基於 Copula 下的馬可夫鏈模型對於卜瓦松序列 數據之線上變化點偵測

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姓名

張哲豪(Che-Hau Chang) 查詢紙本館藏

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統計研究所

論文名稱

基於 Copula 下的馬可夫鏈模型對於卜瓦松序列數據之線上變化點偵測
(Online Bayesian Changepoint Estimation via the Copula-based Markov Chain Model for Poisson Time Series)

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至系統瀏覽論文 (2024-9-2以後開放)

摘要(中)

識別序列數據中的變化，稱為改變點偵測，已成為各個領域越來越重要的話
題。改變點偵測法可以分為即時和線下，我們主要針對即時改變點的方法做研究與推廣，稱之為 EXact Online Bayesian Changepoint Detection (EXO)，已經對於真實資料顯示出合理的結果。其中，對於資料型態，EXO 假設資料點間是相互獨立的，在真實資料中，資料間其實是有一定的相關性的，對於這種有相關性的資料，我們使用 Clayton copula 之下的馬可夫鏈模型，邊際分配的部分我們使用卜瓦松去描述這種間斷型的資料。從模擬得知在強相關性的情況下，這個模型有較好的準確性。並在實證資料中這個模型與 EXO 方法得到相同的結果。

摘要(英)

Detecting the structure change in sequential data, known as changepoint detection,has become increasingly important in various fields. As the changepoint detection method
can be categorized by online and offline, this research focuses on the online way called EXact Online Bayesian Changepoint Detection (EXO). However, EXO assumes that the
datapoints are independent of each other, but this may be unrealistic. For real data, there is a certain relation between the datapoints. Therefore we consider the Markov chain model under the Clayton copula with the Poisson distribution as the marginal distribution to describe the data with the dependence structure and illustrate the performance in simulation studies. The data analysis comes from empirical studies.

關鍵字(中)

★ 改變點
★ Clayton copula
★ 馬可夫鏈模型
★ 貝式推論
★ 卜瓦松分配

關鍵字(英)

★ changepoint
★ Clayton copula
★ Markov model
★ Bayesian Inference
★ Poisson distribution

論文目次

Contents
1 Introduction 1
2 Proposed Model and the Methodology 3
2.1 Copula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Poisson Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Bayesian Online Changepoint Detection . . . . . . . . . . . . . . . . . . . 5
2.4 Bayesian Online Changepoint Detection with the Clayton Copula . . . . . . 9
3 Simulation Study 13
3.1 Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4 Empirical Study 19
5 Conclusion 21
5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

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指導教授

孫立憲(Li-Hsien Sun)

審核日期

2022-8-20

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