Statistics PhD Defense - 06/24/25

Jun 24 3:00 pm
Speaker

Tobias Oketch

Title

Statistics Seminar Series

Subtitle

Markov Chain Monte Carlo Techniques - Innovations in Lifetime Data Analysis and Missing Value Imputations

Physical Location

Allen 14

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.

PhD Advisors:

Dr. Mohammad Sepehrifar and Dr. George V. Popescu