Bayesovsko statističko zaključivanje ; Bayesian Statistical Inference

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. ; 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.