Summary statistics for inhomogeneous marked point processes

TL;DR

This paper introduces new summary statistics for inhomogeneous marked point processes, especially with discrete marks, based on n-point correlation functions, and demonstrates their application on wildfire data.

Contribution

It develops ratio-unbiased estimators for these statistics and explores their relationships and explicit forms under specific models.

Findings

New summary statistics for inhomogeneous marked point processes.

Derived ratio-unbiased estimators for the proposed statistics.

Applied methods successfully to wildfire data.

Abstract

We propose new summary statistics for intensity-reweighted moment stationary marked point processes with particular emphasis on discrete marks. The new statistics are based on the n-point correlation functions and reduce to cross J- and D-functions when stationarity holds. We explore the relationships between the various functions and discuss their explicit forms under specific model assumptions. We derive ratio-unbiased minus sampling estimators for our statistics and illustrate their use on a data set of wildfires.