Bayesovsko zaključivanje za standardnu devijaciju

master's thesis

• Title (english): Bayesian inference for standard deviation
• Author: Maša Bunjevac
• Mentor: Snježana Lubura Strunjak (mentor)
• Committee member: Snježana Lubura Strunjak (predsjednik povjerenstva)
• Committee member: Pavle Goldstein (član povjerenstva)
• Committee member: Zoran Vondraček (član povjerenstva)
• Committee member: Hrvoje Šikić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; Zagreb
• Defense date and country: 2021-09-22, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES

Abstract

U ovom radu, bavimo se Bayesovim zaključivanjem. U uvodu je opisano statističko zaključivanje i primjena Bayesovog teorema. U prvom poglavlju, defnirani su pojmovi potrebni za razumijevanje Bayesovog zaključivanja i statističku analizu. Nakon toga, uvodimo Bayesovu paradigmu i uspoređujemo je s frekvencionističkom. Konačno, na primjeru prikazujemo ideju aposteriorne distribucije. U drugom poglavlju, bavimo se Bayesovim zaključivanjem za standardnu devijaciju za razne neprekidne apriorne distribucije. Nakon toga, navodimo aposteriorne distribucije pridružene zadanim apriornim distribucijama. Na kraju poglavlja, prikazujemo neke osnovne statističke procjene koje radimo za standardnu devijaciju normalne razdiobe. U trećem poglavlju, na nekoliko primjera dobivenih računalnim simulacijama, provodimo statističku analizu koristeći ranije navedena izlaganja. Sve metode implementiramo u R-u.

Abstract (english)

In this paper, Bayesian inference is presented. In the introduction, statistical inference and application of Bayes' Theorem are described. In the first chapter, concepts needed for understanding Bayesian inference and statistical analysis are defined. Then, Bayesian paradigm is presented and compared to frequentist perspective. Finally, the idea of posterior distribution is presented on an example. In the second chapter, Bayesian inference for standard deviation for various continuous priors is presented. Then, corresponding posterior distributions are listed. Finally, some fundamental statistical estimates on normal standard deviation are presented. In the third chapter, statistical analysis made by computer simulations is used on a few examples using previous statements. All methods are implemented in R.

• Keywords: statističko zaključivanje; Bayesov teorem; Bayesova paradigma; aposteriorna distribucija; apriorna distribucija
• Keywords (english): statistical inference; Bayes' Theorem; Bayesian paradigm; posterior distributions
• Language: croatian
• URN:NBN: urn:nbn:hr:217:125120
• Study programme: Title: Finance and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2021-10-25 12:48:28