Spatial Prediction via Two-Stage Kriging with Voronoi-based Segmentation

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题名:	Spatial Prediction via Two-Stage Kriging with Voronoi-based Segmentation
作者:	陳咨亦;CHEN, ZI-YI
贡献者:	統計研究所
关键词:	計算效率;克利金;非平穩過程;空間預測;Voronoi分割法;Computational Efficiency;Kriging;Nonstationary Process;Spatial Prediction;Voronoi Segmentation
日期:	2025-06-18
上传时间:	2025-10-17 12:13:08 (UTC+8)
出版者:	國立中央大學
摘要:	隨著大數據時代的來臨，在廣泛且異質性高的區域所收集的空間資料，往往展現出複雜的非平穩狀態，對傳統如克利金等地理統計方法造成嚴峻挑戰。為因應此問題，本研究提出一種適應性之兩階段克利金分析架構，結合Voronoi分割以提升非平穩情境下的空間預測能力。在第一階段中，本方法利用局部空間相關性統計量量化資料的異質性，並據以建構具有近似平穩特性的Voronoi子區域，然後於各子區域內執行局部克利金預測。為解決分割邊界的不連續性並提升整體預測曲面的平滑性，第二階段針對子區域中心與隨機子抽樣點等代表性位置，再次進行克利金配適，以整合第一階段之預測結果並完成全域的空間預測。模擬研究測試多種非平穩狀態與抽樣設計，結果顯示本方法在維持預測準確度的同時，大幅降低計算複雜度，並優於傳統克利金法。最後，本方法應用於 MODIS白天地表溫度的資料，驗證其在實際資料分析上的可行性。;In the era of big data, spatial datasets collected over large and heterogeneous regions often exhibit complex nonstationary behavior, posing significant challenges for traditional geostatistical methods such as kriging. To address these challenges, this study proposes an adaptive two-stage kriging framework that leverages Voronoi-based segmentation to enhance spatial prediction under nonstationarity. In the first stage, a local dependence statistic is applied to quantify spatial heterogeneity, which guides the construction of Voronoi subregions with approximately stationary properties. Within each subregion, local kriging is performed to generate initial predictions. To overcome boundary discontinuities and ensure a smooth global predictive surface, the second stage applies kriging to a selected set of representative locations, including subregion centroids and several subsampling locations, using the first-stage predictions as input. Simulation results across various nonstationary scenarios and sampling designs demonstrate that the proposed method substantially reduces computational complexity while maintaining competitive predictive accuracy relative to standard kriging. Finally, the method is applied to Moderate Resolution Imaging Spectroradiometer (MODIS) daytime land surface temperature data, confirming its effectiveness and scalability in real data applications.
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