專題演講 主講人：曾聖澧教授 (國立中山大學應用數學系)
題 目：Robust Testing and Contiguous Segmentation for Nonstationary Spatial Data
主講人：曾聖澧教授 (國立中山大學應用數學系)
時 間：112年10月6日(星期五)上午10:40-11:30
(上午10:20-10:40茶會於綜合一館428室舉行)
地 點：綜合一館427室
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摘要
In geostatistics, the assumption of stationarity is commonly applied to the underlying processes of interest. While these assumptions remain valid within constrained spatial domains, their applicability diminishes when addressing large geographical domains or intricate spatial phenomena. We introduce an innovative methodology tailored for the evaluation of stationarity assumption frequently employed in geostatistics. We look at a particular kind of nonstationarity, where the spatial covariance varies across the spatial domain. Our method utilizes robust local estimates of spatial covariances to calculate a statistic representing neighboring spatial dependency and employs Voronoi tessellations to cluster data locations for hypothesis testing. Additionally, when the assumption of stationarity is violated, we present a systematic framework for discerning nonstationary patterns. This is achieved by dividing the region into several contiguous subregions with more homogeneous and close-to-stationary properties. The optimal number of partitions is determined using the Bayesian information criterion, ensuring the accuracy and efficiency of our method. It is worth noting that our proposed method is applicable to gridded data or irregularly spaced data, making it a versatile tool for exploring a wide range of spatial datasets.
Keywords: Geostatistics; Robust testing; Spatial nonstationarity; Voronoi tessellations.
