Spatial kriging for replicated temporal point processes

TL;DR

This paper introduces a kriging approach for spatial prediction of temporal point process intensities using multiple replications, avoiding isotropy assumptions, with applications to bike demand data.

Contribution

It develops a novel nonparametric kriging method for spatially predicting temporal point process intensities using replicated data, with theoretical properties and real-world application.

Findings

Effective prediction of bike demand patterns

New estimators for mean and covariance functions

Method performs well in simulations and real data

Abstract

This paper presents a kriging method for spatial prediction of temporal intensity functions, for situations where a temporal point process is observed at different spatial locations. Assuming that several replications of the processes are available at the spatial sites, this method avoids assumptions like isotropy, which are not valid in many applications. As part of the derivations, new nonparametric estimators for the mean and covariance functions of temporal point processes are introduced, and their properties are studied theoretically and by simulation. The method is applied to the analysis of bike demand patterns in the Divvy bicycle sharing system of the city of Chicago.