聚類探測是空間統計其中一個很重要的課題。隨著人們越來越關注涉及環境危害的公共衛生問題，發展用於分析地域公共衛生事件的統計方法顯得尤為迫切。在本篇論文中，我們首先會介紹兩种聚類探測的方法，分別是Kulldorff 掃描統計量與聚合式階層分群演算法。然後，我們會詳細介紹空間相關性，雖然它在Kulldorff 掃描統計量方法中沒有被考慮在內，但卻是一種反映空間數據的重要指標。接著，我們將討論Bayesian 階層結構，它是目前在擬和空間數據所普遍採用的方法，而我們選擇Poisson 對數線性條件自相關模型並進行詳細介紹。通過對比上述介紹的方法，我們總結出各種方法在空間數據的聚類探測的優勢與不足。最後，我們以2015 年臺灣南部地區爆發的登革熱數據作為本次論文的實例加以分析。

Cluster detection is one of the most important topics in spatial statistics. With increasing
public health concerns about environmental risks, the development of statistical methods for analyzing spatial health events becomes immediate. In this thesis, we first introduce two cluster detection approaches named the Kulldorff’s scan statistics and hierarchical agglomerative clustering algorithm. In addition, we illustrate spatial autocorrelation which is an important factor but overlooked in Kulldorff’s scan statistics. Moreover,
Bayesian hierarchical structure, which is a modern method to fit spatial data with spatial autocorrelation, is illustrated by using Poisson log-linear conditional-autoregressive (CAR)
model. By comparing the above methods, we summarize their advantages and drawbacks
on cluster detection for spatial data. Finally, we analyze the dengue fever outbreak over south Taiwan in 2015 as an empirical study.

[論文審定書+i]
[誌謝+ii]
[摘要+iii]
[Abstract+iv]
[1 Introduction+1]
[2 Background+2]
[2.1 Spatial Data Type+2]
[2.2 Spatial Point Process+4]
[3 Methodology+5]
[3.1 Testing the homogeneity of event rate+5]
[3.2 Kulldorff’s scan statistic+6]
[3.3 Hierarchical agglomerative clustering algorithm+10]
[3.4 Spatial autocorrelation+13]
[3.5 Bayesian modeling and cluster detection+18]
[4 Empirical Study+24]
[5 Conclusion+42]
[References+42]

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