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**1 - 6**of**6**### doi:http://dx.doi.org/10.5705/ss.2012.018s MULTIPLE CHANGE-POINT DETECTION VIA A SCREENING AND RANKING ALGORITHM

"... Abstract: Let Y1; : : : ; Yn be a sequence whose underlying mean is a step function with an unknown number of the steps and unknown change points. The detection of the change points, namely the positions where the mean changes, is an important problem in such fields as engineering, economics, climat ..."

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Abstract: Let Y1; : : : ; Yn be a sequence whose underlying mean is a step function with an unknown number of the steps and unknown change points. The detection of the change points, namely the positions where the mean changes, is an important problem in such fields as engineering, economics, climatology and bioscience. This problem has attracted a lot of attention in statistics, and a variety of solutions have been proposed and implemented. However, there is scant literature on the theoretical properties of those algorithms. Here, we investigate a recently developed algorithm called the Screening and Ranking algorithm (SaRa). We characterize the theoretical properties of SaRa and show its superiority over other commonly used algorithms. In particular, we develop a false discovery rate approach to the multiple change-point problem and show a strong sure coverage property for the SaRa. Key words and phrases: Change-point detection, copy number variation, false dis-covery rate, high dimensional data, screening and ranking algorithm. 1.

### C © 2013 Biometrika Trust Printed in Great Britain

"... Highlights, trends and influences are identified associated with the pages of Biometrika subsequent to the editorship of Karl Pearson. Some key words: Biometrika; General statistical methodology; History of statistics. 1. ..."

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Highlights, trends and influences are identified associated with the pages of Biometrika subsequent to the editorship of Karl Pearson. Some key words: Biometrika; General statistical methodology; History of statistics. 1.

### dashes show the 100 largest z[i] values Frequency

, 1000

"... • Observe zi ∼ N(µi, 1) for i = 1, 2,..., N • Select the m biggest ones: z(1)> z(2)> z(3)> · · ·> z(m) • Question: µ values? What can we say about their corresponding • Selection Bias selected z’s. The µ’s will usually be smaller than the ..."

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• Observe zi ∼ N(µi, 1) for i = 1, 2,..., N • Select the m biggest ones: z(1)> z(2)> z(3)> · · ·> z(m) • Question: µ values? What can we say about their corresponding • Selection Bias selected z’s. The µ’s will usually be smaller than the

### • Marginal Density

, 1000

"... • Observe zi ∼ N(µi, 1) for i = 1, 2,..., N • Select the m biggest ones: z(1)> z(2)> z(3)> · · ·> z(m) • Question: µ values? What can we say about their corresponding • Selection Bias selected z’s. The µ’s will usually be smaller than the ..."

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(Show Context)
• Observe zi ∼ N(µi, 1) for i = 1, 2,..., N • Select the m biggest ones: z(1)> z(2)> z(3)> · · ·> z(m) • Question: µ values? What can we say about their corresponding • Selection Bias selected z’s. The µ’s will usually be smaller than the

### Reconstructing DNA Copy Number by Joint Segmentation of Multiple Sequences

, 2012

"... Variations in DNA copy number carries information on the modalities of genome evolution and misregulation of DNA replication in cancer cells; their study can be helpful to localize tumor suppressor genes, distinguish different populations of cancerous cell, as well identify genomic variations respon ..."

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Variations in DNA copy number carries information on the modalities of genome evolution and misregulation of DNA replication in cancer cells; their study can be helpful to localize tumor suppressor genes, distinguish different populations of cancerous cell, as well identify genomic variations responsible for disease phenotypes. A number of different high throughput technologies can be used to identify copy number variable sites, and the literature documents multiple effective algorithms. We focus here on the specific problem of detecting regions where variation in copy number is relatively common in the sample at hand: this encompasses the cases of copy number polymorphisms, related samples, technical replicates, and cancerous sub-populations from the same individual. We present an algorithm based on regularization approaches with significant computational advantages and competitive accuracy. We illustrate its applicability with simulated and real data sets. 1 ar