Conditional probability, Islam, and terrorism screening

If a non-muslim had committed the exact same act based on some extremist views would it have been considered a terrorist act or a guy going postal? Is it possible that the probability of an act being defined as “terorist” depends a great deal on who committed the act in the first place? Is the guy (Christian guy) who shot the abortion doctor a terrorist? It would seem so to me.

Interesting thought provoking article. Have a few issues with:

“In screening for Terrorists, we can compute the “risk” ratio, or relative terrorism “risk” of being a Muslim. This is calculated by

Pr (Terrorist | Muslim )
————————————————
Pr (Terrorist | Non-Muslim )

which is a very small number divided by a number that is near zero, which means the relative risk will be somewhat high. ”

But more because I am based in the UK where 52 people died in the July 7th Bombings but 2782 died as a result of terrorism in the Troubles in Northern Ireland, Ireland and Britain. I realise you are using approximations to explain a point, but just shoes how qualitative data should always be considered as well (Peace process in Ireland, wars in Afghanistan and Iraq etc.).

Thanks for your quick reply – is there any information you can give on at what stage further information on probabilities about people becomes useless? Rather vague concept and doubtless depends on what the probability is regarding, but essentially I would imagine there must always be a limit where noise in the data exceeds added benefits of more information?

e.g you could add things to the right hand side of the above model but adding knowledge on the place, the general population, history, educational background, ethinic background, favourite colour – anything really, does this extra information always add something?

Apologies if you don’t understand my question, as I am not sure I do!

Today does Webster define what constitutes a terrorist or does the media or does the government?

A great example on the difference between P(A|B) and P(B!A). Hmmm, the conditional probabilities are defined on the basis of relative frequency arguments!

Isn’t there a word or term used to describe an unreasonable fear of Mullims? Something–phobia? I searched on goolge, but couldn’t find the answer.

You will never be able to create a statistical model for determining if a Muslim is a terorist. First, the term terrorist implies a person outwardly directed by a central planning agency or organization.

Religious terroism has to be understood in terms of an individual member of a religious faith that conflates violence against non-believers with religious rites.

What you actually have in Islam is a religion which exhorts its individual members to jihad and to some that means violent agression against anyone they deem an infidel non-believer.

I often hear from Muslim apologists that “only” ten percent of Muslims actively believe in the form of jihad that leads its practitioners into murder. That means 100 million Muslims want to cut my head off and destroy my culture. We don’t hear a resounding smackdown of their co-religionists from the other 90 million.

The only test you will be able to use to divine a religious terrorist is Occam’s Razor

Mr. Briggs,

You are right that it’s the basic definition of a probability. Also, the term relative frequency is used for the ratio (frequency)/(sample size), which is used to estimate/model the probability and theoretically approaches the probability as the sample size increases.

Here is the question: How does a objective Bayesian estimate the probabilities in this post?

Ah, terrorism. I studied the issue quite a bit in grad school.

Let’s just say that there is no really “good” definition. I don’t say this to be some sort of semantic English major-type: it’s just not easy to define. The dictionary definition isn’t half-bad, but it’s too limited, IMO. After all, we often call attacks on military and government “terrorism” depending on the methods. We also have been known to call similar acts on civilians things other than terrorism.

However, I question whether this guy was a terrorist. Not because I think we should be careful with the use of the word per se, but simply because he seemed to be out of his gourd. I suspect he was probably more of a “Columbine-type,” but within a different context. Crazy, violent, but not necessarily bent on a political goal. It appears, at least based on the info I’ve gleaned, that he went on those message boards for the same reason that the various school shooters went on their various weird message boards. Weird seeks out weird.

Granted, my assertion is based on limited information as well, so I may be wrong.

Bill,

Nice minefield you’re walking into, there.

I always walk this one carefully since the last thing I need to be labeled is a Muslim-hater or something of the sort (I’m too indifferent to care.)

However, I will say this much: the liberal urban Muslim who drives a Camry to work and “forgets” to pray five times a day is a real Muslim. So is the Bedouin with the crazy camel caravan in Arabarabstan. They’re both “real” Muslims. Just like I’m a real Jew, and the Hassidim I see on the way to work, with their disdain for all things urban and secular, are “real” Jews.

