Modeling Conflict Dynamics with Spatio-temporal Data

This chapter gives a high-level, non-technical, introduction to the motivation behind the approach adopted to studying conflict in this book and the underlying mathematical principles.

This chapter lays the theoretical foundations for the approach to spatio-temporal modeling from data typically found in conflict data sets. The chapter begins by outlining the basic principles of point-process theory, starting from the definition of the Poisson distribution and ending with a description of the log-Gaussian Cox process and the point-process likelihood function. The chapter proceeds to discuss two important classes of spatio-temporal models, the stochastic partial differential equation (SPDE) and the stochastic integro-difference equation (SIDE). Dimensionality reduction techniques to reduce these models into state-space form are then given. Recrusive estimation algorithms for estimation with a state-space model are then derived and are followed by a strategy to include unknown parameters within the estimation framework through variational Bayes. The chapter concludes with a section on implementation tools. This includes details on non-parametric methods for obtaining descriptive statistics from events, a basis function placement method and a variational-Laplace algorithm for inference under the point-process likelihood.

This chapter applied the techniques of Chap. 2 to the WikiLeaks Afghan War Diary and follows closely the treatment in 2012a doi: 10.1073/pnas.1203177109. The chapter begins by giving an overview of the conflict in Afghanistan which began in 2001 and the WikiLeaks release. An exploratory study of the data set is given which includes consistency checks, a non-parametric analysis and an evaluation of fixed effects (e.g. population density) on the conflict intensity. Results from the non-parametric analysis are used to elicit a spatio-temporal model which is then reduced to a state-space model amenable to the algorithms of Chap. 2. The chapter proceeds to discuss the results and show how important information, such as statistical descriptions of escalation and volatility, may be extracted from the analysis. The chapter concludes by assessing prediction accuracy and showing that uncertainty has been reliably quantified using this approach.