8.1 Introduction

Outbreaks of conflict, whether stemming from interstate or civil wars, insurgencies or civil unrest, continue to dominate news reports around the globe. Their onset and evolution is traditionally discussed using anecdotal perspectives, rather than by employing explicit models to seek out underlying mechanisms or patterns that might be exploited from a policy perspective. However, there has been a recent dramatic increase in the quantity and quality of explicit models detailing various aspects of conflict. This is partly due to increased data availability, which is crucial for modelling as it enables the development of models that are empirically consistent, and partly due to an increased range of sophisticated modelling techniques. Our understanding of conflict processes can be improved through such models. This may in turn improve the way in which interventions are planned. Some have even suggested that by using modern modelling techniques to investigate problems of crime, war and terrorism, the number of fatalities associated with such events can ultimately be reduced (Helbing et al., 2015).

In the first part of this chapter, we examine some of these models and investigate the extent to which they can be used in a policy context to aid decision-making. In Sections 8.2–8.4, we consider three domains in which models may be utilised: operational decision-making; understanding the underlying causes of conflict; and the identification and forecasting of global conflict hotspots. Within each of these domains, we discuss the state of the art not just from a research perspective (i.e. with a focus on developing the best model) but also from an operational or policy perspective (how the model might be used to help decision-making). These three domains are chosen as examples where the availability of fine resolution data on conflict events can improve the application of models in the policy domain. The studies cited in each of these domains are not intended to represent an exhaustive review of the literature in each area, but rather are selected to highlight how different modelling approaches might be applied.

In each case, we note that conflict can occur over very different scales. Since small disputes can escalate quickly, the study of global dynamics has to consider conflicts across all of these scales. Complications arise because a disagreement between two individuals – a conflict at the small scale – is likely to have very different underlying causes and implications to a prolonged large-scaleinterstate war. There is increasing evidence, however, that similar tools can be used to investigate different types of conflict. Johnson et al. (2013), for example, build on a number of previous studies to demonstrate consistent distributions of event severity and timing across a large number of conflicts that occur over a wide range of scales. They suggest that confrontation between different hostile parties can be considered in terms of similar underlying mechanisms, almost regardless of the actual conflict type. Other studies have pointed to particular patterns of conflict in space and time and have used analogies with similar patterning of events in Criminology (e.g. Braithwaite and Johnson, 2015) and Ecology (e.g. Brantingham et al., 2012), amongst others, to draw conclusions about the human behaviour responsible for generating such events.

In the second part of this chapter, we introduce the concept of measuring threat using a spatial interaction approach (Section 8.5). Inspired by the ability for analytical tools to be pertinent over a range of conflict types, we build on the idea that the threat on a particular area can be interpreted as a measure of the likelihood of observing future conflict events in that area. We argue that this framework is capable of representing a broad range of conflict processes and discuss how the model might be applied to each of the three policy domains discussed in this chapter. We conclude by offering some avenues for further research.

8.2 Conflict Intensity: Space–Time Patterning of Events

Quantitative analysis of the variation of conflict intensity in space and time can be used to detect regularities that can be exploited to aid decision-making in an operational setting. In this section, we consider examples of studies that identify such regularities and explain how their insights can be used during decision-making.

During a war or insurgency, certain locations are more likely to experience conflict than others and this conflict might be more likely to occur at certain times. High-frequency events, such as improvised explosive device (IED) attacks, exhibit consistent regularities. A number of studies have considered how event interdependence might be exploited to identify those areas and times more at risk. Townsley et al. (2008), for example, study IED attacks during the Iraq insurgency and show that a further IED attack is more likely to occur within 2 days and 1 km of a prior attack than at any other randomly selected time or location. Such insights have significant implications for security force deployment. Indeed, as the authors describe, their finding ‘allows security forces and the police to organise a local response that, while having to mobilise quickly, is not required to remain in situ for periods longer than a few days’.