The Inquisitors of España? Real Christians. (But always unexpected, of course.)

The Tamil Tigers? Real Hindus. (And Commies, but that’s a separate issue.)

The issue, at least in my mind, shouldn’t be whether or not they’re “really _____.” It should be what kind of eye we cast on that crazy 10%. I’ll say this as bluntly as possible: it is my belief that at least 10% of EVERY religion would slit your throat and leave you for dead given enough of a reason.

Sturgeon’s Law: 90% of everything is crud. The same applies to people. And if we remember Hobbes, we know that behind every handshake is a knife ready to stab you in the back. I’m a real humanist, as you can see.

As is often the case, my disagreement with Briggs comes from my belief that his assumptions are bad.

Pr (Terrorist | Muslim )
————————————————
Pr (Terrorist | Non-Muslim )

The assumption this ratio is high, is bad. It is biased by the media emphasizing the religion of the person, but only when he is a Muslim. It is biased by defining the act as a terrorist act because it was done by a Muslim. It shows an obvious disregard for the countless terrorist acts done by the IRA, Green Peace, the xxxxLiberation Front, FARC, Combat 18, Sons of Freedom etc, and of course the entire host of politically sanctioned terrorists, revolutionaries and counter-revolutionaries who are heroes when they win and terrorists when they lose.

John,

I did my graduate thesis on terrorism and some hackneyed statistical analysis to see if there’s any relationship between terrorism and civil liberties. Regardless of the many many serious problems with my model, something interesting came to light for me: the vast majority of terrorist attacks worldwide were not committed by Muslims, but actually by the LTTE.

Muslim-based attacks were in second place.

Unfortunately, my data didn’t treat ALF and all those enviro-extremists as terrorists, so I have no idea where they rank. I know, however, that a prof. at my alma mater had arson committed by one of those groups, so they’re out there being jackasses.

Still, in the US I suspect at least a plurality of attacks have been committed by Muslim extremists, but that doesn’t tell us much.

clarity = matt. thanks!

Too bad Casey, Napolitano, the FBI and other “fablers” out there can’t apply the same statistical analysis model to the possibility of retributionists harming or harassing other, innocent Muslims. Its almost as if – but that couldn’t happen, could it? – there were some type of pressure group hounding them into voicing those concerns.

Dr. Briggs,

Could you please post an easy, step-by-step example to demonstrate how Bayesian statistics works? Thank you.

Ari, you say:

“We often call attacks on military and government “terrorism” depending on the methods. We also have been known to call similar acts on civilians things other than terrorism.”

I would say just the opposite. A terrorist targets civilians with the intention of spreading fear among the general population. Someone who attacts the millitary, offices of the government, or assets that are strategic for the government to maintain controll wouldn’t be a terrorist.

a miner panning for gold

I don’t know if it has been mentioned already, since the thread about “big oil”, a simple google search of William Briggs brings up this as the top hit:

William M. Briggs, Statistician & Consultant
But I don’t think finding this recipe is what people had in mind when they searched for keyword combinations “Briggs & Big Oil”, “Dr. William Briggs …

As with everything, much depends upon definition. The plain fact is, at least in the united States, the working definition of “terrorism” is inextricably linked with Islam. This creates a measure of circular reasoning, which I see no way around. That is not, however, a critical blow to the conclusions drawn.

If we redefine “terrorism” to mean, say, “any planned act in which people are murdered without expectation of monetary gain,” we’d count far more non-Muslims. But Muslims represent less than 2% of America’s population. For this new Pr (Terrorist | Muslim ) / Pr (Terrorist | Non-Muslim ) to drop to 1, non-Muslims need to commit over 50 terrorist acts for each Muslim act. I don’t have the statistics in front of me, but I’d be surprised if that turns out to be the case in America, at this time. Obviously other countries, and other eras, have different statistics. But those numbers have little significance to the Ft. Hood shooting, which clearly inspired this post.

Matt,

LTTE = Tamil Tigers. They’re that group that just got “pacified” in Sri Lanka.

