Bayesovska analiza doživljenja

master's thesis

• Author: Irena Malović
• Mentor: Miljenko Huzak (mentor)
• Committee member: Miljenko Huzak (predsjednik povjerenstva)
• Committee member: Bojan Basrak (član povjerenstva)
• Committee member: Eduard Marušić-Paloka (član povjerenstva)
• Committee member: Mirko Primc (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

Modele doživljenja je općenito dosta teško za modelirati. Bayesovski pristup analizi doživljenja uvelike olakšava modeliranje problema, pogotovo u biomedicini u kojoj i nalazimo najveću primjenu poluparametarskih modela kojima smo se bavili u ovom radu. Za svaki od modela u radu iznijeli smo načine dolaska do apriorne distribucije, izveli smo funkciju vjerodostojnosti i aposteriornu distribuciju. U bayesovskom pristupu analizi doživljenja veliku ulogu ima i Gibbsova metoda uzorkovanja, koja je jedna od MCMC metoda. Ona nam omogućava dobivanje aposteriorne distribucije za model. Velika prednost bayesovskog pristupa je da nam on omogućava da iz starijih istraživanja izvučemo neke pretpostavke za model novog istraživanja, ukoliko su ona slična. Klinička istraživanja su najbolji primjer toga, primjerice studije o različitim bolestima kao što su rak, AIDS i slične. Naravno, postoje i nedostaci ovog pristupa. Jedan od glavnih je to što se bazira na subjektivnosti statističara. Odabir krive apriorne distribucije može rezultirati krivim rezultatima. Bayesovski pristup u analizi doživljenja je jako korisno oružje, pogotovo od kada su razvijeni jaki statistički softveri koji olakšavaju implementaciju tih modela, no ono se mora znati i pravilno koristiti.

Abstract (english)

It is well known that survival models are generally quite hard to fit. Bayesian paradigm in survival analysis greatly eases semiparametric models, especially in biomedicine where the semiparametic models, that are evaluated in this paper, are mostly used. For each of the models in this paper, we presented ways to reach a priori, we performed the likelihood function and the posterior distribution. Gibbs sampler, which is one of the MCMC sampling algorithms, plays an important role in the Bayesian paradigm in survival analysis. It allows us to obtain the posterior distributions for the model. The great advantage of Bayesian paradigm is that it allows us to draw some assumptions from earlier research and, if they are similar, use them for the model of the new research. This can be seen in clinical studies where, for example, researchers study variety of diseases such as cancer, AIDS and similar. However, there are some disadvantages to this approach. The greatest flaw is that it is based on the statistician’s subjectivity. If the wrong prior distribution is chosen, wrong results can occur. Bayesian paradigm in survival analysis can be a powerful tool, especially when there is good software available that eases the implementation of this models. However, it is required to know how to use it properly.

• Keywords: Modeli doživljenja; bayesovskoi pristup; poluparametarski modeli
• Keywords (english): survival models; Bayesian paradigm; semiparametric models
• Language: croatian
• URN:NBN: urn:nbn:hr:217:213013
• 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: Open access
• Created on: 2019-01-21 11:46:21