Burglary in London: insights from statistical heterogeneous spatial point processes

To obtain operational insights regarding the crime of burglary in London, we consider the estimation of the effects of covariates on the intensity of spatial point patterns. Inspired by localized properties of criminal behaviour, we propose a spatial extension to mixtures of generalized linear models from the mixture modelling literature. The Bayesian model proposed is a finite mixture of Poisson generalized linear models such that each location is probabilistically assigned to one of the groups. Each group is characterized by the regression coefficients, which we subsequently use to interpret the localized effects of the covariates. By using a blocks structure of the study region, our approach enables specifying spatial dependence between nearby locations. We estimate the proposed model by using Markov chain Monte Carlo methods and we provide a Python implementation

Interpretable models for spatially dependent and heterogeneous phenomena

Over the past decades, we have seen an increase in the availability of data that includes spatial information. Incorporating spatial information in models may result in performance improvements, which may then be used to better inform decision-making processes. When modelling spatial data, typical assumptions such as independence of observations across locations, no longer hold. As a consequence, careful methodology is required. This thesis addresses the modelling of two common types of data encountered in spatial modelling: measurements of a quantity at pre-specified locations (e.g., sensor measurements), and events for which geographical location and time are recorded. We develop effective approaches for modelling spatial data in an interpretable manner, thus making it suitable for application domains where the transparency of a model is a desired property. We demonstrate the developed approaches with empirical simulation studies.Open Acces