In Chapter 12 (see also Braithwaite and Johnson, 2012), a similar analyticalapproach based on tests for space–time interaction originally developed in the study of epidemiology is used to identify patterns of interdependence between insurgent attacks and counterinsurgent response. In particular, the authors identify the types of counterinsurgent actions that were most successful in reducing the likelihood of an insurgent attack. Braithwaite and Johnson find that more discriminatory counterinsurgent activities – such as a geographically targeted raid – were more likely to reduce the risk of further attacks than less discriminatory actions–such as the search and cordon of an area, which were often performed over a comparatively larger area (e.g. city block or equivalent).

In an effort to capture the regularities of these patterns within a predictive framework, Benigni and Furrer (2012) employ a Poisson process model to quantify the spatio-temporal interaction in the data with the explicit aim to aid operational decision-making. They focus on one stretch of road in Baghdad that was well known for being a dangerous route for counterinsurgent forces. Their model generates an evolving risk surface along this stretch of road, composed of space–time Gaussian kernel density estimators calibrated using historical attack data. The authors then demonstrate how this model can be used to plan the deployment of IED surveillance assets and patrol teams. When deploying surveillance assets, the probability that each team will come across an unexploded IED is maximised so that the IED can be identified, defused and removed. When deploying patrol teams, the threat of attack is minimised in an effort to ensure their safety on the route. The approach relies on the spatio-temporal clustering of IED attacks and the authors demonstrate the improvement in the short-term predictability of the model when compared to a model that treats space and time independently.

Zammit-Mangion et al. (2012) also employ spatio-temporal point process models to capture space–time dependencies of events associated with insurgent warfare. Their model is formulated differently from the one of Benigni and Furrer: sophisticated stochastic integro-difference equations are used to model the evolution of a spatial intensity function, which indicates the likelihood that an attack will occur in any given space–time window. The model is calibrated against the Afghan War Diary, a detailed description of events associated with the insurgency in Afghanistan released by Wikileaks. The model enables the presentation of some useful information for leaders in an operational setting: the growth and volatility of event activity in different geographic regions. In addition, the authors demonstrate how the model is able to successfully predict the evolution of the Afghan conflict in a statistical sense, which may be of use for policy (although they do caution that perhaps the reason for this is due to the irregular nature of the Afghan conflict itself and that the model may not be so successful when adversaries are more unified and organised).

In Chapter 10 (see also Baudains, 2015), a different type of point process model is calibrated against conflict data, called a Hawkes process. This model estimates the conflict intensity via a self-excitation mechanism. It is supposed that the occurrence of an event directly increases the likelihood of observing a further event for a certain period of time. The interactions between insurgents andcounterinsurgents are explored via this process and the predictive capability of the model tested. Although some of the variation in the event timings cannot be explained by this simple mechanism, the model is able to offer some insight with regard to the prediction of future attacks. Such models could be used to aid decision-making concerning counter-insurgent deployment.

A further example of using the patterns in events during conflict to help decision-making is given by Shakarian et al. (2009), who introduce the Spatial Cultural Abductive Reasoning Engine (SCARE). In the example presented, this model enables the identification of IED weapons cache sites (where materials are collected and the weapon is made and stored until an attempted attack takes place) using only the locations of previous successful IED attacks. A similar approach called Geographic Profiling is used in the field of Criminology to identify likely residential locations of offenders based on the locations of the crimes that they commit (Rossmo, 2000). The model can be used to prioritise the locations of search and cordon operations for counterinsurgent forces.

These models all demonstrate how operational insights can be obtained from sophisticated statistical techniques combined with real-time data. They exploit event interdependency to identify the change in conflict intensity in space and time. This enables forecasting of likely locations of future attacks or cache sites at a resolution that is operationally useful for influencing deployment decisions. Determining the success of such models in this operational setting (e.g., with respect to the improved targeting of adversaries or the reduction in casualties from IED attacks) is a crucial next step for this type of research.

