隨著人類在軟硬體上的進步，影像資料的解析度越來越高，細節越 來越豐富。在資料分析時卻也面臨變數維度大量增加隨之而來的檢定力 下降與計算複雜度大增的問題。目前主流的做法便是將資料維度降低後 再做下一步的分析。本文旨在保持資料固有的結構下對具有時空效應的 成對圖像資料進行獨立性檢定。在本文中我們提出兩階段獨立性檢定法， 分開處理高維度空間影像資料的維度縮減問題，以及處理成對低維度時 間序列之獨立性檢定。在階段一中我們將原始資料投影至主要的多分辨 率薄板樣條 (MRTS) 基底函數所展開的空間中，在保留原始資料的固有 相關結構的同時能夠有效地降低資料維度;而在階段二中我們將降維後 的資料以成對低維度時間序列之獨立性檢定加以分析與推論。我們藉由 模擬資料試驗分別在基於虛無假設成立時以及在對立假設成立時分別比 較各種獨立性檢定方法的表現，並將這些方法應用在海平面溫度與降雨 量之遙相關分析中。

With the advancements in hardware and software, the resolution of image data has been continuously increasing, leading to richer details. However, data analysis encounters challenges such as decreased statistical power and increased computational complexity due to the substantial increase in variable dimensions. The most popular approaches are to reduce the data dimensionality before conducting further analysis. This thesis aims to test independence between paired image data with spatiotemporal dependence while preserving the inherent spatial and temporal structures. A two-stage independence testing method is proposed, combining dimension reduction for high dimensional spatial image data and an independent test for paired low-dimensional time series. In the first stage, we project the original data onto a space spanned by the primary MultiResolution Thin-plate Splines (MRTS) basis functions. This projection effectively reduces the data dimensionality while preserving the inherent spatial correlation structure of the original data. In the second stage, we analyze and infer the independence of the dimension-reduced data using an independence test for paired low-dimensional time series. We compare the performance of these independence testing methods through simulation experiments under the null hypothesis and alternative hypothesis, respectively. Additionally, we apply these methods to the teleconnection analysis of sea surface temperature and rainfall datasets.

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