Detekcija točaka promjene

master's thesis

• Title (english): Detection of change points
• Author: Gabrijel Turčić
• Mentor: Bojan Basrak (mentor)
• Mentor: Snježana Lubura Strunjak (sumentor)
• Committee member: Bojan Basrak (predsjednik povjerenstva)
• Committee member: Snježana Lubura Strunjak (član povjerenstva)
• Committee member: Filip Najman (član povjerenstva)
• Committee member: Miljenko Marušić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-11-30, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Cilj ovog rada je bio navesti neke osnovne pojmove i rezultate teorije sekvencijalnog testiranja i detekcije točaka promjene. U prvom poglavlju bavili smo se sekvencijalnim testiranjem hipoteza kroz različite mogućnosti pristupanja spomenutom problemu. Promotrili smo optimalna vremena zaustavljanja koja su bila rješenja problema sekvencijalne detekcije te uveli mjere uspješnosti koje su ta ista vremena zaustavljanja opisivale. U drugom poglavlju smo uveli neke osnovne pojmove problema detekcije točaka promjene. Dotaknuli smo se koncepta lažnih uzbuna i zašto su one važne u promatranju ovakvih problema. Rad je završen simulacijskom studijom u kojoj je sekvencijalni test SPRT implementiran u jeziku R i korišten za testiranje pripadnosti niza nekoj distribuciji. Uz sam test implementirane su i njegove karakteristične funkcije koje su nam omogućile bolju analizu same simulacije.

Abstract (english)

The aim of this paper was to state some basic terms and results of the theory of sequential testing and detection of change points. In the first chapter, we dealt with the sequential testing of hypotheses using different approaches to the problem. We observed the optimal stopping times that were solutions to the sequential detection problem and introduced measures of success that these same stopping times described. In the second chapter, we introduced some basic concepts of the change point detection problem. We touched upon the concept of false alarms and why they are important in these type of problems. The work was completed with a simulation study in which the sequential SPRT test was implemented in R. Along with the test itself, its characteristic functions were also implemented, which enabled us to better analyze the simulation itself.

• Keywords: teorije sekvencijalnog testiranja; detekcije točaka promjene; koncept lažnih uzbuna; sekvencijalni test SPRT; jezik R
• Keywords (english): theory of sequential testing; detection of change points; concept of false alarms; sequential SPRT test; R
• Language: croatian
• URN:NBN: urn:nbn:hr:217:522477
• 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: 2022-12-20 12:56:21