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master's thesis
Bayesovsko statističko zaključivanje
2019. urn:nbn:hr:126:122053
Nuić, Antonio
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Probability and Mathematical Statistics Research Group

Cite this document

Nuić, A. (2019). Bayesovsko statističko zaključivanje (Master's thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:122053

Nuić, Antonio. "Bayesovsko statističko zaključivanje." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:122053

Nuić, Antonio. "Bayesovsko statističko zaključivanje." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:122053

Nuić, A. (2019). 'Bayesovsko statističko zaključivanje', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 14 January 2021, https://urn.nsk.hr/urn:nbn:hr:126:122053

Nuić A. Bayesovsko statističko zaključivanje [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2019 [cited 2021 January 14] Available at: https://urn.nsk.hr/urn:nbn:hr:126:122053

A. Nuić, "Bayesovsko statističko zaključivanje", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:126:122053

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Metadata
TitleBayesovsko statističko zaključivanje
Title (english)Bayesian Statistical Inference
AuthorAntonio Nuić
MentorMirta Benšić (mentor)
Committee memberNenad Šuvak (predsjednik povjerenstva)
Committee memberMirta Benšić (član povjerenstva)
Committee memberDanijel Grahovac (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 country2019-04-19, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
Tema rada je bayesovsko statističko zaključivanje. Nakon definicije osnovnih pojmova iz vjerojatnosti objašnjene su razlike u Bayesovskom pristupu u odnosu na klasični pristup statističkom zaključivanju. Objašnjeni su pojmovi apriorne i aposteriorne distribucije i diskutirana je važnost funkcije vjerodostojnosti i Bayesove formule. Potom je navedeno nekoliko različitih pristupa izboru apriorne distribucije i dana je teorija koja se tiče procjene parametra, testiranja hipoteza i procjene pouzdanih intervala. Dodatno, nakon primjedbe da se pri zaključivanju o aposteriornoj distribuciji pojavljuju integrali koje je teško ili nemoguće egzaktno izračunati (primjerice, pri računanju očekivanja ili varijance aposteriorne distribucije dan je Metropolis-Hastings algoritam za simulaciju realizacija iz aposteriorne distribucije. Na nekoliko primjera pokazano je kako Metropolis-Hastings algoritam funkcionira.
Abstract (english)
Topic of the work is bayesian statistical inference. After the definition of basic terms from the probability theory, differences between Bayesian and classical approach to statistical inference were explained. Also, it was explained what prior and posterior distributions are, and the importance of likelihood function and Bayes’ formula were discussed. Then, several methods of choosing prior distribution were listed and theory regarding parameter estimation, hypothesis testing and confidence interval estimation was given. Furthermore, it was noted that integrals which are difficult or impossible to calculate often appear when making an inference about posterior distribution (for example, when calculating expectation or variance of the posterior distribution). To solve this, Metropolis-Hastings algorithm, which is used to sample from posterior distribution, was given. Several examples were used to demonstrate how Metropolis-Hastings algorithm works.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:122053
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 on2019-04-24 06:46:43