Art Carden  

Better Living Through Statistics: Muslim Terrorists Edition

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As I've written before, I'm excited about Bryan's forthcoming The Case Against Education (ooh! Here's a FEE podcast version on YouTube!). Here's another piece of advice that continues the Bubble/Serenity conversation started by Bryan and David. At the margin, you can probably live a much more peaceful life by familiarizing yourself with Bayes' Theorem.

A simple application of Bayes' Theorem will dissolve lots and lots and lots of things you fear, but irrationally. The fear du jour in light of the Boston Marathon bombing: Muslim Rage.

Undoubtedly, you probably once asked a math teacher "when am I ever gonna use this?" In light of recent developments in the investigation of Monday's bombing at the Boston Marathon, I have an answer: you'll use this when you're surrounded by demagogues calling for the waste of additional resources screening members of a minority group (if not members' outright persecution) based on the despicable actions of a small handful of people.

Here's a great post from two years or so ago in which William Easterly lampoons the statistical illiteracy of people who want to persecute or "profile" Muslims based on Muslims' role in 9/11 and other attacks and that is relevant again in light of their alleged role in the Boston bombing. The upshot: even if the probability that someone is a Muslim given that he is a terrorist is 100%--meaning that all terrorists are Muslims, which they aren't--the probability that a Muslim is a terrorist is not. In fact, the probability of a Muslim being a terrorist is, according to Easterly's calculations, 0.007% or 0.0007% (depending on which one features a typo--but even with an order-of-magnitude typo in the downward direction the probability is basically low enough to ignore).

I think a lot of people scared of Muslim Rage understand this more intuitively when we're dealing with crimes committed by white people, crimes committed with guns, and crimes committed by white people with guns. Consider school shootings. A quick Google search turned up this piece about Katherine Newman's book Rampage: The Social Roots of School Shootings. Apparently, all of the school shooters Newman studied have been white males (this article offers counterexamples, but let's just go with "all school shooters are white males" for sake of the example). Most of us understand that even if all school shooters are white males, it's a mistake to be suspicious of all white males because they might be school shooters. A lot of us also understand that even if all school shooters are gun owners, it's a mistake to be suspicious of all gun owners because they might be school shooters. Being suspicious of Muslims generally because a lot of terrorists are Muslims is the exact same mistake.

Will most people reallocate their time and energy away from reading the news and toward studying Bayes' Theorem? I doubt it: they'll remain rationally irrational and vote accordingly. Some will, though, and those who do will lead more peaceful lives as a result.

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COMMENTS (34 to date)
Russ Nelson writes:

She only studied white male shooters, you say? Well, then I can safely say that 100% of the shooters she studied are white males. Therefore 50% of the white population are committing 100% of mass shootings. That's twice as much!

Clearly there is something wrong with white people.

No, seriously, I had somebody make that argument with me. Clearly there is something wrong with their ability to follow a chain of reasoning.

MingoV writes:
Most of us understand that even if all school shooters are white males, it's a mistake to be suspicious of all white males because they might be school shooters.
That's true, but a significant number of people are suspicious of all males for the rare crime of child molestation (by a stranger). All a man has to do is watch a child playing in a park to fall under suspicion by parents or caregivers who don't care about probabilities and likelihoods. "It's for the children," seems to be a code phrase for "Shut down your brain."
jason braswell writes:

While Bayesian reasoning (and how counterintuitive most of us find it) is no doubt important, I wonder if this lesson might have the opposite psychological effect that you suggest. After all, you're saying that even with a superb test for identifying terrorists, we're very unlikely to find them.

They're even trickier than we thought!!

Renato Drumond writes:

When the majority has a quality which predicts bad behavior, the event will be viewed as random. However, when it's the minority which has the predictive quality, the event will be seen as determined by that quality. I think most people see that way (for evolutionary reasons, maybe?): it's difficult to run away if the danger is everywhere (the majority), but easy when you can perceive a specific danger (the minority).

brian h. writes:

This is something I never see addressed by open borders advocates. If there is one prospective immigrant population where 700 out of every million immigrants will be a terrorist, and another population where 70 out of a million will be terrorists, and you can only let in a certain number, why not pick the group with lower terror/crime/welfare base rates? Why do we have to pick our immigrants randomly or by factors like family reunification instead of by how much they contribute?

