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: | , , , , |
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| Format: | Journal Article |
| Language: | English |
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Institute of Mathematical Statistics
2022
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| Subjects: | |
| Online Access: | http://purl.org/au-research/grants/arc/DP130104470 http://hdl.handle.net/20.500.11937/91583 |
| _version_ | 1848765555052380160 |
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| author | Baddeley, Adrian Davies, Tilman M Rakshit, Suman Nair, Gopalan McSwiggan, Greg |
| author_facet | Baddeley, Adrian Davies, Tilman M Rakshit, Suman Nair, Gopalan McSwiggan, Greg |
| author_sort | Baddeley, Adrian |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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 |
| first_indexed | 2025-11-14T11:37:06Z |
| format | Journal Article |
| id | curtin-20.500.11937-91583 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:37:06Z |
| publishDate | 2022 |
| publisher | Institute of Mathematical Statistics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-915832023-05-17T05:26:31Z Diffusion Smoothing for Spatial Point Patterns Baddeley, Adrian Davies, Tilman M Rakshit, Suman Nair, Gopalan McSwiggan, Greg Science & Technology Physical Sciences Statistics & Probability Mathematics Adaptive smoothing bandwidth heat kernel kernel estimation lagged arrival method Richardson extrapolation BANDWIDTH SELECTION DENSITY-ESTIMATION CROSS-VALIDATION KERNEL INTENSITY ESTIMATORS MATRICES LATTICE 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 2022 Journal Article http://hdl.handle.net/20.500.11937/91583 10.1214/21-STS825 English http://purl.org/au-research/grants/arc/DP130104470 http://purl.org/au-research/grants/arc/DP130102322 Institute of Mathematical Statistics fulltext |
| spellingShingle | Science & Technology Physical Sciences Statistics & Probability Mathematics Adaptive smoothing bandwidth heat kernel kernel estimation lagged arrival method Richardson extrapolation BANDWIDTH SELECTION DENSITY-ESTIMATION CROSS-VALIDATION KERNEL INTENSITY ESTIMATORS MATRICES LATTICE Baddeley, Adrian Davies, Tilman M Rakshit, Suman Nair, Gopalan McSwiggan, Greg Diffusion Smoothing for Spatial Point Patterns |
| title | Diffusion Smoothing for Spatial Point Patterns |
| title_full | Diffusion Smoothing for Spatial Point Patterns |
| title_fullStr | Diffusion Smoothing for Spatial Point Patterns |
| title_full_unstemmed | Diffusion Smoothing for Spatial Point Patterns |
| title_short | Diffusion Smoothing for Spatial Point Patterns |
| title_sort | diffusion smoothing for spatial point patterns |
| topic | Science & Technology Physical Sciences Statistics & Probability Mathematics Adaptive smoothing bandwidth heat kernel kernel estimation lagged arrival method Richardson extrapolation BANDWIDTH SELECTION DENSITY-ESTIMATION CROSS-VALIDATION KERNEL INTENSITY ESTIMATORS MATRICES LATTICE |
| url | http://purl.org/au-research/grants/arc/DP130104470 http://purl.org/au-research/grants/arc/DP130104470 http://hdl.handle.net/20.500.11937/91583 |