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  • Μικρογραφία εικόνας
    Τεκμήριο
    Modelling count data using independent mixture and Hidden Markov models
    (2017-12-21) Papoulias, Ioannis; Athens University of Economics and Business. Department of Statistics; Besbeas, P.
    The most common distribution for modeling unbounded count data is the Poisson distribution as applications of the Poisson distribution are widely spread in the literature. However, in many real-world scenarios the sample variance is greater than the sample mean and the observation are dependent.In this thesis, I address these problems by proposing at first modeling count data using Negative Binomial distribution. Secondly, by using independent mixture models with Poisson and Negative Binomial distribution.Lastly, by using Poisson and Negative Binomial Hidden Markov Models. Hidden Markov models (HMMs) are a popular approach for modeling sequential data, typically based on the assumption of a first or higher-order Markov chain. I devise efficient training and inference algorithms for my models and I demonstrate the efficacy and usefulness of my approach for strong dependent count data.