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master's thesis
Analiza kompleksnosti skrivenih Markovljevih modela
Zagreb: University of Zagreb, Faculty of Science, 2015. urn:nbn:hr:217:062529
Valčić, Irma
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Valčić, I. (2015). Analiza kompleksnosti skrivenih Markovljevih modela (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:062529

Valčić, Irma. "Analiza kompleksnosti skrivenih Markovljevih modela." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:062529

Valčić, Irma. "Analiza kompleksnosti skrivenih Markovljevih modela." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:062529

Valčić, I. (2015). 'Analiza kompleksnosti skrivenih Markovljevih modela', Master's thesis, University of Zagreb, Faculty of Science, accessed 09 January 2025, https://urn.nsk.hr/urn:nbn:hr:217:062529

Valčić I. Analiza kompleksnosti skrivenih Markovljevih modela [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2015 [cited 2025 January 09] Available at: https://urn.nsk.hr/urn:nbn:hr:217:062529

I. Valčić, "Analiza kompleksnosti skrivenih Markovljevih modela", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:217:062529

Metadata
TitleAnaliza kompleksnosti skrivenih Markovljevih modela
AuthorIrma Valčić
MentorPavle Goldstein (mentor)
Committee memberPavle Goldstein (predsjednik povjerenstva)
Committee memberMirko Primc (član povjerenstva)
Committee memberMiljenko Marušić (član povjerenstva)
Committee memberNela Bosner (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2015-07-13, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu analizirali smo skrivene Markovljeve modele, statistički alat koji danas nalazi sve veću primjenu u različitim područjima. Dali smo njihovu formalnu definiciju, opisali neke algoritme za rad sa skrivenim Markovljevim modelima i implementirali ih u programskom jeziku Python. Konstruirali smo i primjer povremeno nepoštene kockarnice kao osnovu za kompliciranije primjene u bioinformatici (npr. modeliranje genoma), proveli simulaciju te pokušali pronaći najbolji model koji bi opisao tako dobivene podatke. Koristili smo nekoliko statističkih metoda za odabir najboljeg modela — maksimizaciju vjerodostojnosti, omjer vjerodostojnosti, AIC i BIC — no niti jedna od tih metoda nije dala dobar rezultat. To ukazuje na kompleksnost skrivenih Markovljevih modela unatoč tome što intuitivno ne djeluju kao nešto iznimno složeno.
Abstract (english)
This thesis explores hidden Markov models, a powerful statistical tool applied in various scientific fields. We give the formal definition of a hidden Markov model, describe several algorithms traditionally used in their analysis and present their implementation in Python. We also construct an example of an occasionally dishonest casino as the basis for more complicated applications in bioinformatics (e.g. genome analysis), simulate data and attempt to find the best model for it. Several statistical methods are used — likelihood maximization, log-likelihood ratio, AIC and BIC — but none of them yield satisfactory results. This indicates the complexity of hidden Markov models even though initially they may not appear particularly difficult.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:062529
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 on2019-02-18 12:56:27