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master's thesis
Bayesovsko zaključivanje za linearnu regresiju
Zagreb: University of Zagreb, Faculty of Science, 2023. urn:nbn:hr:217:383055
Kolar, Agata
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Kolar, A. (2023). Bayesovsko zaključivanje za linearnu regresiju (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:383055

Kolar, Agata. "Bayesovsko zaključivanje za linearnu regresiju." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:383055

Kolar, Agata. "Bayesovsko zaključivanje za linearnu regresiju." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:383055

Kolar, A. (2023). 'Bayesovsko zaključivanje za linearnu regresiju', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:383055

Kolar A. Bayesovsko zaključivanje za linearnu regresiju [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2023 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:383055

A. Kolar, "Bayesovsko zaključivanje za linearnu regresiju", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:217:383055

Metadata
TitleBayesovsko zaključivanje za linearnu regresiju
Title (english)Bayesian inference for linear regression
AuthorAgata Kolar
MentorSnježana Lubura Strunjak (mentor)
Committee memberSnježana Lubura Strunjak (predsjednik povjerenstva)
Committee memberZvonko Iljazović (član povjerenstva)
Committee memberMatko Ljulj (član povjerenstva)
Committee memberHrvoje Planinić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2023-05-24, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu opisuju se metode Bayesovskog zaključivanja za linearnu regresiju. U prvom poglavlju uvodimo osnovne definicije i rezultate iz teorije vjerojatnosti i matematičke statistike koji su bitni za razumijevanje Bayesovog teorema i temeljnih koncepata iz Bayesovske statistike. U drugom poglavlju donosimo iskaze diskretne i neprekidne verzije Bayesovog teorema, zajedno s dokazima i primjerima. Navedeni teoremi čine temeljnu okosnicu za Bayesovsko statističko zaključivanje. Uvode se ključni pojmovi u Bayesovskoj statistici: apriorna i aposteriorna distribucija. U trećem poglavlju uvodimo model jednostavne i višestruke linearne regresije te korište-njem metode najmanjih kvadrata određujemo procjene parametara za modele. Također, navodimo i osnovne pretpostavke o vjerojatnosnoj distribuciji slučajnih grešaka u modelu bez kojih ne bismo mogli donositi validne zaključke o nepoznatim parametrima modela linearne regresije. U posljednjem, petom poglavlju, predstavljamo primjenu obrađenih metoda Bayesovskog zaključivanja kroz nekoliko primjera. Zadaci su riješeni u programskom jeziku R.
Abstract (english)
In this paper, we describe Bayesian inference methods for linear regression. In the first chapter, we introduce basic definitions and results from probability theory and mathematical statistics that are essential for understanding Bayes’ theorem and fundamental concepts of Bayesian statistics. In the second chapter, the discrete and continuous versions of Bayes’ theorem are presented, along with proofs and examples. These theorems form the basic framework for Bayesian statistical inference. Key concepts in Bayesian statistics are introduced: prior and posterior distribution. In the third chapter, we introduce the model of simple and multiple linear regression, and, using the least squares method, we determine estimates of the parameters for the models. We also state basic assumptions about the probability distribution of random errors in the regression model, without which we would not be able to make valid conclusions about the unknown parameters of the linear regression model. The examples are solved in the programming language R.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:383055
Study programmeTitle: Financial and Business Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-02-09 11:07:08