The more I look back on my data, the more I realize how poor a lot of the sets are. Anyway, just glancing at what little I have left of my data set (it got lost in the Great Hard Drive Wipe of 2008) shows me that from 1980 to 2007 four countries suffered over 1000 deaths total from terrorism: Colombia, Lebanon, India, and the US. Pakistan, Russia, and Algeria came in close to one thousand.

Sri Lanka had fewer deaths, but many more injuries.

What does this tell us?

Well, not much. Outside of the 3000 deaths in the US, which is because of one large, horrific attack being successful, most of the others were amassed over the course of many years. Colombia is clearly not suffering from Muslim extremism, and while the terrorist group in Russia is Muslim, I don’t know that I would put them in the Wahabbist nutjob category myself.

Now, it’s true that the data set I have points to a strong Muslim bias, but that doesn’t tell us much worldwide, IMO. Muslims are by no means a monolithic group.

Interestingly, Japan reports more injuries from terrorism than any other country besides Kenya. I have no idea how they figure that out– maybe they report the data differently from other countries? I can only think of a few major terrorist attacks there from 1980 to 2007, and none of them had injuries in that range.

I also can’t say how eco-terrorists get counted in my set. Boy, this is rough!

Doug,

We seem fairly comfortable calling the attacks on the Marine barracks in Beirut and the USS Cole terrorist attacks.

I don’t know that I think they are, but that’s one thing they’ve been called.

Assumptions about someone because s/he is Muslim may indicate prejudice but not racism because Islam is a religion not a race.

I have a different scenario for you. Suppose you heard on the radio a breaking news story: “Shots reported at Orlando’s Gateway Center. Several are dead, many more are wounded. Eyewitnesses claim this was mass murder.”

You ask yourself two questions: (A) Was the mass murderer a Caucasian, and (B) Your neighbor is a Caucasian; is he likely to be a mass murderer?

A can be written like this:
Pr (Caucasian | Mass Murderer )

B can be written like this:
Pr (Mass Murderer | Caucasian )

To estimate B, Pr (Mass Murderer | Caucasian ), we count all Mass Murderers and then divide into it the number of Caucasians who were Mass Murderers. This fraction is very small; there are a lot of Caucasians and very few of them are Mass Murderers; that is, it is very unlikely B is true.

To estimate A, Pr (Caucasian | Mass Murderer ), we count up all the Mass Murderers we have known and divide into it the number of them that were Caucasian. This fraction is very large; most, and close to all, for the last thirty-ish years, Mass Murderers have been Caucasian; that is, it is very likely A is true.

Thus, it is not racist and it is rational with the information we have, to conclude A is likely true. But it certainly is racist and not rational to assume your Caucasian neighbor is a Mass Murderer, given just the information we posses (news reports and recent history).

On the other hand, if, in trying to answer B, you were to add information that your neighbor is known to own guns, was recently fired, divorced, struggling financially and posting hostile remarks on social networks then

Pr (Mass Murderer | Caucasian & posts etc. ) is very high.

However, these results do not help us with the problem of screening for mass murders at the mall, or at work, so we must also calculate

Pr (Mass Murderer | Non-Caucasian)

To calculate it, we count up all Non-Caucasians and divide into this the number of them that were Mass Murderers. This fraction is exceedingly small, near zero.

In screening for Mass Murderers, we can compute the “risk” ratio, or relative mass murder “risk” of being a Caucasian. This is calculated by

Pr ( Mass Murderer | Caucasian )
————————————————
Pr ( Mass Murderer | Non-Caucasian )

which is a very small number divided by a number that is near zero, which means the relative risk will be somewhat high.

Using just this information suggests it is rational—and not racist—to prevent Mass Murder by concentrating screening resources on those men who are Caucasian and not, say, on those who are Black or Asian.

Matt,

You’re referring to John Allen Muhammad. Now here’s a sort of fun question: do we count him as a Muslim as a member of The Nation of Islam, or as something else? He’s certainly not a Wahabbist like the 9/11 guys, but he’s something alright.

