This dissertation examines the application of self-exciting point processes to crime and introduces a new model that accounts for both spatial covariates and self-excitation, exploring its benefits over simple lagged regressions and other commonly used methods.
The dissertation begins with an in-depth review of the available literature on self-exciting point processes before introducing a novel model that accounts for both spatial covariates and self-excitation, and exploring its benefits over simple lagged regressions and other common methods. After reviewing computational issues in fitting the model, methods for parameter inferences are explored through simulations; a review of a set of residual diagnostics animations lays the groundwork for the exploration of the model’s behavior under various forms of model misspecification, followed by practical advice for the interpretation of model fits. To demonstrate the proposed model’s usefulness, the paper provides an analysis of large databases of Pittsburgh and Baltimore crime records, linking crime rates to several relevant spatial covariate and lending indicator events, and comparing several model variations.