- 學位論文
以加權法則偵測時空資料平均值偏移
Detecting mean shifts in spatiotemporal data using weighted rules
摘要
本研究探討時空資料的監控問題，發展時空統計量技術以偵測時空上的資料是否有平均值偏移現象，在過去的時空偵測程序主要以概似比檢定為基礎，使用累和管制圖作為概念，累積資料在時間及空間上的變異。然而概似比檢定需要偏移相關參數為已知或可良好估計，但在實際問題中，偏移的區域範圍、幅度、時間點等，往往為未知參數。因此本論文發展以指數加權移動平均值管制圖為基礎的時空統計方法，透過整合空間資料及對時間軸加權，有效偵測異常時空型態資料。離偵測時間點越近的資料，將賦予較高之權重；而對時空型態資料作空間軸加權時，距離監控中心越近的資料，將賦予較高之權重。在此概念下發展出六種不同的加權手法，檢測手法無需預知偏移相關參數，僅需對觀察值進行不同方式的加權，便達到有效偵測異常時空資料的目標。本研究並模擬分析六種加權模型對不同異常模式的偵測效果，以輔助決策者制定改善政策或探究發生異常之原因。文末以新墨西哥(New Mexico)州男性罹患甲狀腺癌之發病情形為例，說明本論文兩種模型於實際案例上之運用。
並列摘要
This research investigates the problem of spatiotemporal surveillance and develops statistical techniques to detect the existence of mean shifts in spatiotemporal data. Previous spatiotemporal test procedures focus on likelihood-ratio based methods. The concept of Cumulative Sum (CUSUM) control chart is also applied to cumulate data variation over time and space. However, likelihood-ratio based tests require known or well estimated parameters including shift coverage, magnitude, and change time which are often unavailable in practice. Therefore, this research develops the spatiotemporal analysis methods based on Exponentially Weighted Moving Average (EWMA) control chart. By integrating spatial data and weighting temporal data over time, the proposed methods can effectively detect mean shifts. The data closer to the current time point and to the investigated shift center receives a higher weight. Six models are constructed under such weighting rules. The proposed methods do not require the information about mean shifts but can effectively detect abnormal spatiotemporal data by directly weighting observations. This research simulates different shift patterns and compares the sensitivity of the six models. The results may help decision makers with setting up policies for improvement or exploring contributing factors. Last, an implementation of male thyroid cancer in New Mexico is carried out to demonstrate the practicability of the proposed methods.