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Enhanced point pattern analysis on nonconvex spatial domains
Thesis (PhD (Mathematical Statistics))--University of Pretoria, 2024.
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| Format: | Thesis |
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University of Pretoria
2025
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| _version_ | 1867613476128555008 |
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| access_status_str | Open Access |
| author2 | Fabris-Rotelli, Inger Nicolette |
| author_browse | Fabris-Rotelli, Inger Nicolette |
| author_facet | Fabris-Rotelli, Inger Nicolette |
| collection | Thesis |
| dc_rights_str_mv | © 2023 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Thesis (PhD (Mathematical Statistics))--University of Pretoria, 2024. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/100680 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:36:45.136Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/100680 Enhanced point pattern analysis on nonconvex spatial domains Fabris-Rotelli, Inger Nicolette u14194237@tuks.co.za Mahloromela, Kabelo UCTD Sustainable Development Goals (SDGs) Point pattern Spatial domain Nonconvex Visibility graph Euclidean distance Thesis (PhD (Mathematical Statistics))--University of Pretoria, 2024. Point pattern analysis is the study of the spatial arrangement of points in space, usually two-dimensional space. The points arise from a stochastic mechanism, termed a point process, whose characteristics are of scientific interest. The properties of point patterns are characterised using statistical measures that are a function of the study area and distance. Consequently, the domain in which points are observed and the distance metric used to quantify proximity between points plays an important role. Convex domains with the Euclidean distance are often used. This choice of domain and distance measure, however, makes an implicit assumption that all points are connected in a space without obstacles. In real-world applications, points may be constrained by their environments, thus a convex window and the Euclidean distance may not correctly capture spatial proximity relationships and restrictions imposed by the domain’s geometry. In this thesis, a presentation of methodology that accounts for the nonconvex structure of the spatial domain in point pattern analysis is provided. Firstly, consideration is given to the selection of nonconvex windows (when unknown) for point patterns realised from a process that is governed by a covariate. The proposed algorithm uses a weighted distance-based outlier scoring scheme that considers the distribution of covariates at observed data point locations. The robustness of the algorithm is demonstrated through a simulation study. Subsequently, a framework is developed to quantify proximity relationships using a graph theoretic approach based on visibility graphs. This characterisation of distance is used to extend first- and second-order point pattern measures for appropriate use on nonconvex domains. Finally, we provide an implementation strategy to efficiently compute summary measures based on a query to the visibility graph. STATOMET, the Bureau for Statistical and Survey Methodology, in the Department of Statistics at the University of Pretoria Environmental Systems Research Institute (ESRI) in South Africa National Research Foundation of South Africa (NRF) : (Grant Number 137785) DST-NRF-SAMRC SARChI, the South Africa National Research Foundation and South Africa Medical Research Council (South Africa DST-NRF-SAMRC SARChI Research Chair in Biostatistics, Grant number 114613) Statistics PhD (Mathematical Statistics) Unrestricted Faculty of Natural and Agricultural Sciences None 2025-02-11T10:08:39Z 2025-02-11T10:08:39Z 2025-05 2024-11 Thesis * A2025 http://hdl.handle.net/2263/100680 https://doi.org/10.25403/UPresearchdata.28375163 en © 2023 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | UCTD Sustainable Development Goals (SDGs) Point pattern Spatial domain Nonconvex Visibility graph Euclidean distance Enhanced point pattern analysis on nonconvex spatial domains |
| title | Enhanced point pattern analysis on nonconvex spatial domains |
| title_full | Enhanced point pattern analysis on nonconvex spatial domains |
| title_fullStr | Enhanced point pattern analysis on nonconvex spatial domains |
| title_full_unstemmed | Enhanced point pattern analysis on nonconvex spatial domains |
| title_short | Enhanced point pattern analysis on nonconvex spatial domains |
| title_sort | enhanced point pattern analysis on nonconvex spatial domains |
| topic | UCTD Sustainable Development Goals (SDGs) Point pattern Spatial domain Nonconvex Visibility graph Euclidean distance |
| url | http://hdl.handle.net/2263/100680 https://doi.org/10.25403/UPresearchdata.28375163 |