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master's thesis
Monte Carlo Markovljevi lanci
2020. urn:nbn:hr:126:112000
Bradvica, Marija Kristina
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Probability, Mathematical Statistics and Data Science Research Group

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Bradvica, M. K. (2020). Monte Carlo Markovljevi lanci (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:112000

Bradvica, Marija Kristina. "Monte Carlo Markovljevi lanci." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:112000

Bradvica, Marija Kristina. "Monte Carlo Markovljevi lanci." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:112000

Bradvica, M. K. (2020). 'Monte Carlo Markovljevi lanci', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:112000

Bradvica MK. Monte Carlo Markovljevi lanci [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2020 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:126:112000

M. K. Bradvica, "Monte Carlo 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:126:112000

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Metadata
TitleMonte Carlo Markovljevi lanci
Title (english)Monte Carlo Markov Chains
AuthorMarija Kristina Bradvica
MentorNenad Šuvak (mentor)
Committee memberDragana Jankov Maširević (predsjednik povjerenstva)
Committee memberNenad Šuvak (član povjerenstva)
Committee memberDanijel Grahovac (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics and Mathematics Teaching)
(Probability, Mathematical Statistics and Data Science Research Group)
Osijek
Defense date and country2020-12-18, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
Monte Carlo simulacije naziv su za numeričku metodu rješavanja matematičkih problema na način da se generira velik broj realizacija slučajnih varijabli. Primjenu su pronašle u problemima koji se mogu svesti na aproksimiranje integrala. Metoda Monte Carlo Markovljevih lanca postupak je kojim se simuliraju uzorci iz zadane distribucije. Pri tome se konstruira ergodski Markovljev lanac tako što se u svakoj iteraciji MCMC algoritma odabire neki parametar i ukoliko je on "bolji" od prethodnog dodaje se u lanac. U ovome radu predstavljena je klasa Metropolis-Hastings algoritama te su pobliže opisani i oprimjereni nezavisni Metropolis-Hastings algoritam i Metropolis-Hastings algoritam sa slučajnom šetnjom. Na kraju rada dana je primjena MCMC algoritama na problem dešifriranja poruke šifrirane supstitucijskom šifrom.
Abstract (english)
Monte Carlo simulations are numerical methods for solving mathematical problems in a way that generates a large number of realization random variables. They have found application in problems that can be reduced to approximating integrals. Monte Carlo Markov chains method is a procedure that simulates samples from default distribution. In doing so, an ergodic Markov chain is constructed by selecting a parameter in each iteration of the MCMC algorithm and adding it to the chain if it is "better" than the previous one. In this paper, a class of Metropolis-Hastings algorithms is presented and the independent Metropolis-Hastings algorithm and the Metropolis-Hastings algorithm with random walk are described and exemplied in more detail. At the end of the paper, the application of MCMC algorithms to the problem of decrypting a message encrypted with a substitution code is given.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:112000
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 on2020-12-21 10:22:52