Kompleksnost skrivenih Markovljevih modela

Rudman, Margareta (2014) Kompleksnost skrivenih Markovljevih modela. Diploma thesis, Faculty of Science > Department of Mathematics.

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This thesis is concerned with a statistical model called hidden Markov model (HMM). We were led to this topic by the paper by J. Ernst and M. Kellis where they apply HMMs to the study of human genome. We give a formal definition of the HMM, give examples of such models and describe algorithms that are used, among others, the forward, the backward and the Viterbi algorithm. Furthermore, we implement and analyze methods for parameter estimation (emission and transition probabilities) for HMMs: the Baum-Welch algorithm and Viterbi training. The Baum-Welch algorithm turned out to be more effective than Viterbi training when tested on simulated examples that we present. However, the Baum.Welch algorithm does not work in practice because of the issues like the local maxima and the choice of the initial parameters. Finally, we apply information criteria AIC and BIC to study complexity of our models.

Item Type: Thesis (Diploma thesis)
Supervisor: Goldstein, Pavle
Date: 2014
Number of Pages: 22
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 08 Jul 2015 09:23
Last Modified: 08 Jul 2015 09:23
URI: http://digre.pmf.unizg.hr/id/eprint/4101

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