Spatial kriging for replicated temporal point processes

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 process are available at the spatial sites, this method avoids assumptions...

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Bibliographic Details
Published in:Spatial statistics 2022-10, Vol.51, p.100681, Article 100681
Main Author: Gervini, Daniel
Format: Article
Language:English
Subjects:
Cox process
Poisson process
Spline smoothing
Tensor-product splines
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Summary: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 process 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.
ISSN:2211-6753
2211-6753
DOI:10.1016/j.spasta.2022.100681