, given a ceiling on the number of searches that you can do.

btilly mentioned (http://news.ycombinator.com/item?id=4154989) that the optimal solution (neglecting game theoretical considerations, which are extremely important!) to the airport screening problem is to set a prior probability cutoff based on resources available, and screen everyone in a group that has P(terrorist|group) above that cutoff, but he didn't elaborate. The gist of the proof, by example, is that if you can only screen 10 people out of a line of 100, then to minimize the chance of a terrorist getting through you should never ever use up one valuable screening on someone with P(terrorist) = .02 if there's someone else with P'(terrorist) = .05. You'd have to be crazy to do so, since that's an extra 3% chance that a terrorist gets through, with no additional benefit.

As for the game theory issues, all I'll add there is that if your prior probabilities are "correct" for the sample coming through the gate, then the strategy still holds. The problem is that if you know that terrorists know that you're profiling and might decide to send in lower probability people, your prior probabilities should change accordingly. How far, who can say...the fact is, our priors are extremely uncertain to begin with in this area, so all of this becomes much more subjective.

It applies whenever a ‘‘bell-ringer’’ event must be found by sampling with replacement, but can be recognized when seen. For example, one can thus sample paths through a trellis or hidden Markov model when their number is too large to enumerate explicitly, but one path can be recognized (e.g., by secondary testing) as the desired bell ringer. It seems peculiar that the method is not better known.

It does seem a little peculiar, although it's not quite as unknown as the author implies; rather, it provides a mathematical justification for one of the hacks we would sometimes try (often helpfully!) if our figure-of-merit was being overly dominated by high-ranking items: take the square root of the probability[0] and use that. :)

[0] Well, once we'd got to the point of this kind of hackery to improve our performance, it typically wasn't much of a probability anymore, at least not as such; call it a "probability-derived score".

The problem? The majority of muslims aren't Arab! There are large numbers of: - asian muslims, Indonesia = world's largest muslim country - black muslims, across various African countries, i.e. The Underwear Bomber - white muslims, in the balkans and Chechnya for example - And of course there's large numbers of muslims in India, Pakistan, and Iran who are not of Arab ethnicity, although they might or might not look similar enough (depending on dress most likely) to get thrown into the same profiling bucket.

The paper goes into the details of how a profiling system would be optimally set up, but the entire issue is moot. The premise that we have a good understanding of what groups should be receiving heightened security screening is itself wrong.

(Note: I couldn't find the statistic with a few minutes of Google searching, so I'll keep looking, but I know I have seen it reported that >50% of muslims in the world are of ethnicities other than Arab.)

Also, no one proposes using Arab ethnicity as a proxy for being Muslim - who cares if someone is Muslim? Arab ethnicity (or being a Muslim) is used probabilistic evidence (not a proxy) for a person being a terrorist.

A naive analysis with a high cost of not finding malfeasors would say that we should sample all people whose probability is above some threshold. (This threshold depends on available resources.)

However a more sophisticated analysis takes into account the possibility of a terrorist dry run to figure out who will be detected, and who not. Then the terrorists can launch their attack knowing that they will not be detected.

There may be fewer available terrorists who register as low probability p, but they can find enough for their attack. For a real life example, screening went up for people from the Middle-East after 9/11. So Al-Qaeda found a London born mulatto named Richard Reid for their next airplane bombing attempt. He didn't fit the profile, sailed right through screening, and only luck and an observant stewardess saved the airplane from the bomb in his shoe.

If you assume that the terrorists have sufficient candidates available, and are aware of the screening protocol, you should assume that they will always use the candidate that they have that is least likely to be caught. Therefore the most efficient use of resources would be to randomly screen everyone with the exact same probability.

If you don't assume that terrorists have unlimited potential candidates, then some profiling is worthwhile. But not that much - the enemy should be assumed to be relying on their most difficult to spot members, so the obvious criteria are not going to be nearly as predictive as you would hope.

I've always found ethnic profiling rather strange. If we assume, correctly, that the vast majority of people are not "malfeasors" and the fact that said "malfeasors" will plan against any and all barriers which we put into place, why on Earth would you think that those you "nab" at airports and the like would be anything but innocent?

Seems like you'd only nab "malfeasors" who would've failed anyway, and in turn antognized a large population for little to no benefit.

What better way to breed "malfeasors" than to select and irritate a large number of people for long periods of time for no particular reason?

Contempt breeds contempt breeds contempt.

One last thought: Malfeasance is a result of some cause. Treating malfeasance is all well and good. But I always assumed that it would've been better to address the root cause that creates "malfeasors", which are (in no particular order); brutal poverty, constant assault and general mistreatment by those other than themselves.

I wonder what would have happened had we flooded the Middle East with cheap food/consumables and paid for hospitals, schools and infrastructure instead of going in and starting a rather prolonged war.

I suppose it probably doesn't matter now - the damage is done.

This is not super surprising mathematically - there's no reason we ever should have assumed that P(terrorist|race) is exactly proportional to the optimal sampling frequency if we want to find terrorists when all we know is race, all we'd assume up front is that there's some relation.

Actually, a recent study shows that malfeasors are the result of the local political posturing in their own countries:

The effort poured into diplomacy and public relations to counter anti-American sentiment among some Muslims has so far ignored the main source of their anti-US feeling - competing political factions in their own countries. ... Blaydes and Linzer conclude that the main explanation for high levels of anti-American opinion in a given country depends, not as previously thought on Muslim perceptions of what America is culturally or what it does politically, but on the degree of competition between the political elites within that country itself.

http://phys.org/news/2012-06-muslims-america-intriguing.html