Spatial point processes and neural networks: A convenient couple

Abstract

Different spatial point process models and techniques have been developed in the past decades to facilitate the statistical analysis of spatial point patterns. However, in some cases the spatial point process methodology is scarce and no flexible models nor suitable statistical methods are available. For example, due to its complexity, the statistical analysis of spatial point patterns of several groups observed at a number of time instances has not been studied in-depth, and there are a few limited models and methods available for such data. In the present work, we provide a mathematical framework for coupling neural network methods with the statistical analysis of point patterns. In particular, we discuss an example of deep neural networks in the statistical analysis of highly multivariate spatial point patterns and provide a new strategy for building spatio-temporal point processes using variational autoencoder generative neural networks.