On spatial point processes with composition-valued marks

TL;DR

This paper develops new statistical methods for analyzing spatial point processes with composition-valued marks, which are vector-valued with sum-to-constant constraints, addressing a gap in current analysis techniques.

Contribution

It extends existing methods to handle composition-valued marks and adapts mark characteristics for this context, enabling analysis of complex non-scalar data.

Findings

Applied methods to tree crown-to-base composition data

Analyzed business sector composition spatial correlations

Demonstrated effectiveness of new methods in real data scenarios

Abstract

Methods for marked spatial point processes with scalar marks have seen extensive development in recent years. While the impressive progress in data collection and storage capacities has yielded an immense increase in spatial point process data with highly challenging non-scalar marks, methods for their analysis are not equally well developed. In particular, there are no methods for composition-valued marks, i.e. vector-valued marks with a sum-to-constant constrain (typically 1 or 100). Prompted by the need for a suitable methodological framework, we extend existing methods to spatial point processes with composition-valued marks and adapt common mark characteristics to this context. The proposed methods are applied to analyse spatial correlations in data on tree crown-to-base and business sector compositions.