Is There An Algorithm To Quantify Terrorism?

A mathematical model to predict terror attacks?
Scientists from University College London have published a paper that suggests terror attacks are not actually random but can be modelled mathematically, perhaps even allowing predictions of attacks to be made.
The paper by Tench, Fry and Gill analyses the “unique dataset of improvised explosive device (IED) attacks during “The Troubles” in Northern Ireland. They use a Hawkes process model, which basically assesses the possible evolutions of a point process, or a group of isolated points in location or time and they form an object studied by probability theory.
Terrorism affects us globally and is not likely to diminish. This is the drive behind this paper, that we live in a time where we need to start studying terrorism and developing scientific methods to predict and prevent strikes from happening. Tench et al state that using mathematical modelling is the ideal way to investigate terrorism as many variables can be explored without real-life consequences.
They are not the first group to investigate terrorism quantitatively. Braithwaite and Johnson investigated the “interactions of insurgent attacks and Coalition counter-insurgency operations in Iraq”. They found space-time patterns which led them to conclude that “ indiscriminate counter-insurgency operations resulted in a backlash effect by insurgents whilst discriminate operations had the opposite effect”.
Lewis et al used self-exciting point process models, also probabilistic theory, to “study violent civilian deaths in Iraq during the U.S.-led invasion”. The timeframe they deduced from the model following violent attacks allowed them to put interventions in place and hence lower the number of violent deaths in Iraq.
Moher studied the terror attacks in Northern Ireland and found that they “ followed a pattern of self-excitation lasting 9.3 weeks.”
What makes the above-mentioned methods relevant is that they look at the problem from a different angle. These methods use mathematics, particularly probabilistic theories, instead of previous political, social and economic based methodologies, which were thought of as the driving forces of terrorism.
Tench et al continue by drawing a parallel with crime pattern theory. Mathematical modelling assumes that “criminal activity forms a series of quantifiable patterns at the macro scale” and uses these patterns to identify crime concentration geographically and temporally and how it evolves. This allows areas of high risk to be targeted with security and preventative measures.
Tench et al focus on the attacks in Northern Ireland from 1970-1998 by the terrorist group Provisional Irish Republican Army (PIRA). They were mainly Catholic and believed they were the true leaders of Ireland. PIRA’s activities are broken down into 5 phases:

• Phase 1- PIRA was in a military format

• Phase 2- PIRA turned into a cell-based structure

• Phase 3- PIRA entered politics through Sinn Fein party

• Phase 4- PIRA leaders secretly looking for cease fire with British Government

• Phase 5- Peace talks establish ceasefire in 1998

Tench et al use a Hawkes self-exciting point process which allows them to analyse each phase separately as well as including long-term influences from the past. Furthermore, they also divide the attacks geographically and analyse them according to the six counties of Northern Ireland, giving them insight into the autonomy levels of the cells. To top it all off, they invoke a multi-dimensional Hawkes process to factor in the involvement of the British Security Forces.
What did they find? Phases 2 and 3 showed that they were relatively self contained in the sense that Phase 1 did not greatly affect the evolution of Phase 2 etc. However Phases 4 and 5 showed that they were much more interconnected with the previous phases. These numerical findings “raise interesting questions relating to the timing of tactical and organisational shifts within the PIRA that may have previously been missed.”  
The second set of data comes from six models that study the temporal patterns of the use of improvised explosive devices (IED) “at different geographical scales.” Looking at Ireland as a whole, the model was correctly predicting the temporal patterns of IED attacks. Looking at Belfast, the model showed predictions in accordance with history when taking past events into account and their effect on future attacks.
When studying the IED attacks in Belfast compared to the six counties of Northern Ireland, further precise information was not predicted by the model. This indicates that there was autonomous activity occurring in the cells over a large geographical area. Taking the British Security Forces interplay into account, two models were tested. The model representing the BSF caused deaths of Catholic civilians leading to PIRA attacks was more accurate than the model describing the influence “of BSF attacks leading to PIRA member deaths”. Tench et al leave us with thoughts on developing their models further, but they would also like to obtain a sociological opinion of their found results.