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Statistica Sinica 22 (2012), 1507-1538




Nancy R. Zhang and David O. Siegmund

Stanford University

Abstract: Change-point models have been widely applied for segmentation of spatial or time-series data. Some recent applications in genomics motivate multi-sequence change-point models for shared changes across multiple aligned sequences. These applications frequently involve data where the number of change-points can be large. In a previous paper we derived a Bayes Information Criterion (BIC) for determining the number of changes in the mean of a sequence of independent normal observations when the number of change-points $m$ is assumed to remain bounded as the number of observations increases. Here we extend that result to the case where $m$ can increase with the sample size and to simultaneous change-points in multiple sequences. Stochastic terms that enter into the new criteria involve integrals and maxima of two-sided random walks with negative drift. The new criteria are applied to the analysis of DNA copy number data.

Key words and phrases: Change-point detection, DNA copy number, segmentation, model selection.

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