Multiple Change Points and Alternating Segments in Binary Trials with Dependence

  • Joachim Krauth
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


In Krauth (2003) we derived modified maximum likelihood estimates to identify change points and changed segments in Bernoulli trials with dependence. Here, we extend these results to the situation of multiple change points in an alternating-segments model (Halpern (2000)) and to a more general multiple change-points model. Both situations are of interest, e.g., in molecular biology when analyzing DNA sequences.


Change Point Binary Sequence Markov Chain Model Bernoulli Trial Mersenne Twister 
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  1. AVERY, P.J. and HENDERSON, D.A. (1999): Fitting Markov chain models to discrete state series such as DNA sequences. Applied Statistics, 48, 53–61.MathSciNetGoogle Scholar
  2. BEDRICK, E.J. and ARAGON, J. (1989): Approximate confidence intervals for the parameters of a stationary binary Markov chain. Technometrics, 31, 437–448.MathSciNetCrossRefGoogle Scholar
  3. BILLINGSLEY, P. (1961): Statistical inference for Markov processes. The University of Chicago Press, Chicago, London.Google Scholar
  4. BRAUN, J.V. and MÜLLER, H.G. (1998): Statistical methods for DNA sequence segmentation. Statistical Science, 13, 142–162.CrossRefGoogle Scholar
  5. BUDESCU, D.V. (1985): Analysis of dichotomous variables in the presence of serial dependence. Psychological Bulletin, 97, 547–561.CrossRefGoogle Scholar
  6. CHURCHILL, G.A. (1989): Stochastic models for heterogeneous DNA sequences. Bulletin of Mathematical Biology, 51, 79–94.MATHMathSciNetCrossRefGoogle Scholar
  7. CROW, E.L. (1979): Approximate confidence intervals for a proportion from Markov dependent trials. Communications in Statistics-Simulation and Computation, B8, 1–24.MATHGoogle Scholar
  8. DEVORE, J.L. (1976): A note on the estimation of parameters in a Bernoulli model with dependence. Annals of Statistics, 4, 990–992.MATHMathSciNetGoogle Scholar
  9. FU, Y.X. and CURNOW, R.N. (1990): Maximum likelihood estimation of multiple change points. Biometrika, 77, 563–573.MathSciNetCrossRefGoogle Scholar
  10. HALPERN, A.L. (1999): Minimally selected p and other tests for a single abrupt changepoint in a binary sequence. Biometrics, 55, 1044–1050.MATHCrossRefGoogle Scholar
  11. HALPERN, A.L. (2000): Multiple-changepoint testing for an alternating segments model of a binary sequence. Biometrics, 56, 903–908.MATHCrossRefGoogle Scholar
  12. HAWKINS, D.M. (2001): Fitting multiple change-point models to data. Computational Statistics & Data Analysis, 37, 323–341.MATHMathSciNetCrossRefGoogle Scholar
  13. JOHNSON, C.A. and KLOTZ, J.H. (1974): The atom probe and Markov chain statistics of clustering. Technometrics, 16, 483–493.MathSciNetCrossRefGoogle Scholar
  14. KIM, S. and BAI, D.S. (1980): On parameter estimation in Bernoulli trials with dependence. Communications in Statistics-Theory and Methods, A9, 1401–1410.MathSciNetGoogle Scholar
  15. KLOTZ, J. (1973): Statistical inference in Bernoulli trials with dependence. Annals of Statistics, 1, 373–379.MATHMathSciNetGoogle Scholar
  16. KRAUTH, J. (1999): Discrete scan statistics for detecting change-points in binomial sequences. In: W. Gaul and H. Locarek-Junge (Eds.): Classification in the Information Age. Springer, Heidelberg, 196–204.Google Scholar
  17. KRAUTH, J. (2000): Detecting change-points in aircraft noise effects. In: R. Decker and W. Gaul (Eds.): Classification and Information Processing at the Turn of the Millenium. Springer, Heidelberg, 386–395.Google Scholar
  18. KRAUTH, J. (2003): Change-points in Bernoulli trials with dependence. In: W. Gaul and M. Schader (Eds.): Between Data Science and Everyday Web Practice. Springer, Heidelberg.Google Scholar
  19. LINDQVIST, B. (1978): A note on Bernoulli trials with dependence. Scandinavian Journal of Statistics, 5, 205–208.MATHMathSciNetGoogle Scholar
  20. LIU, J.S., NEUWALD, A.F., and LAWRENCE, C.E. (1999): Markovian structures in biological sequence alignments. Journal of the American Statistical Association, 94, 1–15.CrossRefGoogle Scholar
  21. MATSUMOTO, M. and NISHIMURA, T. (1998): Mersenne twister: A 623-dimensionally equidistributed uniform peudorandom number generator. ACM Transactions on Modeling and Computer Simulation, 8, 3–30.CrossRefGoogle Scholar
  22. MOORE, M. (1979): Alternatives aux estimateurs à vraisemblance maximale dans un modèle de Bernoulli avec dépendance. Annales des Sciences Mathématiques du Québec, 3, 119–133.MATHGoogle Scholar
  23. PRICE, B. (1976): A note on estimation in Bernoulli trials with dependence. Communications in Statistics-Theory and Methods, A5, 661–671.MATHGoogle Scholar
  24. ROBB, L., MIFSUD, L., HARTLEY, L., BIBEN, C, COPELAND, N.G., GILBERT, D.J., JENKINS, N.A., and HARVEY, R.P. (1998): epicardin: A novel basic helix-loop-helix transcription factor gene expressed in epicardium, branchial arch myoblasts, and mesenchyme of developing lung, gut, kidney, and gonads. Developmental Dynamics, 213, 105–113.CrossRefGoogle Scholar
  25. VENTER, J.H. and STEEL, S.J. (1996): Finding multiple abrupt change points. Computational Statistics & Data Analysis, 22, 481–504.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 2005

Authors and Affiliations

  • Joachim Krauth
    • 1
  1. 1.Department of PsychologyUniversity of DüsseldorfDüsseldorfGermany

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