Not sure I completely agree with Ted’s claim “The plain fact is, at least in the united States, the working definition of “terrorism” is inextricably linked with Islam”. That may be true in the short view with younger commenters, but as an old geezer I still vividly remember other terrorist groups in the UK, Europe, the middle east and even – sorry about this – the group that slaughtered Sharon Tate, et al.

In my fragile mind there are quite a few more violent-prone groups that fit under the “terrorist” tent, but to simply state 15 minutes into an investigation of a mass murder incident by an apparent Muslim that “there are no signs this was an act of terrorism” is not only absurd and foolish, but forever casts the entity making said statement as an advocate of “doublespeak”. The proper response should have been “We don’t know but we are looking into it”. Period.

49erDwee:

Point taken. Everyone’s intimate knowledge of history begins some time after birth. Mine, as you suggest, is on the shorter side.

Was the Symbionese Liberation Army, at the time, widely regarded as a terrorist group? I’d always thought of them as more of a rich white kids’ street gang. Though, now that I think of it, several street gangs might be appropriately labeled as terrorist. I do feel a bit sorry for them, though. How many of them died for their cause? And those poor Symbionese people still haven’t been liberated.

At the time they were thought to be “terrorist” in that their bank heists were undertaken using grossly excessive force [and forces] as a means of intimidating victims, terrorizing the citizenry and “making a political statement”. Such things are now commonplace, but before they came along not many hold-ups “went bad” – meaning bad for the victims. In fact a few career criminals were usually able to rob one teller and make good their escape while the rest of the staff and customers remained totally unaware. THOSE were the professionals, in my book. It always seemed to me the SLA were rank amateurs when it came to relieving others of their money and goods. But I digress.

I don’t think I forgot the admonition you mentioned. I just didn’t include the bold sentence. I don’t know what you meant when you wrote that swapping “Middle-age White Guy” for “Caucasian” would be more what I had in mind, but I did use Caucasian for a reason which was to exclude Hispanics. I assumed that your example was not meant to be based on fact, and there is a perception that certain types of mass killings (malls, workplaces, etc) are done almost exclusively by white, non-hispanic males. And the perception is all important because the example can support a prejudice even though it never claims to be true. While it can be interesting to discuss issues based on what if this is true scenarios, I think it’s important to be clear that it is hypothetical and not muddy the waters as you did by mixing in your views on fear of being called a racist and what George Casey is saying and thinking.

JD

Yes, the perception is that such crimes are disproportionately committed by whites. The actual facts, however, don’t support that perception. The perpetrators of the most egregious crimes are surprisingly evenly distributed among the races. Such crimes are the work of the truly defective, as opposed to the merely violent, or uncivilized. Such behavior is probably related more to actual malfunctions in the brain, than to the general tendencies of various groups.

So, to that oft asked question, “Why are most American serial killers white?” The answer is simply that most Americans are white.

While I disagree with the way the author assumes Gaussian distributions for what may well be randomness, (physical brain damage, etc) this page gives some of the only numbers I can point you to, without buying a book:
http://www.lagriffedulion.f2s.com/serial.htm

Ted,
The point I was trying to make was that both Briggs’ example and my modified version are based not on facts but on perceptions. Briggs hasn’t claimed that there are figures to back up his example, so what was the purpose? Why make up an imaginary Muslim terrorist risk ratio which leads to the conclusion that it is rational “…to prevent terrorism by concentrating screening resources on those soldiers who are Muslims…”?

The question should be “Why are most American serial killers white males?” which is not what most Americans are, so I suppose I should have said Non-Caucasian or female in my risk ratio. If we’re trying to maximize our resources and protect malls and workplaces from mass murderers then I don’t think it matters whether the percentage of serial killers is consistent across male racial groups. In fact, if the world population of serial killers is racially consistent, using world figures would give a misleading risk ratio of less than 1 for this country.

We shouldn’t ignore the fact that Briggs’ risk ratio applies to all Muslims not just the soldiers, so given the right amount of fear and/or prejudice I’m sure the cost of screening all the Muslims in this country won’t be as big a factor.

