Activity profiles of many terrorist groups with different ideological (e.g., political, religious, and socio-economic) affiliations and across distant geographies are now available via open-source databases such as the ITERATE database (ITERATE, 2006), the Global Terrorism Database (GTD) (LaFree & Dugan, 2007), the RAND Database on Worldwide Terrorism Incidents (RDWTI) (RDWTI, 2009), etc. These databases capture a good representative subset of all attacks made by different terrorist groups and are thus useful in studying broader terrorism trends. In spite of the availability of this data, extensive quantitative studies such as modeling and inferencing are still lacking in many aspects. In particular, broader questions of interest that could be answered with a quantitative analysis include the best model fits that could be possible for terrorist activity and what these models intuitively mean in terms of terrorist behavior and dynamics, inferencing problems such as early detection of spurts and downfalls (see brief definitions of some of the terms introduced in this chapter in Table 16.1) in activity 346and what they mean in terms of changes in organizational dynamics, etc. While some of these aspects have been addressed via qualitative methods in the wider terrorism literature earlier, a quantitative approach could provide additional approaches/methodologies/techniques for uses in the field and render human biases less important. Brief Description of Certain Terms Used in This Chapter Spurt/Downfall Sudden increase/decrease in the activity of a terrorist group. Intentions Ideological attributes (e.g., political, religious, linguistic, socio-economic, cultural, etc.) that contribute towards the grievance profile of a certain terrorist group. Capabilities Assets (e.g., manpower, material, skill-sets) that allow a group to terrorize and realize its Intentions. Tactics Specific attack attributes (e.g., attacks that capture a higher degree of resilience or coordination) that are used by the group to achieve short- and long-term objectives. Resilience Ability of the group to sustain terrorist activity over a number of days. Coordination Ability of the group to launch multiple attacks over a given time-period. Changepoint detection A statistical theory of detection of abrupt changes in an observation’s density by trading off false alarms of non-existent changes with quick detection of true changes. Majorization theory A theory of comparing two positive vectors (with the same sum) so as to decide whether one of them is more well-spread than the other (e.g., income inequality). Parametric Typically associated with a model or parameter(s). Non-parametric Typically oblivious of models and not explicitly learning model parameters.