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master's thesis
Skriveni Markovljevi lanci
2020. urn:nbn:hr:126:053896
Stjepanović, Sanja
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Probability and Mathematical Statistics Research Group

Cite this document

Stjepanović, S. (2020). Skriveni Markovljevi lanci (Master's thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:053896

Stjepanović, Sanja. "Skriveni Markovljevi lanci." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:053896

Stjepanović, Sanja. "Skriveni Markovljevi lanci." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:053896

Stjepanović, S. (2020). 'Skriveni Markovljevi lanci', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 24 January 2023, https://urn.nsk.hr/urn:nbn:hr:126:053896

Stjepanović S. Skriveni Markovljevi lanci [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2020 [cited 2023 January 24] Available at: https://urn.nsk.hr/urn:nbn:hr:126:053896

S. Stjepanović, "Skriveni Markovljevi lanci", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:126:053896

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Metadata
TitleSkriveni Markovljevi lanci
Title (english)Hidden Markov Chains
AuthorSanja Stjepanović
MentorNenad Šuvak (mentor)
Committee memberMirta Benšić (predsjednik povjerenstva)
Committee memberNenad Šuvak (član povjerenstva)
Committee memberSuzana Miodragović (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics)
(Probability and Mathematical Statistics Research Group)
Osijek
Defense date and country2020-10-09, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Applied Mathematics and Mathematical Modeling
Abstract
Skriveni Markovljevi lanci su poznati alat za matematičko modeliranje problema koji mogu biti karakterizirani pomoću jednog nama skrivenog proces \(x_{n},n\in \mathbb{N}_{0}\) koji emitira drugi nama vidljiv opservacijski proces \(y_{n},n\in \mathbb{N}_{0}\). Ovakvi modeli su pronašli primjenu u raznovrsnim područjima znanosti poput bioinformatike, komunikacijske tehnologije te financijske matematike, a neke primjere smo naveli u samom radu. Skriveni Markovljev model je sasvim određen poznavanjem njegovih matrica prijelaznih i emitiranih vjerojatnosti Π i Φ te početne distribucije skrivenog lanca λ. Sama funkcionalnosti skrivenih Markovljevih modela se zasniva na tri osnovna problema, a pod uvjetom poznavanja parametara modela možemo riješiti problem izglađivanja pomoću Forward-Backward algoritma i problem dekodiranja pomoću Viterbi algoritma, koja su oba navedena u radu i ilustrirana na primjerima. U slučaju potrebe procjene samih parametara modela, što je poznato pod nazivom problem treniranja, koristimo se Baum-Welch algoritmom, koji je također pojašnjen u radu.
Abstract (english)
Hidden Markov chains are a powerful tool for mathematical modeling of problems that can be characterized by one hidden process \(x_{n},n\in \mathbb{N}_{0}\) which emits another visible observational process \( y_{n},n\in \mathbb{N}_{0}\) . Such models have found its application in various scientific fields such as bioinformatics, communication technology and financial mathematics, and we have given some examples in the paper itself. The hidden Markov model is completely determined by knowing its matrices of transition and emission probabilities Π and Φ and the initial distribution of the hidden chain λ. The functionality of hidden Markov models is based on three basic problems, and provided we know the parameters of the model we can solve the smoothing problem using the Forward-Backward algorithm and the decoding problem by using the Viterbi algorithm, both of which are listed in the paper and illustrated on examples. In case we need to estimate the parameters of the model themselves, which is known as the training problem, we use the Baum-Welch algorithm, which is also explained in the paper.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:053896
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
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 on2020-10-23 06:10:45