Temporal Considerations for Spatial Event Prediction

A significant amount of research and practice in the law enforcement arena focuses on spatial and temporal event analysis. Although some efforts integrate spatial and temporal analysis, the majority of the previous work focuses on modeling events in one area across time periods or modeling multiple areas within single temporal intervals. This dissertation attempts to close the gap between spatial and temporal analysis by focusing on the challenges of integrating spatial and temporal features in criminal site selection problems. Since the criminal environment contains multiple actors intermingled in a spatial region, the challenge for the analyst is identifying patterns both spatially and temporally based on the criminal's site-selection criteria. This dissertation uses a three-pronged approach to study (1) the identification and inclusion of temporal distances into a feature-space model; (2) the application of hierarchical modeling for temporal intervals; and (3) the consideration of a random field construct for modeling site-selection event data. We evaluate each approach on both a simulated data set and a sample data set from a small US city. We compare results of the different methodologies using a test statistic based on measuring performance across a space-time surveillance plot. We found that a two-stage analytical approach assists us in identifying when spatial-temporal modeling might offer significant improvements in predictive performance. Additionally, the integration of a hierarchical structure with the feature-space generalized linear model provides a method that accounts for temporal considerations in the criminal's site-selection process. These temporal features can be ``pulse events'' that indicate temporary shifts in spatial-temporal patterns or transitions at the discrete temporal interval level that might account for low-level seasonality within the criminal's site-selection process. Finally the development of an expanded feature-space model provides benefits similar to those of a Markov random field model without the computational demands of the Bayesian construct for hierarchical modeling. These methods for identifying and including temporal information into spatial analysis methodologies offer benefits not only in the law enforcement and military communities, but also to the business and environmental sectors.