Some recent developments in statistics for spatial point patterns

TL;DR

This paper reviews recent advances in statistical methods for spatial point patterns, including new models, inference techniques, and computational approaches developed over the past decade.

Contribution

It introduces new classes of spatial point process models, discusses estimation and inference methods, and addresses computational challenges in the analysis of spatial point patterns.

Findings

Development of new classes of spatial point process models

Advances in estimation and inference techniques

Extensions of summary statistics for inhomogeneous processes

Abstract

This paper reviews developments in statistics for spatial point processes obtained within roughly the last 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 briefly considered too. Concerning non-parametric inference, we consider extensions of functional summary statistics to the case of inhomogeneous point processes as well as new approaches to simulation based inference.