Theses and Dissertations
Advisor
Sepehrifar, Mohammad
Committee Member
Popescu, George
Committee Member
Zhang, Jialin
Committee Member
Woody, Jonathan
Committee Member
Zhou, Qian; Wu, Tung-Lung
Date of Degree
8-7-2025
Original embargo terms
Immediate Worldwide Access
Document Type
Dissertation - Open Access
Major
Mathematical Sciences (Statistics)
Degree Name
Doctor of Philosophy (Ph.D.)
College
College of Arts and Sciences
Department
Department of Mathematics and Statistics
Abstract
This dissertation develops scalable Bayesian solutions for two critical challenges in modern data analysis: modeling failure times and imputing missing biological data. First, we introduce an adaptive semi-parametric MCMC framework for Weibull lifetime modeling, addressing the lack of conjugate priors and multidimensional sufficient statistics. Using hierarchical modeling and the No-U-Turn Sampler (NUTS) in STAN, we evaluate 24 prior combinations across 72 simulated datasets. The method yields robust parameter estimates under increasing and decreasing hazard rates and proves effective in predicting prostate cancer patient survival. Second, we assess imputation strategies for high-throughput proteomics data, where missingness distorts signal integrity. We compare MCMC, MICE, QRILC, and Random Forest methods using MAE, NRMSE, and correlation analyses. Among them, MCMC best preserves data structure across varying missingness and dimensionality. Together, these contributions demonstrate the versatility and robustness of Bayesian modeling for structured and unstructured data environments, offering practical tools for inference under uncertainty.
Recommended Citation
Oketch, Tobias Omondi, "Markov Chain Monte Carlo techniques– innovations in lifetime data analysis and missing value imputations" (2025). Theses and Dissertations. 6683.
https://scholarsjunction.msstate.edu/td/6683