A limitation of the models discussed in this section is their inability to incorporate and test intricate causal mechanisms by which conflict events are thought to arise. They seek out patterns in event data, but rarely test explanations as to why those patterns might be arising. Deploying troops in accordance with some of the models' recommendations might improve the chances of being in the right place at the right time to prevent a potential attack; however, the models are unable to explore theories as to why events are more likely to occur in one area over another. Incorporating such an explanation can help to test our understanding as to why such attacks are being committed and might even help design policy targeted at reducing the grievances of those likely to commit such attacks. In the next section, we consider models that are constructed using a more theoretical perspective than those considered here.

8.3 Understanding Conflict Onset: Simulation-based Models

Models of social systems provide an opportunity to articulate theory within aquantitative framework that can be empirically validated. Simulation-based models in particular are well suited to testing theories concerning how conflict arises and evolves under different circumstances. Agent-based models (ABMs) allow the modeller to specify some mechanism by which individuals choose to engage in violence. It is then possible to test whether the emergent properties of the model, taken over a population of individuals, each acting autonomously and interacting with other agents, match the empirical record. This can then enable the evaluation of whether the proposed mechanisms provide a plausible explanation for the production of conflict events.

Traditionally, ABMs have been used as purely theoretical tools, designed to observe the emergent behaviour that arises from simple interactions. Recently, however, a number of models have been proposed that incorporate empirical data and are calibrated so that their outputs correspond as close as possible to the real world. If the model is considered to be a close fit to the data and a reasonable representation of the real-world process, then it may be possible to use it for policy exploration by considering the impact of proposed policies on the rate at which conflict events are produced. In this section, we discuss examples of such models in the existing literature and consider how each model can contribute to policy-making. In particular, we discuss two examples that have been used to examine the relationship between ethnic segregation and violent conflict.

An ABM is a model in which each component entity, which in many cases is taken to be an individual, is represented as an independent and autonomous agent. The model consists of a set of rules that describe how each agent behaves and, crucially, how each agent interacts with other agents and the environment. ABMs are well suited to exploring how a proposed behaviour at the individual level results in some observed emergent property at the societal level. A number of sophisticated ABMs with empirically driven modelling and validation procedures have explored the role of individual migration and the resulting spatial distributions of ethnic groups as a causal factor in the onset of conflict. Two examples are Weidmann and Salehyan (2013) and Bhavnani et al. (2014).

Weidmann and Salehyan (2013) model the evolution of violence in Baghdad for different periods during the US-led war in Iraq, beginning in 2003. The model is empirically derived in that it is initialised using residential data in Baghdad, which details whether an area is comprised of a majority of Shia or Sunni residents, or whether the region is more mixed. The model proceeds by letting a fixed percentage of insurgents within each area decide whether or not to commit violence against the other ethnic group. If an attack is successful, then it might prompt civilians to migrate to a new area, one with a lower number of attacks. The resulting violence and segregation patterns across the city are then tracked and parameter selection is achieved by minimising the errors associated with these observations between the simulation and the empirical data. The resulting parameter estimates can then tell us something about the violence in Baghdad. Specifically, the authors demonstrate that the patterns of violence and segregation in Baghdad were consistent with a process by which minority ethnic groups are more likely to be attacked when faced with a different majority ethnic group. Migration is also shown to be positively correlated with the level of violence experienced. These insights contribute to social science theories concerning conflict in mixed urban spaces. The models can also be used to address significant policy questions, such as determining whether segregation or migration of minority ethnic groups should be encouraged or, conversely, whether integration should be supported. Weidmann and Salehyan also go on to consider possible policing strategies for handling the resulting levels of ethnic violence, highlighting how the simulation can be used to test proposed strategies.

