Diffusion Smoothing for Spatial Point Patterns
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 thesmoothing kern...
| Main Authors: | , , , , |
|---|---|
| Format: | Journal Article |
| Language: | English |
| Published: |
Institute of Mathematical Statistics
2022
|
| Subjects: | |
| Online Access: | http://purl.org/au-research/grants/arc/DP130104470 http://hdl.handle.net/20.500.11937/91583 |
| Summary: | 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 thesmoothing kernel is the heat kernel on the spatial domain. This paper developsdiffusion smoothing into a practical statistical methodology for twodimensionalspatial point pattern data. We clarify the advantages and disadvantagesof diffusion smoothing over Gaussian kernel smoothing. Adaptivesmoothing, where the smoothing bandwidth is spatially-varying, can beperformed by adopting a spatially-varying diffusion rate: this avoids technicalproblems with adaptive Gaussian smoothing and has substantially betterperformance. We introduce a new form of adaptive smoothing using laggedarrival times, which has good performance and improved robustness. Applicationsin archaeology and epidemiology are demonstrated. The methods areimplemented in open-source R code |
|---|