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Modèle d'évolution avec dépendance au contexte et Corrections de statistiques d'adéquation en présence de zéros aléatoires

Abstract : In this thesis we study the context-dependent evolution of DNA sequences. In the first part we define a simple substitution model that not only distinguishes between transitions and transversions, but also allows for left-neighbor dependencies such as the CpG effect. We show that this model can be formulated as a hidden Markov model and we use the Baum-Welch algorithm to perform the parameter estimation. The model is then applied to estimate real substitution rates. In the second part we develop corrections for classical goodness of fit test statistics with composite hypotheses for multinomial data in the presence of random zeros. Indeed, independence tests on the evolution of triplets of neighbor nucleotides involve contingency tables with numerous empty cells, and can be written as goodness of fit tests on sparse vectors. Thus, Pearson's and Kullback's statistics cannot be used. From these, we derive corrected statistics that share the same asymptotic behavior and apply these corrections to test independence on the evolution of nucleotide sequences. Finally, we propose applications to epidemiological and ecological data.
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https://tel.archives-ouvertes.fr/tel-00490844
Contributor : Audrey Finkler <>
Submitted on : Wednesday, June 9, 2010 - 5:35:54 PM
Last modification on : Friday, June 19, 2020 - 9:22:04 AM
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Audrey Finkler. Modèle d'évolution avec dépendance au contexte et Corrections de statistiques d'adéquation en présence de zéros aléatoires. Mathématiques [math]. Université de Strasbourg, 2010. Français. ⟨NNT : 2010STRA6041⟩. ⟨tel-00490844⟩

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