As long as we are limiting immigration, why not pick the best? This would also have the effect of increasing support for increasing the total number of immigrants. But as far as I can tell, no open-borders people actually advocate this as a good compromise. I suspect it has to do with the fact that they don't really care about immigrants, they just want the people who dare oppose them to suffer.

gwern writes:

brian, is there any need for them to advocate that when that (a Canada-style system) is the usual position among non-open-borders proponents of immigration reform and even heavy restrictionists like Steve Sailer?

eric1 writes:

Similarly, if I get a positive result on an AIDS test it's no big deal, because I probably do not have AIDS?

You are conflating the error of assuming a signal is perfect with what happens when you use the signal in a bayesian sense: one is illogical and so bad, the other logical and so good.

Am I the only one to find it bizarre that the entire city of Boston was essentially locked down, its citizens confined to their homes, public transit disabled....because of one terrorist hiding in one neighborhood?

Brian writes:


No, you're not the only one. Bizarre indeed.
And Art is right--being able to reject improbable fears by way of statistics makes life much more peaceful and enjoyable. Let's call it the Bayesian bubble!

Methinks writes:

"...why not pick the group with lower terror/crime/welfare base rates?"

So, you're saying no white males? :-)


You didn't actually expect "law-enforcement" to allow this opportunity to terrify everyone into believing that we would be lost if we didn't subjugate ourselves to their brute force pass by unexploited, did you? In eyes of the state no probability is too small and no liberty too sacred.

Krishna writes:
M = Muslim
NM = Non-muslim
T = Terrorist

P(M) = 1/13000
P(NM) = 12999/13000
P(T) = x

P(M/T) = 95/100
P(NM/T) = 5/100

P(T/M) = (95/100 * x ) / (1/13000)
= 12350x

P(T/NM) = (5/100 * x) / (12999/13000)
= 0.05x

P(T/M)/P(T/NM) = 12350/.05 = 247000

Given the limited resources of the security agencies, and the fact that the classification into N/NM is made fairly easily and reliably, wouldn't you advocate using this information to pick people to profile?

Ian writes:

Seung-Hui Cho, a Korean, shot and killed thirty three people at Virginia Tech in 2007.

One Ko Goh, a Korean, shot and killed seven people at Oikos University in 2012.

Kimveer Gill, a Punjabi, shot and killed two people at Dawson College in 2006.

Gamil Rodrigue Liass Gharbi, an Arab, shot and killed fifteen people at the Montreal École Polytechnique in 1989.

Napoleon Lavarias Caliguiran, a Phillipino, shot and killed three people at San Jose State in 2011.

Jeff Weise, a Native American, shot and killed nine people at Red Lake Senior High School in 2005.

Nathaniel Brazill, a black, shot and killed one of his teachers at Lake Worth Middle School in 2000.

Nicholas Elliot, a black, shot and killed one of his teachers at Atlantic Shores Christian School in 1988 (intended and tried to kill more, but missed his shots and his gun jammed).

Ian writes:

When a school shooting happens, just about every white person who hears of it is repulsed and saddened. When a jihadi attack on whites/the West happen, a majority of Muslims are, if not elated, at least understanding.

There is no document in Western Culture that I am aware of that encourages or condones school shootings. The Koran not only allows but mandates jihadi violence against unbelievers.

A much smaller percentage of white males do school shootings than muslim males engage in violent jihadi activities.

Methinks writes:

My goodness, Ian, aren't you just an instant expert on Islam, what most people think and comparative religion?

I'm pretty sure you have no idea what you're talking about and you've read neither the Koran nor the Bible, not to even mention any hint of understanding of the various sects of any religion and associated documents. Nor is there any reason to believe that you know what "most people" think.

I realize that most Muslims have olive skin and that can be scary for sheltered white folk with more preconceptions than education, but let's look at facts, shall we?

First of all, Islam is a religion, not a race. Thus, there are white male Muslims. "White" and "non-Muslim" are not synonyms.

Second, on what do you base your assertion that there are fewer "white-male" (whatever that means) terrorists than Muslim terrorists.? So far, Adam Lanza has managed to kill more people than these two Boston suspects (who also look pretty white to me).

Third, regardless of race, ethnic group and religion, the common denominator amongst all terrorists seems to be the "Y" chromosome. The overwhelming majority of terrorists, regardless of race, ethnic group or religion are MALE! This is an undisputed fact. We should profile and view all men with suspicion at all times. You should all probably be forced to wear a chip. And maybe a bell around your neck so you can't sneak up on anyone.

