Abstract
In applications, such as biological ones, the segmentation of very long binary sequences is necessary. For example, such problems arise in DNA analysis. Some properties of a DNA sequence can be coded as a binary sequence and it should be separated into the homogeneous increments. In this paper, we propose a new approach for the segmentation of long binary sequences. Our approach is based on a transformation of an initial sequence into a sequence of real numbers. We will call such sequence a diagnostic sequence. After that, in the case of sequences generated by the stochastic mechanisms, we propose to apply the nonparametric change-point detection algorithm of Brodsky-Darkhovsky to the diagnostic sequence. If we don’t know the type of generating mechanism of the sequence, we propose to utilize our theory of \(\varepsilon \)-complexity to create new diagnostic sequences of \(\varepsilon \)-complexity coefficients. Subsequently, the change-point detection algorithm of Brodsky-Darkhovsky is applied to these diagnostic sequences. We verify the performance of the proposed methods on simulations.
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Acknowledgements
Boris Darkhovsky gratefully acknowledges the partial support of this study by the Russian Foundation for Basic Research (project no. 17-29-02115). We would like to thank the anonymous reviewers for their suggestions and comments.
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Darkhovsky, B., Piryatinska, A. (2019). Detection of Changes in Binary Sequences. In: Steland, A., Rafajłowicz, E., Okhrin, O. (eds) Stochastic Models, Statistics and Their Applications. SMSA 2019. Springer Proceedings in Mathematics & Statistics, vol 294. Springer, Cham. https://doi.org/10.1007/978-3-030-28665-1_12
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DOI: https://doi.org/10.1007/978-3-030-28665-1_12
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