``Bottom-up" and ``top-down" identify two fundamental approaches to modeling complex systems. As the name suggests, a bottom-up approach analyzes how elements on a micro scale affect observations on the macro scale. On the other hand, top-down approaches use macro scale data to identify patterns evolved from the micro scale. This thesis details two models, agent-based and data driven, designed for complex systems. These models are applied to the complex system of street gang violence.

The first method employed is agent-based and is used to explain potential geographic influences in the formation of street gang rivalries. In this framework each agent possesses certain properties and movement rules. The agents then move and interact with the simulated environment and other agents. From these simple rules the emergent behavior of the location of interactions and the rivalry network are observed.

The second method addresses the need to infer process parameters and identify gangs involved in violent crimes in the presence of incomplete data. The violent events among gangs can be viewed as realizations of a self-exciting point process on the rivalry network. For many of the events in the data, the time of the event is known, but the rivalry association is not. Using the structure of the point process a method is proposed that simultaneously estimates the process and infers the rivalry affiliation for the unknown events. We call this method the Estimate

There are two major findings in this dissertation. The first is that the proposed agent-based model used to simulate the gang rivalry network observed in Hollenbeck provided better results than a simplified model and a Geographic Threshold graph. The second major finding is that the Estimate & Score algorithm is a computationally efficient method that produces comparable results to previous work and is better than chance. It also successfully approximates the process parameters in the presence of incomplete data.