Lee Kelly writes:

You're right. The probability of any randomly selected member of the U.S. population being a terrorist is extremely low, and it's extremely low even for that subset of the U.S. population who are Muslim. Indeed, it remains extremely low even for that subset of the U.S. population who are Muslim, male, and are under 30 years old. There just aren't that many terrorists, and the vast majority of people who come into contact with terrorists are not harmed. For average Joe, the risk of being victim of terrorism is so remote that it barely warrants consideration. Just because someone is male, Muslim, and under 30 means very little. They're only a faction of 1 percent more likely to be a terrorist, and even then the probability of being a victim of a terrorist act is minuscule.

However, it can remain true that Muslim men under 30 are several times more likely to be terrorists than average. When dealing with large numbers of people, this can make a big difference. For example, if police were to somehow apprehend every would-be terrorist, then the number of Muslim men under 30 would likely dwarf every other demographic. In this case, the small difference in probability is no longer small enough to just ignore. Suppose police were rounding up terror suspects from a large population. If the set of suspects isn't consistently dominated by young Muslim men, then the police are likely doing a bad job of identifying suspects.

I don't like racial, ethnic, religious, or any other kind of profiling by legal authorities. I'm just pushing back a little, because I can. Also, Bayes's theorem is overrated.

Jeff writes:

The fact of being a white male doesn't offer us any clues as to what might motivate the kind of violent behavior (like mass shootings) that some white males occasionally perpetrate. To be a Muslim, by contrast, is to hold a set of beliefs which quite clearly can and sometimes do motivate acts of violence. Witness the reaction to the cartoons published by that Danish newspaper a few years ago.

If you were to be suspicious of all Muslims, even 90 year old grandmothers, that would indeed be absurd. But the correct conclusion isn't that being a Muslim is just an innocent, irrelevant trait like having curly hair or a mole on your left cheek; the takeaway is that you're casting too wide a net and you need some additional characteristics besides "Muslim" to help you identify potential terrorists. "Male," "unmarried," "devout," "has spent time in Pakistan/Yemen recently," etc. The same holds true for white males.

Prashanth Perumal writes:

Art, something tells me Bryan Caplan might have a problem with your story.

Ian writes:

It's not the olive skin that scary, it's the terrorism and jihad. No one has bad opinions about South East Asians just for their olive skin.

The percentage of Muslims whose ancestors came from North of Croatia and West of Belarus (ie "Europe") is miniscule. The overlap of "Muslim" and "White" is minimal (and such as there are tend to be the dregs/outsiders of white society anyway).

The number of Muslim males who engage in terrorism/violent jihad wherever they find "the other" (attacking and killing Christians in Nigeria, the Ivory Coast, Egypt, the Philippines, South Sudan/Darfur, Lebanon, Syria, on the Somali/Ethiopian border - attacking and killing Hindus, Christians, and Sikhs in India - attacking and killing Jews in Israel - attacking and killing Secularists and Christians all over the USA, in Madrid, in London, in the Caucus, in Afganistan, inside Russia - attacking and killing Buddhists in Thailand and Malay - attacking and killing members of other Muslim sects in Pakaistan, Iraq, and Lebanon) has to be, one would imagine, in the tens of millions. The number of jihadis is, comparively, a significant fraction of the entire number of white men in the world, full stop.
Muslims represent just 1% of the U.S. population, yet account for 82% of all domestic terrorism convictions.

As for scripture,

Quran (8:12) - "I will cast terror into the hearts of those who disbelieve. Therefore strike off their heads and strike off every fingertip of them"

Quran (9:29) - "Fight those who believe not in Allah nor the Last Day, nor hold that forbidden which hath been forbidden by Allah and His Messenger, nor acknowledge the religion of Truth, (even if they are) of the People of the Book, until they pay the Jizya with willing submission, and feel themselves subdued."

Quran (9:123) - "O you who believe! fight those of the unbelievers who are near to you and let them find in you hardness."

"Most of the Islamic doctrine is political, not religious. Islam is a political ideology ... Political Islam is the doctrine that relates to the unbeliever, the kafir ... The Trilogy not only advocates a religious superiority over the kafir—the kafirs go to Hell whereas Muslims go to Paradise—but also its doctrine demands that Muslims dominate the kafir in all politics and culture. This domination is political, not religious. As mentioned earlier, the Koran has 61% of its text devoted to the kafir. The Sira (Mohammed’s biography) has about 75% of its text devoted to the kafir and jihad."

