Point Process Modeling with Spatiotemporal Covariates for Predicting Crime

Abstract

Self-exciting point processes are widely used to model events occurring in time and space whose rate depends on the past history of the process, such as earthquakeaftershocks, crime, and neural spike trains. By modeling the event rate as the sum of a background (or immigrant) process, often an inhomogeneous Poisson process, andan offspring process consisting of events triggered by previous events, self-exciting point process models naturally account for complex clustering behavior. When themodel is physically motivated, as are models of earthquake aftershock sequences, model parameters have direct interpretations in terms of the generative mechanism.In this thesis, I focus in particular on the application of self-exciting point processes to crime. Crime rates are known to vary greatly in space within a city, as a result of many demographic and economic factors, and crime often exhibits “nearrepeats,” when one crime is followed by another soon after, either from retaliation or because offenders tend to return to the same areas. Point process models havebeen used to predict crime, but the available models can be improved: they cannot explicitly account for spatially varying covariates and estimate their effects, and there are no inference tools that could be used to test criminological theories or evaluate interventions. After extensively reviewing the literature on self-exciting point processes, I introducea new model which accounts for both spatial covariates and self-excitation, and explore its benefits over simple lagged regressions and other commonly used methods. After discussing computational issues in fitting the model, I use simulations to explore methods for parameter inference, review a set of residual diagnostics and animations, and use these diagnostics to explore the model’s behavior undervarious forms of model misspecification, giving practical advice for the interpretation of model fits. To demonstrate the model’s utility, I then analyze large databasesof Pittsburgh and Baltimore crime records, linking crime rates to several relevant spatial covariate and leading indicator events, and comparing several model variations.