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Diffusion Smoothing for Spatial Point Patterns
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DOI：10.1214/21-STS825.png)
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Abstract
En 中文
Traditional kernel methods for estimating the spatially-varying density of points in a spatial point pattern may exhibit unrealistic artefacts, in addition to the familiar problems of bias and over- or under-smoothing. Performance can be improved by using diffusion smoothing, in which the smoothing kernel is the heat kernel on the spatial domain. This paper develops diffusion smoothing into a practical statistical methodology for two-dimensional spatial point pattern data. We clarify the advantages and disadvantages of diffusion smoothing over Gaussian kernel smoothing. Adaptive smoothing, where the smoothing bandwidth is spatially-varying, can be performed by adopting a spatially-varying diffusion rate: this avoids technical problems with adaptive Gaussian smoothing and has substantially better performance. We introduce a new form of adaptive smoothing using lagged arrival times, which has good performance and improved robustness. Applications in archaeology and epidemiology are demonstrated. The methods are implemented in open-source R code.
Keywords:
Adaptive smoothing
bandwidth
heat kernel
kernel estimation
lagged arrival method
Richardson extrapolation
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