Regarding the SLA, the only symbiote that I can remember being liberated was an arc in the Amazing Spider-Man (retold in Spider-Man 3). A symbiote without a host cannot survive.

I am told that when I was a small child, the FBI came knocking on the door to tell my parents that they believed I was a target of the SLA and that I needed protection. My mother told them that I they were being ridiculous. There was no way that a group of terrorists wanted to take care of a 5 year old. My dad would be a much better target, and he could take care of himself.

A few years later we found out that my uncle and Nancy Ling Perry were an item in her pre-terrorist days.

JD,

My point was only that serial killers probably don’t make a good demonstration of this type of reasoning. That the large majority of them are white correlates well with the fact that the large majority of Americans are white. In the case of Muslims and terrorists, American non-Muslims outnumber Muslims by well over 50 to 1. Anything even approaching parity between such disparate groups is strong evidence of a link, thereby providing the foundation of the assumptions made by Briggs.

I’m limiting my comments to Americans because I’m far too ignorant of world wide numbers to formulate any supportable opinion. While I welcome such input, I can provide none of my own.

Great discussion on this post. I think I’ll steal this example for my classes.

This also reminds of when Mr. JH applied for an FBI job a long long time ago, it turned out that I, an alien, became the one under scrutiny for his security clearance. Luckily, FBI had no way to find out how many cockraoches I had ever killed. If they did, they would conclude that I am a mass killer.

I would think that they had screened Hasan before he joined the military. How do we screen for a loonie? If one is worried about the accuracy of a criminal background check, how can we justify the accuracy here?

Well, using the risk ratio defined by P[Terrorist (T) | Muslim(M)] / P[Terrorist | Non-Muslim(NM)] is seemingly “rational”. However, such calculation can be easily misused. Note that I am not saying that we should not take any actions.

First, there is a small number of Muslims in the military, the figure P(T|M) is sensitive to the number of terrorist incidents. While P(T|NM) is not since the number of NM is large. The fact that both P(T) and P(M) are very small makes the probability justification fallible. Large groups such as Non-Muslim or Caucasian win all the time.

Second, I probably can target any group, more so, a minority group. Let me give an example without any factual number, but I know that you would agree with me. We all know that the majority of the mass shootings were committed by men under 50. Note that the numbers of men and women under 50 are comparable. So, let’s calculate the risk

P(mass shooter | Men under 50) / P(mass shooter | Woman under 50).

(Pause for a quick calculation)

Is your answer more than, say, 10? Being such androphobic and misandric (not!), I conclude that all men (but not women) under 50 should carried an ID card indicating his tendency of being a mass shooter.

I also have problems with the justification that there is only small number of them so the cost is small. This also logically implies not only that no action should be taken against any large group of people, but also that minorities are therefore an easy target. It sure is nice not to be a minority in many ways. (I finally understand the Chinese saying: “A large number is beautiful”, my translation, of course.)

 

Ted,
Maybe Briggs will jump in and help us out because I still think your interpretation is not quite right. Assuming the percentage holds true for all races, the correlation with the racial majority still doesn’t matter. If you think that screening for serial killers at malls and workplaces should be done, and you want to concentrate your resources then in the U.S. you screen for white males. In Asia you would screen for Asian males. You do not screen women or minority males in any society. One problem would be that not all areas of the U.S. are predominately white, so my overall risk ratio would hide the true risk ratio in a mainly black or hispanic area. Of course, in my version based on the perception that serial killers are mainly white males, minority areas would be more like Briggs’ example with few white males to screen. If Briggs’ example is correct, and I didn’t botch my cut and paste version, then you can’t dispute the risk ratio, but keep in mind that the numbers are made up. The example was crafted to have a high risk ratio.

Without real figures isn’t the issue a broader one of when, if ever, the government should treat people differently based on the actions of others of the same race, religion or creed? Off hand I’m against doing that. I prefer the idea of reasonable individual suspicion not class suspicion. I don’t even like the fact that I’m part of the government’s national worker database created to catch deadbeat parents. I’d be really ticked off, and just as incapable of doing anything about it, if because I’m a divorced, unemployed, middle aged white male who owns guns that my next employer will be subjecting me to an extensive background check to determine if I’m a likely mass murderer.

