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Testing the Order of Markov Dependence in DNA Sequences

Author

Listed:
  • M. L. Menéndez

    (Polytechnical University of Madrid)

  • L. Pardo

    (Complutense University of Madrid)

  • M. C. Pardo

    (Complutense University of Madrid)

  • K. Zografos

    (University of Ioannina)

Abstract

DNA or protein sequences are usually modeled as probabilistic phenomena. The simplest model is created on the assumption that the nucleotides at the various sites are independently distributed. Usually the type of nucleotide at some site depends on the type at another site and therefore the DNA sequence is modeled as a Markov chain of random variables taking on the values A, G, C and T corresponding to the four nucleotides. First order or higher order Markov models provide better fit to a DNA sequence. Based on this remark, the aim of this paper is to present and study a family of test statistics for testing order Markov dependence in DNA sequences. This new family includes as a particular case the classical likelihood ratio test. A simulation study is presented in order to find test statistics, in this family, with a better behaviour than the likelihood ratio test.

Suggested Citation

  • M. L. Menéndez & L. Pardo & M. C. Pardo & K. Zografos, 2011. "Testing the Order of Markov Dependence in DNA Sequences," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 59-74, March.
    • Handle: RePEc:spr:metcap:v:13:y:2011:i:1:d:10.1007_s11009-008-9107-1
    DOI: 10.1007/s11009-008-9107-1
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    References listed on IDEAS

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    1. P. J. Avery & D. A. Henderson, 1999. "Fitting Markov chain models to discrete state series such as DNA sequences," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(1), pages 53-61.
    2. L. Pardo & D. Morales & M. Salicrú & M. Menéndez, 1993. "Theϕ-divergence statistic in bivariate multinomial populations including stratification," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 223-235, December.
    3. Menendez, M.L. & Pardo, J.A. & Pardo, L. & Zografos, K., 2006. "On tests of independence based on minimum [phi]-divergence estimator with constraints: An application to modeling DNA," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1100-1118, November.
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    Citations

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    Cited by:

    1. Papapetrou, M. & Kugiumtzis, D., 2013. "Markov chain order estimation with conditional mutual information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(7), pages 1593-1601.
    2. Papapetrou, M. & Kugiumtzis, D., 2020. "Tsallis conditional mutual information in investigating long range correlation in symbol sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    3. Andreas C. Georgiou & Alexandra Papadopoulou & Pavlos Kolias & Haris Palikrousis & Evanthia Farmakioti, 2021. "On State Occupancies, First Passage Times and Duration in Non-Homogeneous Semi-Markov Chains," Mathematics, MDPI, vol. 9(15), pages 1-17, July.

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