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Drifting Markov Models with Polynomial Drift and Applications to DNA Sequences

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  • Vergne Nicolas

    (University of Evry)

Abstract

In this article, we introduce the drifting Markov models (DMMs) which are inhomogeneous Markov models designed for modeling the heterogeneities of sequences (in our case DNA or protein sequences) in a more flexible way than homogeneous Markov chains or even hidden Markov models (HMMs). We focus here on the polynomial drift: the transition matrix varies in a polynomial way. To show the reliability of our models on DNA, we exhibit high similarities between the probability distributions of nucleotides obtained by our models and the frequencies of these nucleotides computed by using a sliding window. In a further step, these DMMs can be used as the states of an HMM: on each of its segments, the observed process can be modeled by a drifting Markov model. Search of rare words in DNA sequences remains possible with DMMs and according to the fits provided, DMMs turn out to be a powerful tool for this purpose. The software is available on request from the author. It will soon be integrated on seq++ library (http://stat.genopole.cnrs.fr/seqpp/).

Suggested Citation

  • Vergne Nicolas, 2008. "Drifting Markov Models with Polynomial Drift and Applications to DNA Sequences," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 7(1), pages 1-45, February.
    • Handle: RePEc:bpj:sagmbi:v:7:y:2008:i:1:n:6
    DOI: 10.2202/1544-6115.1326
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    Citations

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    Cited by:

    1. Sébastien Massoni & Madalina Olteanu & Patrick Rousset, 2010. "Career-path analysis using drifting Markov models (DMM) and self-organizing maps," Post-Print hal-00443530, HAL.
    2. Singer Meromit & Engström Alexander & Schönhuth Alexander & Pachter Lior, 2011. "Determining Coding CpG Islands by Identifying Regions Significant for Pattern Statistics on Markov Chains," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-27, September.
    3. G. Nuel, 2019. "Moments of the Count of a Regular Expression in a Heterogeneous Random Sequence," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 875-887, September.
    4. Yousif Alyousifi & Kamarulzaman Ibrahim & Mahmod Othamn & Wan Zawiah Wan Zin & Nicolas Vergne & Abdullah Al-Yaari, 2022. "Bayesian Information Criterion for Fitting the Optimum Order of Markov Chain Models: Methodology and Application to Air Pollution Data," Mathematics, MDPI, vol. 10(13), pages 1-16, June.
    5. Vlad Stefan Barbu & Nicolas Vergne, 2019. "Reliability and Survival Analysis for Drifting Markov Models: Modeling and Estimation," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1407-1429, December.

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