Very long and noisy sequence data arise from biological sciences to social science including high throughput data in genomics and stock prices in econometrics. Often such data are collected in order to identify and understand shifts in trends, for example, from a bull market to a bear market in finance or from a normal number of chromosome copies to an excessive number of chromosome copies in genetics. Thus, identifying multiple change points in a long, possibly very long, sequence is an important problem. In this article, we review both classical and new multiple change-point detection strategies. Considering the long history and the extensive literature on the change-point detection, we provide an in-depth discussion on a normal mean change-point model from aspects of regression analysis, hypothesis testing, consistency and inference. In particular, we present a strategy to gather and aggregate local information for change-point detection that has become the cornerstone of several emerging methods because of its attractiveness in both computational and theoretical properties.

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DNA copy number change is an important form of structural variation in human genome. Somatic copy number alterations (CNAs) can cause over expression of oncogenes and loss of tumor suppressor genes in tumorigenesis. Recent development of SNP array technology has facilitated studies on copy number changes at a genome-wide scale, with high resolution. Quantitative analysis of somatic CNAs on genes has found broad applications in cancer research. Most tumors exhibit genomic instability at chromosome scale as a result of dynamically accumulated genomic mutations during the course of tumor progression. Such higher level cancer genomic characteristics cannot be effectively captured by the analysis of individual genes. We introduced two definitions of chromosome instability (CIN) index to mathematically and quantitatively characterize genome-wide genomic instability. The proposed CIN indices are derived from detected CNAs using circular binary segmentation and wavelet transform, which calculates a score based on both the amplitude and frequency of the copy number changes. We generated CIN indices on ovarian cancer subtypes' copy number data and used them as features to train a SVM classifier. The experimental results show promising and high classification accuracy estimated through cross-validations. Additional survival analysis is constructed on the extracted CIN scores from TCGA ovarian cancer dataset and showed considerable correlation between CIN scores and various events and severity in ovarian cancer development. Currently our methods have been integrated into G-DOC. We expect these newly defined CINs to be predictors in tumors subtype diagnosis and to be a useful tool in cancer research. / Master of Science

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This thesis aims to give a comprehensive account of some of the most recent methods of a change point estimation. The literature on the change point estimation shows a variety of approaches to deal with this subject. Among them, tests based on the popular CUSUM process, likelihood ratio tests, wild binary segmentation and some of the most recent techniques on the change point estimation in panel data are all covered by this paper. The case of dependent panels is discussed as well. The practical part of the study is focused on application of the wild binary segmentation method on weekly log-returns of the Dow Jones stock index. Firstly, we fit a GARCH model to the analysed time series. We next use the wild binary segmenatation method to detect structural changes in the mean of the original time series. Next, we apply the same method to the residuals from the GARCH fit. We analyse several penalization criteria proposed by previous studies and evaluate their effects on the estimated number and locations of the change points in the given data set. 1