Some Recent Developments in Statistics for Spatial Point Patterns

Abstract

This article reviews developments in statistics for spatial point processes obtained within roughly the past decade. These developments include new classes of spatial point process models such as determinantal point processes, models incorporating both regularity and aggregation, and models where points are randomly distributed around latent geometric structures. Regarding parametric inference, the main focus is on various types of estimating functions derived from so-called innovation measures. Optimality of such estimating functions is discussed, as well as computational issues. Maximum likelihood inference for determinantal point processes and Bayesian inference are also briefly considered. Concerning nonparametric inference, we consider extensions of functional summary statistics to the case of inhomogeneous point processes as well as new approaches to simulation-based inference.