Statistics and Computing

, Volume 26, Issue 1–2, pp 263–276 | Cite as

Comparing change-point location in independent series

  • A. Cleynen
  • S. Robin


We are interested in the comparison of the positions of the change-points in the segmentation of independent series. We consider a Bayesian framework with conjugate priors to perform exact inference on the change-point model. This work is motivated by the comparison of transcript boundaries in yeast grown under different conditions. When comparing two series, we derive the posterior credibility interval of the shift between the locations. When comparing more than two series, we compute the posterior probability for a given change-point to have the same location in all series. All calculations are made in an exact manner in a quadratic time. The performances of those approaches are assessed via a simulation study. When applied to yeast genes, this approach reveals different behavior between internal and external exon boundaries.


Segmentation Change-point comparison Credibility intervals Bayesian inference Negative binomial 



The authors deeply thank Sandrine Dudoit, Marie-Pierre Etienne, Emilie Lebarbier, Eric Parent and Gavin Sherlock for helpful conversations and comments on this work. Part of this work was supported by the ABS4NGS ANR project (ANR-11-BINF-0001-06).


  1. Armijo, L.: Minimization of functions having Lipschitz continuous first partial derivatives. Pac. J. Math. 16(1), 1–3 (1966)zbMATHMathSciNetCrossRefGoogle Scholar
  2. Bai, J., Perron, P.: Computation and analysis of multiple structural change models. J. Appl. Econ. 18, 1–22 (2003)CrossRefGoogle Scholar
  3. Dobigeon, N., Tourneret, J.-Y., Scargle, J.D.: Joint segmentation of multivariate astronomical time series: Bayesian sampling with a hierarchical model. IEEE Trans. Signal Process. 55(2), 414–423 (2007)MathSciNetCrossRefGoogle Scholar
  4. Ehsanzadeh, E., Ouarda, T.B., Saley, H.M.: A simultaneous analysis of gradual and abrupt changes in Canadian low streamflows. Hydrol. Process. 25(5), 727–739 (2011)CrossRefGoogle Scholar
  5. Feder, P.I.: The log likelihood ratio in segmented regression. Ann. Stat. 3, 84–97 (1975)zbMATHMathSciNetCrossRefGoogle Scholar
  6. Hukov, M., Kirch, C.: Bootstrapping confidence intervals for the change-point of time series. J. Time Ser. Anal. 29(6), 947–972 (2008)MathSciNetCrossRefGoogle Scholar
  7. Johnson, N., Kemp, A., Kotz, S.: Univariate Discrete Distributions. Wiley, New York (2005)zbMATHCrossRefGoogle Scholar
  8. Mandal, S.S., Chu, C., Wada, T., Handa, H., Shatkin, A.J., Reinberg, D.: Functional interactions of RNA-capping enzyme with factors that positively and negatively regulate promoter escape by RNA polymerase II. Proc. Natl. Acad. Sci. USA 101(20), 7572–7577 (2004)CrossRefGoogle Scholar
  9. Muggeo, V.M.: Estimating regression models with unknown break-points. Stat. Med. 22, 3055–3071 (2003)CrossRefGoogle Scholar
  10. Picard, F., Lebarbier, E., Hoebeke, M., Rigaill, G., Thiam, B., Robin, S.: Joint segmentation, calling, and normalization of multiple CGH profiles. Biostatistics 12(3), 413–428 (2011)CrossRefGoogle Scholar
  11. Proudfoot, N., Furger, A., Dye, M.: Integrating mRNA processing with transcription. Cell 108, 501–512 (2002)CrossRefGoogle Scholar
  12. Reeves, J., Chen, J., Wang, X.L., Lund, R., QiQi, L.: A review and comparison of change-point detection techniques for climate data. J. Appl. Meteorol. Climatol. 46(6), 900–915 (2007)CrossRefGoogle Scholar
  13. Rigaill, G., Lebarbier, E., Robin, S.: Exact posterior distributions and model selection criteria for multiple change-point detection problems. Stat. Comput. 22, 917–929 (2012)Google Scholar
  14. Risso, D., Schwartz, K., Sherlock, G., Dudoit, S.: GC-content normalization for RNA-Seq data. BMC Bioinform. 12(1), 480 (2011)CrossRefGoogle Scholar
  15. Tian, B., Hu, J., Zhang, H., Lutz, C.: A large-scale analysis of mRNA polyadenylation of human and mouse genes. Nucleic Acids Res. 33, 201–212 (2005) Google Scholar
  16. Toms, J., Lesperance, M.: Piecewise regression: a tool for identifying ecological thresholds. Ecology 84(8), 2034–2041 (2003)CrossRefGoogle Scholar
  17. Wager, T.D., Waugh, C.E., Lindquist, M., Noll, D.C., Fredrickson, B.L., Taylor, S.F.: Brain mediators of cardiovascular responses to social threat: part i: reciprocal dorsal and ventral sub-regions of the medial prefrontal cortex and heart-rate reactivity. NeuroImage 47(3), 821–835 (2009)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.AgroParisTechParisFrance
  2. 2.INRAParisFrance

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