Uvod u Bayesovu statistiku

master's thesis

• Title (english): Introduction to Bayesian Statistics
• Author: Tamara Anna Horvat
• Mentor: Ivan Ivec (mentor)
• Committee member: Ivan Ivec (predsjednik povjerenstva)
• Committee member: Nenad Antonić (član povjerenstva)
• Committee member: Marko Erceg (član povjerenstva)
• Committee member: Sonja Štimac (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-09-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Tema ovog rada uvod je u Bayesovsko statističko zaključivanje. Nakon definicija osnovnih pojmova iz područja statistike i vjerojatnosti, naveden je i dokazan Bayesov teorem te je prikazana njegova uporaba na nekoliko primjera. Navedeni su osnovni elementi Bayesovskog zaključivanja, dana su objašnjenja pojmova apriorne i aposteriorne distribucije te je dana definicija funkcije vjerodostojnosti, a objašnjena je i njezina važnost. Navedene su različite distribucije koje su potkrijepljene primjerima, a navedeni su i primjeri Bayesovskog zaključivanja za binomnu, Poissonovu te normalnu razdiobu. Konačno, navedena je i usporedba Bayesove i klasične frekvencijske statistike.

Abstract (english)

The topic of this graduate thesis is the introduction to Bayesian statistical inference. After the definitions of basic terms in the field of statistics and probability are given, the Bayesian theorem is proved and its use is shown on several examples. In the following chapters, the basic elements of Bayesian reasoning are given along with concept explanations of prior and posterior distributions. The credibility function is defined and its overall importance is explained. Different distributions are defined and explained along with examples, and different examples of Bayesian inference for binomial, Poisson and normal distribution are presented. The final chapter offers a comparison of Bayesian and classical frequency statistics.

• Keywords: statistika; vjerojatnost; Bayesov teorem; klasična frekvencijska statistika
• Keywords (english): statistics; probability; the Bayesian theorem; classical frequency statistics
• Language: croatian
• URN:NBN: urn:nbn:hr:217:099162
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2021-02-25 12:38:24