The partial K function

TL;DR

This paper introduces a partial K function for spatial point process analysis, allowing for better detection of interactions between point types by accounting for effects of other points and covariates.

Contribution

The paper presents a novel partial K function that extends the traditional K function to account for dependencies and covariates, improving spatial interaction analysis.

Findings

Partial K function can reveal hidden dependencies between point types.

Bias correction and hyperparameter selection are discussed for accurate analysis.

Application to Lansing Woods dataset demonstrates practical utility.

Abstract

The K function and its related statistics have been an enduring tool in the analysis of spatial point processes, providing an easy to compute and interpret summary statistic for characterising the interactions between points of one type, or between two different types of points. In this paper, we introduce a partial K function, enabling us to account for some of the effects of the other point types when analysing point-point interactions. The partial K function we introduce reduces to the usual K function when the other points are independent of the points of interest and has a similar interpretation. Using examples, we demonstrate how the partial K function can unpick dependence between point types that would otherwise be hidden in the usual K function. We also discuss important bias correction steps and hyperparameter selection. In addition, we introduce an extension to account for other spatial covariates, and demonstrate the methodology on the Lansing Woods dataset.