Publication Date


Document Type


First Advisor

Ryu, Duchwan

Degree Name

Ph.D. (Doctor of Philosophy)

Legacy Department

Department of Mathematical Sciences


Bayesian functional data analysis (BFDA) provides flexible statistical inferences under harsh circumstances such as a large volume of data, considerable measurement errors and missing observations. Considering a sequence of segments and functional data analysis on each segment, where neighboring segments can be dependent, demanding computation is indispensable and analysis is sometimes infeasible for large number of segments. We consider a utilization of BFDA to identify differentially methylated regions (DMRs). Out of numerous existing methodologies to detect DMRs, there still does not exist a standard approach to identify DMRs especially under the assumption of dependency among genomic regions. In this dissertation, we model the dependency of neighboring segments with a transition model, and utilize a sequential Monte Carlo method to cope with the computational difficulties.The proposed methodology was examined through simulation studies and was applied to the lung Adenocarcinoma patients data. For validation we have also shown our approach is effective in finding the true DMRs, while effectively controlling the number of false positives and we compare our results with bumphunter as a competing method.


104 pages




Northern Illinois University

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