On using Reproducible Hilbert Spaces for the analysis of Replicated Spatial Point Processes

TL;DR

This paper introduces a novel approach using Reproducing Kernel Hilbert Spaces to analyze replicated spatial point processes, enabling advanced statistical testing and classification methods.

Contribution

It demonstrates how spatial point processes can be embedded in RKHS, allowing the application of kernel-based statistical tests and classification techniques.

Findings

Successfully identified differences between classes of point patterns.

Applied MBox and MANOVA tests within RKHS framework.

Achieved classification of new spatial point process observations.

Abstract

This paper focuses on the use of the theory of Reproducing Kernel Hilbert Spaces in the statistical analysis of replicated point processes. We show that spatial point processes can be observed as random variables in a Reproducing Kernel Hilbert Space and, as a result, methodological and theoretical results for statistical analysis in these spaces can be applied to them. In particular and by way of illustration, we show how we can use the proposed methodology to identify differences between several classes of replicate point patterns using the MBox and MANOVA tests, and to classify a new observation, using Discriminant Functions.