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master's thesis
Kompleksnost skrivenih Markovljevih modela
Zagreb: University of Zagreb, Faculty of Science, 2014. urn:nbn:hr:217:519340
Rudman, Margareta
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Rudman, M. (2014). Kompleksnost skrivenih Markovljevih modela (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:519340

Rudman, Margareta. "Kompleksnost skrivenih Markovljevih modela." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:519340

Rudman, Margareta. "Kompleksnost skrivenih Markovljevih modela." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:519340

Rudman, M. (2014). 'Kompleksnost skrivenih Markovljevih modela', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:519340

Rudman M. Kompleksnost skrivenih Markovljevih modela [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2014 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:519340

M. Rudman, "Kompleksnost skrivenih Markovljevih modela", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2014. Available at: https://urn.nsk.hr/urn:nbn:hr:217:519340

Metadata
TitleKompleksnost skrivenih Markovljevih modela
AuthorMargareta Rudman
MentorPavle Goldstein (mentor)
Committee memberPavle Goldstein (predsjednik povjerenstva)
Committee memberJuraj Šiftar (član povjerenstva)
Committee memberMiljenko Marušić (član povjerenstva)
Committee memberIvica Nakić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2014-07-11, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu bavimo se statističkim modelom, skrivenim Markovljevim modelom (eng. hidden Markov model ili kraće HMM) za što nas je motivirala njegova primjena u radu s ljudskom genomom znanstvenika J. Ernsta i M. Kellisa. U radu dajemo formalnu definiciju skrivenog Markovljevog modela, dajemo primjere takvih modela te opisujemo algoritme koje koristimo, između ostalih i forward, backward te Viterbijev algoritam. Nakon toga implementiramo i analiziramo postupke za procjenu parametara (emisijske i tranzicijske vjerojatnosti) HMM-a: Baum-Welch algoritam i Viterbijevo treniranje. Baum-Welch algoritam se pokazao efikasniji na primjerima koje navodimo ali unatoč tome zaključujemo da ne radi u praksi zbog niza problema kao što su lokalni ekstemi i izbor inicijalnih parametara. Također, kriteriji za procjenu kompleksnosti modela koje smo promatrali, AIC i BIC, pokazali su se nekorisni.
Abstract (english)
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.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:519340
Study programmeTitle: Mathematical Statistics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-02-05 14:36:10