Predicting the intensity of partially observed data from a revisited kriging for point processes

TL;DR

This paper introduces a method to predict local intensity of spatial point processes by combining kriging with regularized counting processes, leveraging the characteristics of an underlying stationary random field.

Contribution

It proposes a novel kriging-based approach for predicting point process intensity using regularized counting processes and their characteristics.

Findings

Effective prediction of local intensity in spatial point processes.

Integration of kriging with regularized counting processes enhances prediction accuracy.

Applicable to large observation windows for spatial data analysis.

Abstract

We consider a stationary and isotropic spatial point process whose a realisation is observed within a large window. We assume it to be driven by a stationary random field $U$. In order to predict the local intensity of the point process, $\lambda (x|U)$, we propose to define the first- and second-order characteristics of a random field, defined as the regularized counting process, from the ones of the point process and to interpolate the local intensity by using a kriging adapted to the regularized process.