Hindu/Indian human rights activist Professor Babu Suseelan said, “Read the Koran. Read Koran if you want to understand the terroristic doctrine and criminal treatise on the world. Of all the Koran, there are 164 specific verses instigating directly muslims to go against the kaffir and the infidel and conduct terrorism to wipe them out. It is surprising, they claim it is a religious book. But in their religious book, there is not a single word about love. I cannot understand in the Koran you read the entire words, you will not see the word ‘love’. Islamic religion is not a religion of love and compassion it is a criminal treatise for hostility, anger, violence and terrorism against infidels ... are you aware more than 98% of terrorists arrested around the world are Muslims? Why?"
"A survey of 600 Muslim students at 30 universities throughout Britain found that 32 per cent of Muslim respondents believed killing in the name of religion is justified ... 40% want Sharia law.
Recent (2009) polls show a disparity of views regarding terrorism, with between 15% and 30% of respondents in most Muslim countries surveyed holding a positive view ... An average of 30% of respondents in Indonesia, Egypt, Pakistan and Morocco held positive views of groups that launch attacks against Americans, while similar numbers held a negative view or a neutral view. With regards specifically to al-Qaeda, in Egypt, 21% of respondents supported their attacks on Americans, while 33% opposed attacks on Americans but supported al-Qaeda's goals ... With regards to feelings about the former al-Qaeda leader Osama bin Laden, Muslims tended to show even stronger support. In Egypt, 44% held positive feelings, 25% held mixed feelings, and 17% held negative feelings ...

Don't bring a knife to gun fight, kid.

Curmudgeon writes:


Even though terrorist acts are extremely spectacular, or are made to be so by the media, the number of victims is in fact rather low in comparison with crimes committed by other types of criminals.

Nevertheless it is highly rational to pay close attention to Muslim immigration, irrespectively of whether many or few homicides are committed. Why? Because, as Jeff says above "To be a Muslim [...] is to hold a set of beliefs". Quite so. A set of beliefs which, from careful inspection, would seem to be differ radically from the tenets of Jews, Christians, Bahais, Buddhists, Hinduists, Parsis, Sikhs, Jains, etc. plus most deists, pantheists, agnostics and atheists. This unpleasant fact is neglected by the vast majority of academics, intellectuals, professionals, lawyers, journalists, politicians, artists, etc., who have absolutely no interest in religions, do not understand them, and lump them all together into one indicriminate bunch thrust in a bag labeled "Dark Ages".

Curmudgeon writes:


For non-Muslims, the most relevant part of this Muslim set of beliefs has to do with the attitude expected from Muslims (let's say Sunni Muslims; Ahmadis are different, because they reject jihad) toward infidels, kuffar. In order to understand this, all one has to do is spend (a fairly considerable) time in order to read the Qur'an carefully (keeping in mind the principle of abrogation in interpreting the verses), and study the Sunna, i.e. (a) in particular the most revered collections of ahadith, those by Bukhari and Muslim; (b) the life of Muhammad (the "beautiful model").

It is also advisable to have some knowledge of the history of Muslim countries, and of the historical relations between Muslim countries and, say, Europe. Being French, I am acutely aware of what has been going on with my neighbours in Northern Africa, Turkey, and the Near East during the last 1350 years or so, and what is going on right now. Even in my own country, as a matter of fact close to the building where I live. In a very imperfect bubble, reality being what it is.

When this work is completed and these observations are made, one can consider the theory that a large influx of Muslim immigrants in *any* non-Muslim country, in particular Western countries, is no different from an influx of non-Muslim immigrants. And one is, I think, rationally entitled to view this pleasant theory with considerable skepticism. Bayes or no Bayes. Bombs or no bombs.

Himanshu Sanguri writes:

Terrorism do not bear any religion or nationality. Some big goons in the world, exploit the poor, deprived and illiterate young mass to commit terrorism. More often, we are witnessing a new kind of terror called "school terror" which is an irrational self centered act out of psychological disorders. Today, the fact is beyond any doubt, that Muslims in western world, tamils in south east Asia are taken as terrorist for granted. This hatred and unrealistic theory of naming the terrorism has further facilitated the goons to condition the mind of rambled youth. The governments of developed and mature nations along with international bodies should treat terrorism via social, educational and economical tools rather than using force and executions on all among the equals. A perfect illustration is the Kashmir valley, where all efforts of Indian government to provide more employment, education and economic independence to the youth of that region has bring about a heart change among the Kashmiri's. Today, Kashmir is feeling a sense of inclusiveness in the growth story of India. People of Kashmir are now rejecting the terrorist groups calls and preaching and focusing more on the prosperity of their offspring's.

Ken B writes:

The relevant figure is not what are the chances that a member of group X is a terrorist, but the ratio between the chances for members of X compared to non members. And the relevant population will rarely be all members of X, but usual lay (in profiling situations) a self selected subset, for instance only those seeking to board a plane. Almost no men with ski masks are bank robbers, but if men in ski masks come into your bank ...

