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Model terrorism
Cindy Merrick, February 7, 2011
Can statistics help us predict and pre-empt terrorist attacks?

The December issue of Discover’s online magazine, “The Mathematics of Terrorism,” describes the latest approach to understanding and modeling terrorism. The research of physicists Neil Johnson, from the University of Miami, Aaron Clauset, from the University of New Mexico, and others, employs statistical methods developed for the study of ecological complexity, but which have been as variously applied as in financial markets and traffic management.

Johnson aggregated data from over 54,000 violent events since the 1960s across nine different insurgencies (not including formal wars). He found that (using techniques credited to Clauset) over the course of an insurgency the events follow a special distribution of number of casualties (injured or dead) per violent event. The model fits what is called a “power-law distribution,” (see Figure 1) in which there are a high number of small-casualty attacks, a few large-scale attacks, and a sharply-descending curve in between. While in many statistical models extreme events are thrown out of the analysis, distributions in a power-law model are specifically characterized by what happens in their left and right “tails.” This is in contrast, for example, to the more popularly known “normal distribution,” or “bell-curve,” in which the left and right tails are considered less statistically important. What is more, models of many of the insurgencies Johnson considered, such as Iraq from 2003 to 2008, Afghanistan from 2001 to 2005, and the second intifada in Israel from 2000 to 2002, clustered around the same actual curve – one that falls at a rate that is remarkably similar across all insurgencies.


Figure 1

 Johnson also gives a second way the data seem to follow a power-law distribution, described in more detail in his paper in Nature, December 2009. The number of attacks per day within an insurgency also results in the same type of curve. That is, there is a high frequency of days where zero or one attack occurred, and a very few occurrences of 7 or 8 attacks in the same day (see Figure 2). Johnson attributes this to a mechanism described as “group decision-making about when to attack based on competition for media-attention.” This is consistent, according to the Discover piece, with current military thinking about the “asymmetrical” nature of conflicts like in Iraq and Afghanistan, in which the enemy is seen as a “loose network of fighters lacking central command.” While all groups want media attention, the lack of central command prevents organization, and, as seen over time, attacks are “bursty,” where periods of quiet are followed by series of attacks.


Figure 2

The anticipated value of such research is, of course, achieving goals like prediction and pre-emption. But in aggregating and viewing data in the manner of Johnson and Clauset, some questions inevitably arise. For example, Discover reports on the differing models of “war” versus “insurgency” without defining either one or the scientific distinction between them – perhaps because no such definitions are clearly given in Johnson’s or Clauset’s papers.

The American Civil War is stated as a war, but the fight between FARC and the Colombian military is an insurgency. Both are events in which political discord led to armed conflicts, body counts include soldiers on both sides and, in some cases, non-combatants and, perhaps most notably, both involve organized rebellion against a legitimate governing power. Even if we are meant to be guided by the discussion of “asymmetrical” warfare as a distinguishing characteristic, this too must be well-defined, and it is not. If such definitions are not made before data is analyzed, one can see how an event may ultimately be defined by the model it is seen to describe, instead of the other way around, as the authors claim. While this would not be bad for historical purposes, it certainly wouldn’t hold any predictive potential.

Secondly, the figures of injured versus dead are considered together, in some cases creating misleading impressions. In Clauset’s 2008 paper “Scale Invariance in Global Terrorism,” he gives three examples of traditional statistical outliers, or “extremal events,” which his model (a power-law distribution) better accounts for. One is the bombing of the World Trade Center in New York on September 11, 2001, in which 2,823 people died. But he also cites the 1995 Sarin gas attack in the Tokyo subway, which “injured or killed over 5,000,” and the 1998 car bombing in Nariobi, “which injured or killed over 5,200.” More precisely, however, a CDC article states that, in the Tokyo event, 12 people died, and 1,000 required  hospitalization of between a few hours to a few days. In Nairobi, the US State Department reports that about 212 people were killed, and 4,000 wounded. These distinctions cause one to ponder the definition of “extremal events,” whether or not it is a subjective one, and how a curve which is defined by its “tails” of extremal events would be affected if we reconsidered such a definition.

Third, it is worth noting that the models of Johnson and Clauset are independent of many contextual parameters, like culture, religion, and direct causes for insurgency. It’s fascinating to wonder, but far from presumable, whether we can hope to understand a fight in any predictive way without accounting for the motivations of the fighters. In using the New York terror attack on September 11, 2001 as a typical example of an extremal event in traditional models, Clauset presumes that the number killed in this event is the datum with the greatest predictive significance. But the World Trade Center, as well as the Pentagon, which was bombed by the same organization on the same day, could be seen to have been chosen not necessarily for their potential kill-sizes, but for the symbolic value of destroying the buildings themselves. In Johnson’s paper is the following quotation from former U.S. Senior Counterinsurgency Adviser David Kilcullen, regarding an insurgent attack on an American convoy in Iraq: “…they’re not doing that because they want to reduce the number of Humvees we have in Iraq by one. They’re doing it because they want spectacular media footage of a burning Humvee.” This suggests that an event in which possibly none are killed or injured could be a high priority for an insurgency. In other words, is counting injuries and deaths the best measure of “success of the attacks,” as defined by the researchers?

The above skepticism is the sort of push-back that Discover says the researchers are getting from many in counterinsurgency circles, but they continue to hope for models that prove to be useful tools in military planning, and find backing for their continued studies from the Pentagon and think-tanks like the Mitre Corporation.



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