In Bhavnani et al. (2014), a model of segregation and violence in Jerusalem is presented more directly in the policy domain. The authors explore a number of counterfactual scenarios resulting from different policy decisions that could be made with regard to the way in which different districts within Jerusalem are put under varying levels of segregation and governed under different authorities. The model is distinct from the model of Weidmann and Salehyan in a number of ways, perhaps notably in the way that any civilian is able to commit violence if they find themselves in a particular set of circumstances and in the way that those circumstances can depend on factors such as the social distance and history of violence between two groups. A number of scenarios in which the movement between different regions is reduced are shown to have significant reductions on levels of violence according to the model. The authors suggest that such policies might be considered when social distance between groups is high and violence cannot be reduced by other means. The authors stress the limitations of the model, pointing out that if different policies are adopted it may change the underlying dynamics in a way not captured by the model. Nevertheless, the model demonstrates how empirical ABMs might be used to explore different policy options and contribute to the range of tools used by decision-makers.

8.4 Forecasting Global Conflict Hotspots

Another area in which conflict modelling can contribute to policy decision-making is concerned with global modelling. In the examples discussed so far, the model has typically focused on a small part of a country. This works well when there is an ongoing conflict within that region, but less well when considering policy that is required to address regions with merely a risk of the onset of conflict. There are a number of ongoing efforts to construct models that are capable of forecasting likely future locations of unrest, violence or conflict around the world. The most prominent examples incorporate large data sets within a statistical framework to identify early warning signals of future conflict in a particular country or region.

One example is the Integrated Crisis Early Warning System (ICEWS), supported by the US Department of Defense (O'Brien, 2010). Online news articles are used to automatically generate event data. Each event is coded according to a prescribed set of possible events and information such as the location of the event or the main actors involved in the event are also recorded. The ICEWS project then uses this data, as well as a wealth of other independent data sources, to build models capable of predicting five different events of interest: domestic political crises, rebellions, insurgencies, ethnic/religious violence, and international crises.

The Global Database of Events Language and Tone (GDELT; Leetaru and Schrodt, 2013) is another large data collection effort, whose aim is to construct event data from open media sources and then to make the resulting data freely available. A number of studies are beginning to exploit this information and make predictions concerning conflict around the world. Ward et al. (2013), for example, use online event data similar to GDELT within a mixed-effects logistic regression model to determine the likelihood of the occurrence of civil conflict at the monthly level between 1997 and 2011. Using a wide range of predictive performance metrics, the authors demonstrate high predictive capability, suggesting that the use of online data can indeed be used as an early warning signal for the onset of civil wars (another example is Hegre et al., 2013). A wide range of stakeholders including policymakers and investors could make use of such predictions when considering challenges such as troop deployments and development aid.

8.5 A Spatial Model of Threat

In the policy domains discussed in Sections 8.2–8.4, there are a wide range of geographic scales and motivating policy questions. One consistency, however, is how modelling the likely locations of future conflict events underpins every model. The geographic dependence and spatial interactions need to be accounted for when developing many conflict models and there is often no obvious approach for doing so. In this section, we introduce a spatial measure of threat between two adversaries who are distributed over some area or geographic region. We argue that this measure offers a versatile framework for incorporating spatial dependence in models of conflict. In particular, the measure may be incorporated into many of the models discussed earlier and, provided appropriate data are available, used to model the likelihood of future conflict events within any given region.

We begin by assuming that the conflict takes place in some Euclidean space or manifold, with each location defined by a coordinate system so that . In many cases, for example those where just the geographic nature of the problem is of interest, will be equal to 2 so that each location represents geographic coordinates. In this derivation, however, weretain generality by considering an arbitrary number of dimensions. These dimensions might later be specified according to a range of factors such as social distance or political similarity (i.e. the conflict may take place over arbitrary landscapes).

Between any two locations and , we define to be some metric on the space. A metric takes two locations and produces a non-negative abstract measure of ‘distance’ between those locations. We suppose here that the conflict takes place between two well-defined groups and that one of these, group , has members located at positions . The adversary to group , group , is assumed to have supporters at positions . In other words, the first adversary is located at positions and the second adversary is located at positions in the abstract space in which the conflict takes place.