Profiling is based on respect for Bayes's Theorem.

Prentiss M Davis writes:

The writer overlooks the fact that many Americans like myself need to associate with white males but we can avoid all Muslims with no problem.
In fact, many like myself never met a Muslim until later in life and the period of Muslim associations is a time best forgotten.

If you were to be suspicious of all Muslims, even 90 year old grandmothers, that would indeed be absurd.

No, it wouldn't be absurd. That grandmother could be part of the terrorists' support group.

Tony N writes:

Ken B,


Steve Sailer writes:

I think you are missing the point, which is that ultra-spectacular terrorist acts give clues about the underlying probability distribution of hostility toward the host country.

DoJ writes:

Ken B nails it. Carden does not understand the math; it's trivial to demonstrate that profiling often yields massive efficiency advantages over the alternatives.

There may be an interesting discussion to have about compensating innocent people who have been subject to profiling; it might allow you to keep the efficiency advantages while solving the fairness problem (basic profiling does of course look bad from the perspective of what Kling calls the "oppressor-oppressed" narrative).

Note that almost all profiling critics who are uninterested in discussing fairer ways of capturing profiling's efficiency benefits can be safely dismissed as too untrustworthy for further engagement: either they are too innumerate to understand the topic, or they are intellectually dishonest and secretly want inefficiency (*openly* arguing for inefficiency, on the other hand, is honest and can lead to some useful exchange of ideas). This is similar to how nuclear power serves as an excellent filter for intellectually honest global warming researchers.

Greg Jaxon writes:

@Patrick Sullivan:
I wished for the real-time budgeting device that added an economic knife twist to the final chase scene of THX-1138 (Lucas 1971).

AppSocRes writes:

Are you unfamiliar with the concept of odds-ratios or do you fail to mention them because computing them in this case would reveal your argument's fatuity?

Ken B writes:

Methinks writes

Third, regardless of race, ethnic group and religion, the common denominator amongst all terrorists seems to be the "Y" chromosome

Indeed, so maybe that should be part of the profile. But your "regardless" is wrong as is your "the", as Ian's is a list of young (another common factor!) men all of the same religion. You should pay more attention to the logic of what you are saying Methinks, methinks.

Ken B writes:

I think one point, consistently obscured by anti profiling advocates, needs to be called out. No one suggests profiling on ONE factor and one factor only. To suggest so is a canard. A combination of several low specificity factors can combine to be quite specific.

And the low specificity is often misrepresented too. Consider "devout". Few devout people want to kill unbelievers when you count in the devout class all the devout Quakers, the devout Jains, the devout Buddhists, the devout nuns.

NZ writes:

You're using statistics to find out the probability that a Muslim will be a terrorist, but that only tells part of the story. What about the probability that a Muslim will knowingly aid and abet another Muslim terrorist? Or not report terrorist plans once he's heard about them? Or donate to organizations which, maybe without his knowledge, fund terrorism? Or support specific ideas which, by virtue of being so supported, gain enough visibility to attract more terrorists? Etc.

Granted, those numbers are a lot harder to estimate accurately, but it doesn't mean it can be safely ignored.

Mike Rulle writes:

Who knew a simple Bayesian formula should ease all concerns? Really? You do ignore the "market impact" of profiling---which I assume our country does. But that is another issue and perhaps adds unneeded complexity.

It is unclear what your point is. I see a straw man within the weeds of your argument. I would prefer you make policy suggestions rather than merely infer most people are disproportionally concerned about Muslim violence using Bayes formula. Says who?

I do not spend very much time worrying about Muslim Americans. And if I did, why should my concern be a linear function of historical data---as you also infer? Why can't it be a polynomial function?

What does Bayes have to say about dirty Nukes and p(Muslim/Dirty Nukes)? I am not opposed to the idea we might spend too much $ and time on Muslim watching---though you have not made that empirical case at all. In 1925 we could have said p(Nazis/starting WWII) was pretty low as well. It was even lower in 1927-28.

But stated intent is hard to ignore.

kelly k writes:

Lee: You say "However, it can remain true that Muslim men under 30 are several times more likely to be terrorists than average." > where exactly are you getting this information? While it is not broken down by age, per FBI statistics of terror plots or acts from 1980-2005 (scroll to bottom:, 6% were from Islamic extremists, 7% were by Jewish extremists, 24% by extreme left wing groups, 42% by latinos, and 16% by 'other' groups. can you say Muslim men are more likely to be terrorists?

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