Bayesian estimation and prediction for inhomogenous spatio-temporal log-Gaussian Cox processes using low-rank models, with application to criminal surveillance

In this paper we propose a method for conducting likelihood-based inference for a class of non-stationary spatio-temporal log-Gaussian Cox processes. The method uses convolution-based models to capture spatio-temporal correlation structure, is computationally feasible even for large datasets and does not require knowledge of the underlying spatial intensity of the process. We describe an application to a surveillance system for detecting emergent spatio-temporal clusters of homicides in Belo Horizonte, Brazil, and discuss the advantages and drawbacks of our model-based approach by comparison with other spatio-temporal surveillance methods that have been proposed in the literature.