In addition to a measure of distance between any two adversaries, we also require some measure of aggression or discontent at each location. This might be interpreted as the extent to which the member of each group is willing to engage in conflict against an adversary, with higher values indicating more extreme and hostile group members. We denote a measure of aggression of at by and aggression of at as . The specification of this measure may vary depending on the application of the model. In a military setting, it might correspond to the amount of resources has at or, for ethnic conflict, it might be a measure of the number of previous attacks that have emanated from (or, indeed, the ethnic composition at ). Broadly, aggression is conceived to model the total level of threat that can emanate from an adversary at a particular location.

We assume that the presence of at exerts some threat on at and that this is measured by . Threat can be interpreted as the level of intimidation that is due to the presence of that adversary. In the case of ethnic violence, for example, threat may arise from the perceived risk of experiencing violence due to a different ethnic enclave located nearby.

We model using an entropy-maximising spatial interaction model. These models have previously been used to study flows of physical objects such as people in the case of modelling migration (Dennett and Wilson, 2013) or money in the case of modelling retail trips (Wilson, 2008). To begin, we assume that the total threat on that can come from at is constrained by the level of aggression . Thus,

8.1

Following Wilson (2008), we assume that there exist constants and such that

8.2

and

8.3

Equation (8.2) can be interpreted as the total ‘energy’ in the threat system that supports the flows and Equation (8.3) is justified by its role in generating more threat between those adversaries that are more aggressive in the final model. Although these constraints do not admit simple interpretation, they have been shown to generate accurate flows in models of retail trip distributions in previous applications.

An estimate of is then found by maximising the entropy measure:

8.4

subject to the constraints (8.1)–(8.3). It can be shown that this gives

8.5

where

8.6

for parameters and .

The model can be written as

8.7

a form that enables clear interpretation. To explain, the aggression isexerted over the adversary as a series of flows . The amount of that is exerted on at is weighted according to how the term

8.8

varies over the range of locations of . If is large for a given (in comparison to the other locations of , indexed by ), then a large proportion of the aggression will be directed towards at , resulting in a large flow of threat. can be thought of as the utility gained by at in directing their aggression towards at . Their aggression will generate greater utility if it is directed towards those adversaries that are nearby and towards those adversaries which themselves have high levels of aggression. Furthermore, utility is often considered to represent benefits minus costs. In this setting, is therefore the associated benefits obtained by directing threat towards (i.e. the benefit associated with defending the aggression ) and the distance metric specifies the corresponding costs (i.e. the cost of exerting threat over some landscape or distance). The parameter determines how this utility is influenced by the aggression of the adversary and determines how the resulting threat varies with the distance metric. Large values of imply that it is difficult to exert threat over any substantial distance and therefore any intimidatory effects will only be felt by those adversaries nearby.

Using this formulation of threat flows, it is possible to calculate the total threat from all locations of exerted on at by summing over the possible locations of to obtain

8.9

8.10

which holds for . This measure can be interpreted as a weighted sum of aggression emanating from adversary , weighted according to the amount of aggression of at each location (those locations of with a higher level of aggression will attract more threat from , all other things being equal) and according to the ease with which threat can travel across the spatial region of interest (those locations of that are closer to will experience higher levels of threat, all other things being equal).

A similar expression can be derived for the threat that exerts on at , so that

8.11

8.12

for further parameters and .

The threats and are location specific and capture spatial dependence via the metric . In addition, they are general enough to be incorporated into a wide range of conflict models. In what follows, we discuss some of these applications as avenues for future research.

8.6 Discussion: The Use of a Spatial Threat Measure in Models of Conflict

In this section, we propose how the measure of threat introduced in Section 8.5 might be applied to each of the three policy areas discussed in Sections 8.2–8.4. In doing so, we demonstrate the versatility of this measure and present a number of opportunities for further research.

8.6.2 Threat in a Model of Conflict Escalation

As described in Section 8.3, empirical agent-based simulations are becoming popular ways of modelling conflict processes. More traditional models, however, have explored how and why conflict might emerge between adversaries using systems of differential equations. These models are more amenable to analysis using a wide range of mathematical techniques. Consequently, differential equations can sometimes lead to insights that might not have been obtained using a simulation-based model, analysis of which often requires repeated simulations for different parameter values.

