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

TL;DR

This paper introduces a novel method for predicting local intensity in stationary isotropic spatial point processes by combining regularized counting processes with a revisited kriging approach.

Contribution

It proposes a new approach that integrates first- and second-order characteristics of regularized counting processes with kriging for intensity prediction.

Findings

Effective prediction of local intensity in spatial point processes.

Improved accuracy over traditional methods.

Applicability to large observation windows.

Abstract

We consider a stationary and isotropic spatial point process, whose a realisation is observed within a large window. In order to predict its local intensity, 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 intensity by using a revisited kriging of the regularized process.