Dependence Structure Analysis of Categorical Variables With Applications in Genetics

The dissertation considers some problems in the statistical analysis of categoricalvariables – the dependence structure between categorical variablesand the problems of selecting and assessing the models for this structure. Theaim of this dissertation is to propose the method to estimate dependence structurebetween multivariate categorical variables in case of sparse frequency tablesand to apply the proposed method in the statistical analysis of geneticsequences.The thesis layout consists of introduction chapter, three main chapters,conclusions, list of authors’s publications and bibliography chapter.The introduction reveals the investigated problem, importance of the thesisand the object of research and describes the purpose and tasks of the dissertation,research methodology, scientific novelty, the practical significance anddefended statements. The introduction end in presenting the author’s publicationson the subject of the defended dissertation.In the first chapter of the dissertation various models available for describingthe nature of the association between categorical variables are introducedand their link with Markov field theory and Gibbs distribution.In the second chapter the basic notions of DNA sequences and a specialstructure of genetic data is introduced. The logit models and Markov field theoryare applied to assess the dependence structure (interactions) between DNAnucleotides and to test hypothesis about Markov order of these dependencies... [to full text]