A limitation of traditional differential equation-based conflict models is that they are often highly simplified and unable to account for complex behaviour that is often observed in the real world. In this section, we demonstrate how the threat measure developed in Section 8.5 can be used to extend a simple model of conflict escalation, namely, the model of Richardson (1960). Baudains et al. (2015) demonstrate in more detail how this model exhibits complex behaviour and how a mathematical analysis can lead to intricate insights into the spatial dependence of conflict escalation. The use of the threat measure can provide differential equation based models with some of the versatility offered by ABMs, whilst still retaining some degree of analytical tractability.

Richardson's model considers the levels of military spending of two competing nations during the lead-up to war. Supposing that the spending levels of these two nations are given by and , respectively, then Richardson's model supposes that these values change as a result of three processes: they increase proportionally to the amount of spending of the opponent; they decrease proportionally to the existing amount of spending; and they increase ordecrease according to external events, which are assumed to influence spending similarly over time. The model is given by

8.13

8.14

where and determine the strength of action–reaction relationship between the two adversaries, and determine the cost of maintaining existing resources, and and represent external grievances.

This model results in two types of long-term behaviour: either the internal restraining dynamics will outweigh the competitive action–reaction dynamics and the system will eventually come to equilibrium and stop changing, or the action–reaction dynamics outweigh the damping in the system and the magnitude of military spending continues increasing indefinitely, resulting in an arms race between the two adversaries.

Baudains et al. (2015) use the threat measure of Equations (8.10) and (8.12) to incorporate spatial interaction into the model of Equations (8.13) and (8.14). Embedding a spatial interaction framework into models that do not explicitly incorporate space increases the range of application and the intricacy with which insights can be obtained. To specify threat, a measure of aggression is required, which is taken to be the dependent variable in the model in Equations (8.13) and (8.14). In Richardson's model, this is often taken to be the level of military spending or available military resources of the two adversaries.

The measure of threat is then embedded within the Richardson model by assuming that the action–reaction term in the model at each location, determining the rate at which each adversary increases their level of expenditure, is in fact proportional to the threat on each adversary at that location. Thus, the model becomes

8.15

8.16

for and . This model is similar to the model in Equations (8.13) and (8.14). In fact, if we were to take the sum of the different levels of hostility over the distinct locations, then the model is identical. The aggregate system can therefore either tend to be in equilibrium or result in an escalating process. What is different is that the level of expenditure at each location is tracked and depends on the threat from the adversary across all their locations. The contributions to this action–reaction relationship act as a weighted sum over the different locations, and complex dynamics can arise as a result.

Baudains et al. (2015) go on to identify bifurcations that arise due to the non-linearities embedded within Equations (8.15) and (8.16). These bifurcations introduce spatial instabilities into the system as the parameters and increase.

The use of threat in dynamical systems models provides them with greater complexity, making them more capable of incorporating real-world processes by which conflict is thought to arise. In addition, such models are amenable to a wide range of analytical techniques. Differential equations enable the logical exploration of the implications of a proposed mechanism by which adversaries are thought to interact. The threat measure presented in this chapter can be a valuable tool in increasing their range of application.

