For a given region, we have a dataset composed of car theft locations along with a linked dataset of recovery locations which, due to partial recovery, is a relatively small subset of the set of theft locations. For an investigator seeking to understand the behavior of car thefts and recoveries in the region, several questions are addressed. Viewing the set of theft locations as a point pattern, can we propose useful models to explain the pattern? What types of predictive models can be built to learn about recovery location given theft location? Can the dependence between the point pattern of theft locations and the point pattern of recovery locations be formalized? Can the flow between theft sites and recovery sites be captured? Origin–destination modeling offers a natural framework for such problems. However, here the data is not for areal units but rather is a pair of dependent point patterns, with the recovery point pattern only partially observed. We offer modeling approaches for investigating the questions above and apply the approaches to two datasets. One is small from the state of Neza in Mexico with areal covariate information regarding population features and crime type. The second, a much larger one, is from Belo Horizonte in Brazil but lacks potential predictors.
- Bayesian framework
- Log Gaussian Cox process
- Nonhomogeneous Poisson process
- Posterior predictive distribution
- Rank probability score