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master's thesis
Monte Carlo i Markovljevi lanci
2023. urn:nbn:hr:126:892899
Kopić, Katarina
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

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Kopić, K. (2023). Monte Carlo i Markovljevi lanci (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:892899

Kopić, Katarina. "Monte Carlo i Markovljevi lanci." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:892899

Kopić, Katarina. "Monte Carlo i Markovljevi lanci." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:892899

Kopić, K. (2023). 'Monte Carlo i Markovljevi lanci', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 24 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:892899

Kopić K. Monte Carlo i Markovljevi lanci [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2023 [cited 2024 December 24] Available at: https://urn.nsk.hr/urn:nbn:hr:126:892899

K. Kopić, "Monte Carlo i Markovljevi lanci", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:126:892899

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Metadata
TitleMonte Carlo i Markovljevi lanci
Title (english)Monte Carlo Markov Chain
AuthorKatarina Kopić
MentorNenad Šuvak (mentor)
Committee memberDanijel Grahovac (predsjednik povjerenstva)
Committee memberDomagoj Matijević (član povjerenstva)
Committee memberNenad Šuvak (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2023-03-24, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
U ovom radu obradili smo primjenu Monte Carlo metode na Markovljevim lancima. Monte Carlo Markovljevi lanci (MCMC) metoda postala je temelj mnogih modernih znanstvenih analiza. Riječ je o stohastičkoj proceduri koja više puta generira slučajne uzorke koji karakteriziraju distribuciju od interesa. Proces generiranja slučajnih uzoraka u MCMC-u uloga je Markovljevog lanca, dok je proces generiranja statistike iz tih slučajnih uzoraka uloga Monte Carlo metode. Osvrnuli smo se na algoritme koji se najčešće koriste u praksi, a radi se o Metropolis–Hastings algoritmu te Gibbsovom uzorkovanju. Na kraju rada smo promotrili primjenu MCMC metode u domeni obrade slika, a riječ je o redukciji šuma sa slike.
Abstract (english)
In this paper, we discussed the application of the Monte Carlo method on Markov chains. The Monte Carlo Markov Chain (MCMC) method has become the basis of many modern scientific analyses. It’s a stochastic procedure that repeatedly generates random samples that characterize the distribution of interest. The process of generating random samples in MCMC is the role of a Markov chain, while the process of generating statistics from these random samples is the role of the Monte Carlo method. We looked at the algorithms that are most often used in practice, namely the MetropolisHastings algorithm and Gibbs sampling. At the end of the paper, we looked at the application of the MCMC method in the domain of image processing, which is the reduction of image noise.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:892899
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 on2023-03-27 09:09:14