A J-function for inhomogeneous spatio-temporal point processes

TL;DR

This paper introduces a new summary statistic for inhomogeneous spatio-temporal point processes based on correlation functions, generalizing the J-function and relating to the inhomogeneous K-function, with practical estimation and simulation examples.

Contribution

It presents a novel inhomogeneous J-function for spatio-temporal point processes, extending existing methods to non-stationary data with explicit formulas and unbiased estimators.

Findings

The new statistic generalizes the J-function for inhomogeneous processes.

Explicit form derived under specific model assumptions.

Demonstrated effectiveness through simulations.

Abstract

We propose a new summary statistic for inhomogeneous intensity-reweighted moment stationary spatio-temporal point processes. The statistic is defined through the n-point correlation functions of the point process and it generalises the J-function when stationarity is assumed. We show that our statistic can be represented in terms of the generating functional and that it is related to the inhomogeneous K-function. We further discuss its explicit form under some specific model assumptions and derive a ratio-unbiased estimator. We finally illustrate the use of our statistic on simulated data.