### Airport Security and Statistics

"Lottery: A tax on people who are bad at math." -Unknown

The debate about profiling during airport security screening is still active today. While profiling can be an excellent way to direct limited resources in the most efficient manner, there seem to be some fundamental misunderstandings about how to do so.

Screening for potential terrorists is the most visible kind of security in the media today. In this application the question of profiling becomes, "What kind of people are most likely to be terrorists?". Unfortunately, the answer to this question has become clouded by people who badly misunderstand the fundamentals involved.

One common argument takes the form of that in an e-mail I recently received plugging the idea that many terrorists are young muslim men (YMM) so our security screeners should focus on YMM. Observe that the logic here is badly flawed: The assumption provided, that most terrorists are YMM, is exactly wrong for guiding profiling. Even if it were true that many or most terrorists were YMM, the data describe a set used to predict the chances of a person being a Muslim male given that the person is a terrorist. This is NOT the correct data to construct a profiling scheme because it is backwards: the data we want is the chance of a person being a terrorist given that the person is a YMM, not the chances of being a YMM given that a person is a terrorist. The fact that these statistics are neither interchangable, nor can be used (without other data) to predict the other is both subtle and critical to understanding the matter.

Consider a simplified version of the problem: I have a tray of 100 coins all pennies and dimes. There are 50 coins which are heads. If I tell you that all of the pennies are heads, can you tell me how many heads are pennies? No, the heads up coins could be 50 pennies or 49 dimes and one penny. The statistic you need to answer the question is the fraction of heads that are pennies. If I told you it was 50%, you would know there were exactly 25 pennies which were heads. Note further that knowing all pennies are heads is NOT the same as all heads are pennies and that in general knowing that "All X are Y" says nothing about how many Y are X.

Consider another hypo: All terrorist are beings that are alive. Are all beings that are alive terrorists? No! Not even close.

Going back to the profiling issue with this statistics matter in mind, we see that the data posited, most terrorists are YMM, does not allow us to predict the chance of a person being a terrorist given that he is a Muslim male. What a security team WOULD need is the RATIO of the chance that a person who is a Muslim male is a terrorist vs. the chance that any given person is a terrorist. Given that ratio, let's call it "X", you can assign a probability of a detailed stop and search to Muslims equal to (X)*(the probability of stopping any given party).

Since we don't know what X is nor could we predict it bsed on the assumption that most terrorists are YMM, we cannot profile YMM efficiently. Any attempt to profile on this data is a stab in the dark at best. While political correctness is not a reason to avoid profiling, the legitimate fear of profiling inefficiently such that the chance of detecting a terrorist is decreased IS a legitimate reason to avoid profiling.

One way that profiling might actually be used to make us safer is to stop screening the pilots since the X ratio for a pilot had better be zero or vanishingly close to it.

The debate about profiling during airport security screening is still active today. While profiling can be an excellent way to direct limited resources in the most efficient manner, there seem to be some fundamental misunderstandings about how to do so.

Screening for potential terrorists is the most visible kind of security in the media today. In this application the question of profiling becomes, "What kind of people are most likely to be terrorists?". Unfortunately, the answer to this question has become clouded by people who badly misunderstand the fundamentals involved.

One common argument takes the form of that in an e-mail I recently received plugging the idea that many terrorists are young muslim men (YMM) so our security screeners should focus on YMM. Observe that the logic here is badly flawed: The assumption provided, that most terrorists are YMM, is exactly wrong for guiding profiling. Even if it were true that many or most terrorists were YMM, the data describe a set used to predict the chances of a person being a Muslim male given that the person is a terrorist. This is NOT the correct data to construct a profiling scheme because it is backwards: the data we want is the chance of a person being a terrorist given that the person is a YMM, not the chances of being a YMM given that a person is a terrorist. The fact that these statistics are neither interchangable, nor can be used (without other data) to predict the other is both subtle and critical to understanding the matter.

Consider a simplified version of the problem: I have a tray of 100 coins all pennies and dimes. There are 50 coins which are heads. If I tell you that all of the pennies are heads, can you tell me how many heads are pennies? No, the heads up coins could be 50 pennies or 49 dimes and one penny. The statistic you need to answer the question is the fraction of heads that are pennies. If I told you it was 50%, you would know there were exactly 25 pennies which were heads. Note further that knowing all pennies are heads is NOT the same as all heads are pennies and that in general knowing that "All X are Y" says nothing about how many Y are X.

Consider another hypo: All terrorist are beings that are alive. Are all beings that are alive terrorists? No! Not even close.

Going back to the profiling issue with this statistics matter in mind, we see that the data posited, most terrorists are YMM, does not allow us to predict the chance of a person being a terrorist given that he is a Muslim male. What a security team WOULD need is the RATIO of the chance that a person who is a Muslim male is a terrorist vs. the chance that any given person is a terrorist. Given that ratio, let's call it "X", you can assign a probability of a detailed stop and search to Muslims equal to (X)*(the probability of stopping any given party).

Since we don't know what X is nor could we predict it bsed on the assumption that most terrorists are YMM, we cannot profile YMM efficiently. Any attempt to profile on this data is a stab in the dark at best. While political correctness is not a reason to avoid profiling, the legitimate fear of profiling inefficiently such that the chance of detecting a terrorist is decreased IS a legitimate reason to avoid profiling.

One way that profiling might actually be used to make us safer is to stop screening the pilots since the X ratio for a pilot had better be zero or vanishingly close to it.