Bayesovska statistika i primjene

master's thesis

• Author: Daniel Marković
• Mentor: Siniša Slijepčević (mentor)
• Committee member: Siniša Slijepčević (predsjednik povjerenstva)
• Committee member: Mladen Jurak (član povjerenstva)
• Committee member: Sonja Štimac (član povjerenstva)
• Committee member: Zvonimir Tutek (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2014-07-14, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu smo se bavili osnovnim konceptima bayesovske statistike. U prvom poglavlju smo definirali pojam vjerojatnosti i uvjetne vjerojatnosti, te smo pomoću njih iskazali bayesov teorem koji je temelj bayesove statistike. U drugom poglavlju smo definirali neke osnovne pojmove bayesovske statistike kao što su apriorna distribucija, funkcija vjerodostojnosti i aposteriorna distribucija. Izbor apriorne distribucije jedan je od ključnih problema bayesovske statistike pa smo mu posvetili cijelo treće poglavlje. U četvrtom poglavlju smo govorili o procjeni parametara, te smo definirali bayesovski procjenitelj za točkovnu procjenu i bayesovske pouzdane intervale. U zadnjem poglavlju se bavimo bayesovskim testiranjem hipoteza.

Abstract (english)

In this work we introduced some basic concepts of Bayesian statistics. In the first chapter, we defined terms of probability and conditional probability, and then used them to state Bayes theorem, which is the cornerstone of Bayesian statistics. In the second chapter, we defined some basic terms of Bayesian statistics like apriori distribution, likelihood function and aposteriori distribution. The choice of apriori distribution is one of the main problems in bayesian statistics, so we dedicated the whole third chapter to it. In fourth chapter, we discussed parameter estimation, and defined Bayesian estimator for point estimate and Bayesian confidence intervals. In the last chapter, we deal with Bayesian hypothesis testing.

• Keywords: bayesov teorem; bayesovski procjenitelj za točkovnu procjenu; apriorna distribucija; bayesovski pouzdani intervali
• Keywords (english): Bayes theorem; Bayesian estimator for point estimate; apriori distribution; Bayesian confidence interval
• Language: croatian
• URN:NBN: urn:nbn:hr:217:598696
• Study programme: Title: Mathematical Statistics; 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: Access restricted to students and staff of home institution
• Created on: 2019-01-22 11:44:27