JD,

I’m just debating the statistics, not the ethics. For full disclosure, I’m 100% opposed to the government even considering human differences. That’s why the statues of Lady Justice all wear blindfolds. A universal requirement of freedom is that the king and the street urchin are held to exactly the same legal standards. I also see the government’s powers as Constitutionally limited to reactive, as opposed to proactive, justice. There’s no such thing as “future crime.” Yes, I’m willing to accept the greater degree of violence that such a system MAY lead to.

Back to the subject at hand.
The underlying usefulness of any type of profiling wouldn’t be in catching the greatest number of criminals. Most such systems would actively ignore a certain number of them. The utility would be in maximizing return on investment. In your example, you most assuredly would catch more mass murderers if you checked only whites, as opposed to only blacks. The question is, would you catch more per dollar spent?

To move into a less emotional subject, let’s say Willy Wonka puts out 5 golden tickets. Your life’s dream is to meet an Oompa Loompa. Willy says there are 4 tickets in Wonka Bars, and 1 in an Everlasting Gobstopper. But, he says he’s making 10,000 of the former, and only 1,000 of the latter. Each is the same price. If you had a large family peanut fortune, your best strategy would be to buy all 11,000, thus guaranteeing a win. But you, sharing a tiny hovel with your mother and 4 bedridden grandparents, can only afford 3 candies. Would you buy 3 at random? Would you buy 3 Wonka Bars, knowing that they contain the majority of tickets? Or would you buy 3 Everlasting Gobstoppers, knowing that each one has better individual odds?

Clearly, the third choice gives the best odds, (3/2,500 vs 3/1,000) IF your resources are limited. In real world examples, resources are always limited. Profiling, therefore, is an attempt to maximize return on investment. But it’s only statistically valid if the group being profiled actually has a greater likelihood of being what you’re looking for. In the case of serial killers, there’s little to no correlation with race, but a strong correlation with sex. Profiling by race would, therefore, give little to no benefit, while profiling by sex would substantially increase ROI.

Back to the original terrorist example. IF, for instance, 20% of terrorist acts are committed by Muslims, and Muslims comprise less than 2% of the population, profiling is statistically warranted. Ethically, of course, is a completely different mater.

Ted,
I think I understand what you’re saying, and I think we’re on the same track. In your example there are a number of choices with different odds from not buying any bars to buying up to 3 bars. Then a decision is made that buying 3 bars is the best use of the money, so buying the Gobstoppers gives the best odds. But how is that decision made? Did you determine a risk ratio, and how did you decide what was an acceptable ratio? Ultimately, it’s you that decides whether buying the bars is warranted.

Let me throw in another example to see if I can illustrate what I’m trying to say. To get a job at a school in California the applicant must have a background check. We’ll assume the check is to determine if the person has a history of child molestation. Someone does a study which shows that before the state started the background checks there was a very small risk of molestation from school employees. Are the background checks a waste of money? I think many people would say that preventing even a very small number of molesters from working in schools is money well spent, so the decision would have little to do with the numbers.

In the terrorist example how would we arrive at our decision? We’d have to define terrorist which might bring the whole thing to a halt before we’d really gotten started. We can see how it’s a problem just by looking at Briggs’ working definition and asking how Hasan or anyone attacking soldiers fits into it since it says violence against civilian targets. And what about military violence against civilians? Do we exclude the atrocities in the Balkans that were committed by the military against Muslims? Or do we just deal with terrorists in the U.S? What is it we want to find out? Are we looking for the risk ratio for politically motivated attacks committed by U.S. soldiers who are Muslim? Including retired personnel? For what time period?

Would we ever arrive at a number that is not disputed? It seems unlikely. I suspect any number would be challenged as being politically motivated. Assume that it’s a relatively high number. Would that tell us that the best use of resources is to screen Muslim soldiers? Maybe other methods are superior. Or assume that it’s a relatively low number. Even though the risk is small, maybe the costs of screening are also low. In the end, there are going to be value judgments and hopefully educated guesses on what action to take.