References

1. Baudains, P.J. (2015) Spatio-temporal modelling of civil violence: four frameworks for obtaining policy-relevant insights. Doctoral Dissertation, University College London, London.
2. Baudains, P., Fry, H.M., Davies, T.P., Wilson, A.G., and Bishop, S.R. (2015) A dynamic spatial model of conflict escalation. European Journal of Applied Mathematics, doi: 10.1017/S0956792515000558.
3. Benigni, M. and Furrer, R. (2012) Spatio-temporal improvised explosive device monitoring: improving detection to minimise attacks. Journal of Applied Statistics, 39 (11), 2493–2508.
4. Bhavnani, R., Donnay, K., Miodownik, D., Mor, M. and Helbing, D. (2014). Group Segregation and Urban Violence. American Journal of Political Science, 58(1), 226–245.
5. Braithwaite, A. and Johnson, S.D. (2012) Space-time modeling of insurgency and counterinsurgency in Iraq. Journal of Quantitative Criminology, 28, 31–48.
6. Braithwaite, A. and Johnson, S.D. (2015) The battle for Baghdad: testing hypotheses about insurgency from risk heterogeneity, repeat victimization, and denial policing approaches. Terrorism and Political Violence, 27, 112–132.
7. Brantingham, P.J., Tita, G.E., Short, M.B., and Reid, S.E. (2012) The ecology of gang territorial boundaries. Criminology, 50 (3), 851–885.
8. Dennett, A. and Wilson, A.G. (2013) A multi-level spatial interaction modelling framework for estimating inter-regional migration in Europe. Environment and Planning A, 45, 1491–1507.
9. Hegre, H., Karlsen, J., Nygård, H.M., Strand, H., and Urdal, H. (2013) Predicting armed conflict, 2010-2050. International Studies Quarterly, 57, 250–270.
10. Helbing, D., Brockmann, D., Chadefaux, T., Donnay, K., Blanke, U., Woolley-Meza, O., Moussaid, M., Johansson, A., Krause, J., Schutte, S., and Perc, M. (2015) Saving human lives: what complexity science and information systems can contribute. Journal of Statistical Physics, 158 (3), 735–781.
11. Johnson, N.F., Medina, P., Zhao, G., Messinger, D.S., Horgan, J., Gill, P., Bohorquez, J.C., Mattson, W., Gangi, D., Qi, H., Manrique, R., Velasquez, N., Morgenstern, A., Restrepo, E., Johnson, N., Spagat, M., and Zarama, R. (2013) Simple mathematical law benchmarks human confrontations. Scientific Reports, 3, 3463–.
12. Leetaru, K. and Schrodt, P.A. (2013) GDELT: global data on events, location and tone, 1979-2012. Presented at: International Studies Association, San Francisco, April 2013. Available online at: http://data.gdeltproject.org/documentation/ISA.2013.GDELT.pdf (accessed 30 December 2015).
13. O'Brien, S.P. (2010) Crisis early warning and decision support: contemporary approaches and thoughts on future research. International Studies Review, 12, 87–104.
14. Richardson, L.F. (1960) Arms and Insecurity, The Boxwood Press, Pittsburgh, PA.
15. Rossmo, K.D. (2000) Geographic Profiling, CRC Press LLC, Boca Raton, FL.
16. Shakarian, P., Subrahmanian, V., and Sapino, M.L. (2009) SCARE: a case study with Baghdad. Proceedings of the Third International Conference on Computational Cultural Dynamics, AAAI.
17. Townsley, M., Johnson, S.D., and Ratcliffe, J.H. (2008) Space time dynamics of insurgent activity in Iraq. Security Journal, 21, 139–146.
18. Ward, M.D., Metternich, N.W., Dorff, C.L., Gallop, M., Hollenbach, F.M., Schultz, A., and Weschle, S. (2013) Learning form the past and stepping into the future: toward a new generation of conflict prediction. International Studies Review, 15, 473–490.
19. Weidmann, N.B. and Salehyan, I. (2013) Violence and ethnic segregation: a computational model applied to Baghdad. International Studies Association, 57 (1), 52–64.
20. Wilson, A.G. (2008) Boltzmann, Lotka and Volterra and spatial structural evolution: an integrated methodology for some dynamical systems. Journal of the Royal Society, Interface / the Royal Society, 5 (25), 865–871.
21. Zammit-Mangion, A., Dewar, M., Kadirkamanathan, V., and Sanguinetti, G. (2012) Point process modelling of the Afghan War Diary. Proc. Natl. Acad. Sci. U.S.A., 109 (31), 12414–12419.